1

1 T2K Experiment

The Tokai to Kamioka long baseline neutrino oscillation experiment, or T2K [?],

is an experiment in Japan to more finely measure the parameters of the lepton

mixing matrix. Long baseline experiments, like T2K, are designed to measure

the masses and mixing angles of the unitary mixing matrix by sending a beam

with well understood energy from a proton accelerator to a large particle detector

positioned to maximize the oscillation probability.

The T2K experiment is composed of a neutrino factory, a near detector, and

a far detector. The neutrino source is a fast extracted proton beam from the

J-PARC proton synchrotron in Tokai, Ibaraki [?], which produces 30 GeV pro-

tons. The far detector, located 295 kilometers away, is the world’s largest water

Cherenkov detector, Super-Kamiokande [?], where neutrino oscillations in atmo-

spheric neutrinos were discovered in 1998 [?]. The near detector is composed of

multiple sub-detectors, placed 280 meters from the beam source in order to mea-

sure the background of the various T2K measurements and help in estimating the

initial flavor content of the beam. T2K is a collaboration of hundreds of physi-

cists from twelve countries. The scale of the effort reflects both the difficulty and

importance of the measurements.

2

1.1 Physics Goals

T2K is designed for several specific physics goals. First is an improved mea-

surement of the oscillation parameters sin(θ23) and ∆m223 . This is found by

measuring the νµ content of the beam at the accelerator, and then measuring the

remaining unoscillated νµ at the far detector. The probability in the three-flavor

approximation for νµ disappearance is [?]

1− P (νµ → νµ)

= sin2 2θ sin2(∆m2

31L

4E) + 4s213s

223(s

223 − c223)

× sin2(∆m2

31L

4E)− c212 sin

2 2θ23(∆m2

21L

4E) sin(

∆m231L

2E)

(1.1)

Several experiments have already measured these oscillation parameters, with

recent measurements by MINOS [?] of sin2(2θ23) >0.90 (90% C.L.) and ∆m223

= (2.32+0.12−0.08) x 10−3 eV2 [?]. T2K hopes to improve the accuracy with which the

parameters are known, especially θ23, and investigate the oscillation on a different

energy scale than the previous long baseline experiments.

The second and most important goal of the T2K experiment is the search for

νµ → νe oscillation by measuring electron neutrino appearance at the far detector.

This particular oscillation is important for several reasons. First, it was designed

to make the first measurement of θ13 from electron neutrino appearance in this en-

ergy range. Secondly, while competing experiments, such as CHOOZ [?] [?], Daya

Bay [?] [?] and RENO [?] have measured disappearance of electron antineutrinos,

with a Daya Bay measurement of sin2 2θ13<0.092±0.016(stat)±0.005(syst), T2K

has the advantage of detecting oscillated electron neutrinos, providing important

constraints. Third, as shown in Eq. 1.1, the νµ disappearance is dependent on the

size and uncertainty on θ13, and having both a νµ disappearance and a νe appear-

ance measurement at the same detector combined with precise θ13 measurements

from reactor experiments will give the most precise θ23 measurements.

3

Third and somewhat more interesting, large values of all the mixing angles are

required to measure the imaginary phase δ, as shown in the mixing matrix [?] [?]

U =

1 0 0

0 c23 s23

0 −s23 c23

X

c13 0 s13e−iδ

0 1 0

−s13eiδ 0 c13

X

c12 s12 0

−s12 c12 0

0 0 1

.

A large value of θ13, as has been seen in Daya Bay, means that long baseline

experiments like T2K and NOvA [?] should be able to make measurements of

the δ parameter. The imaginary phase of the mixing matrix, if non-zero, can be

used to determine the strength of the CP violation in the neutrino sector. This

is fundamentally interesting in its own right and might contribute to a deeper

understanding of the matter-antimatter asymmetry of the universe as discussed in

Chapter ??. Reducing the uncertainty on the parameter θ23 is also very important

in order to precisely constrain δ, as it currently contributes one of the largest

uncertainties [?].

1.2 The T2K Beam

The T2K neutrino beam is created from the collision of protons that have been

accelerated to a kinetic energy of 30 GeV [?]. This acceleration is done in three

accelerators, a linear accelerator (LINAC), a rapid cycling synchrotron (RCS)

and the main ring (MR). First, hydrogen (H−) is accelerated to 400 MeV in the

LINAC, and the electrons are stripped by charge stripping foil at the injection

point of the RCS.

In the RCS, the beam of protons is accelerated up to 3 GeV. Acceleration

in synchrotrons is done by radio frequency (RF) cavities. The nature of the

acceleration is such that the protons naturally form into separate bunches. The

4

Figure 1.1: a)Particles entering an RF cavity at the right moment are accelerated

b)Particles that arrive slightly too early or slightly too late will not receive the necessary

acceleration, and will be pushed in the direction that aligns them with the Vref [?].

electric field accelerates particles maximally at the wave peak and minimally at

the wave trough. Particles arriving just before the wave peak will be accelerated

so that they arrive later in the next cycle, while particles arriving just before

the wave trough will be slowed as shown in Fig.1.1. This results in the particles

clustering in the middle, separated in time by an amount equal to the period of

the field [?].

For T2K, bunches created by the RCS are injected into the MR. In the MR

they are accelerated to their full kinetic energy. Various parameters of the main

ring are described in Table 1.1. In fast extraction mode, eight bunches per spill

are extracted within a single turn by a set of five kicker magnets. This beam is

pointed toward the far detector by the primary beamline, and then interacts with

a stationary graphite target in the secondary beamline.

1.2.1 Beam Modeling

Particle production and interactions for the beam are predicted by a chain of

Monte Carlo simulations as shown in Fig. 1.2 [?]. First, 30 GeV protons are

simulated upstream of the baffle using a Monte Carlo particle generator called

5

Circumference 1567 m

Beam Power ∼750 kW

Beam Kinetic Energy 30 GeV

Beam Intensity ∼3 x 1014 p/spill

Spill Cycle ∼0.5 Hz

Number of Bunches 8/spill

RF Frequency 1.67-1.72 MHz

Spill Width ∼5 µs

Table 1.1: Machine design parameters for the JPARC MR for the data in this thesis

FLUKA. FLUKA was chosen because it shows better agreement with data from

the NA61 [?] experiment compared to other particle generators. Position and

momentum information of secondary particles exiting from the target and from

their parents and decay chains is then used by the T2K simulation package

JNUBEAM [?].

JNUBEAM uses the GEANT3 framework to track particles. Precise simula-

tion of the particle interactions in beam components including the baffle, target,

three horn magnets, helium vessel, decay volume, beam dump and muon monitor,

which will be discussed in the next section, are necessary to accurately predict

the trajectories and energy of the different particles,. JNUBEAM information is

used to predict the neutrino flux at the near and far detectors.

The flux simulations are tuned using information from the NA61 experiment.

Located at CERN, on of the main goals is to look at the interaction of 30 GeV

protons on a graphite target. Currently proton interaction data from a T2K

replica target and a thinner graphite target have been taken. Figure 1.3 shows

the experimental setup. The primary goal of these studies was to measure the

rate of secondary pion and kaon production from these interactions.

6

Figure 1.2: Various components of simulation that are used to make flux predictions

for T2K [?].

Figure 1.3: The NA61 detector. NA61 uses 30 geV protons on a graphite target like

T2K to give precise predictions of particle production [?].

A comparison of pion production data in NA61 with FLUKA Monte Carlo is

shown in Fig. 1.4. Data from NA61 covers about 90% of the pion phase space,

and about 60% of the kaon phase space as shown in Fig. 1.5. Systematics from

7

Figure 1.4: A comparison of pion production data from NA61 with FLUKA predic-

tions [?].

Figure 1.5: Phase space of the π+ (left) and K+ (right) that produce neutrinos in the

beam. The color represents the size of the contribution to the neutrino flux. The phase

space covered by NA61 for π+ and for NA61, Eichten et al. [?] and Allaby et al.[?] for

K+ are highlighted [?].

the beam simulation uncertainties will be discussed in further chapters.

1.2.2 Beam Components

The primary beamline is composed of a preparation section, an arc section and a

final focusing section as shown in Fig. 1.6. The preparation section uses normal

conducting magnets to align the beam so that it can be turned in the arc section.

8

Figure 1.6: Components of the T2K Beamline [?].

Superconducting magnets in the arc section are used to tune the beam direction

such that Super-Kamiokande is between 2 and 2.5 degrees away. Normal con-

ducting magnets in the final focusing section then align the beam again before it

enters the secondary beamline [?].

The primary beamline is also equipped with many devices for measuring prop-

erties of the beam. Preventing beam loss and assuring that the composition of

the beam is well understood are important for producing a stable neutrino beam.

Current transformers, electrostatic monitors, segmented secondary emission mon-

itors and beam loss monitors are used to measure the intensity, profile, position

and loss of the proton beam. Fig. 1.7 shows pictures of the monitors and their

location in the primary beamline.

Current transformers (CT) measure the intensity of the beam with a 50 turn

toroid wrapped around an iron core. To calibrate the CT a second coil is wound

around the core, and an applied current shaped to emulate the beam passing

through the coil is measured. The CT can measure the intensity of the beam to

9

Figure 1.7: Left: Photographs of the primary beamline monitors. Upper left: CT.

Upper right: ESM. Lower left: SSEM. Lower right: BLM. Right: Location of the

primary beamline monitors [?].

within 2%, the relative fluctuations of the intensity to within a 0.5% precision,

and the beam timing to within 10 ns.

Electrostatic monitors (ESM) are composed of four cylindrical segmented elec-

trodes arranged at equal distances around the beam direction. The current that

is measured by each electrode is compared, without interfering destructively with

the beam. This gives the beam distance from each electrode, which is expected

to be equal if the beam were located in the center of the monitor, which is the

desired goal. From the ESM, the beam position is known to within 450 µm, which

is comfortably within the design requirement of 500 µm.

During beam tuning, segmented secondary emission monitors (SSEM) are used

to measure the beam width and divergence. Protons from the beam hit the vertical

and horizontal strips, composed of two titanium foils surrounding an HV foil, that

make up the SSEM. These interactions produce secondary electrons in proportion

to the number of incident protons, which induce currents on the strips that can

then be measured. Since the beam interacts with the foil, there is a beam loss

10

of about 0.005% due to irradiation of nearby components, so the SSEM can not

be used during data taking. The systematic uncertainty on the beam width from

this measurement is 200 µm compared to the requirement of 700 µm.

Beam loss monitors (BLM) are proportional counters with a mixture of argon

and carbon dioxide gas. These are installed near the beam pipe, which means any

beam passing through them represents a “loss”. If more than a certain amount

of beam is lost during a spill, a beam abort interlock signal is fired, stopping the

beam.

The secondary beamline contains the target station, the decay volume and

the beam dump. Protons enter the target station through the beam window,

which separates the vacuum of the primary beamline from the helium gas of the

secondary beamline. A large block of graphite called a baffle collimates the beam

and protects the surrounding devices from the high energy protons.

The proton beam profile in the secondary beamline is then imaged using a

device called an optical transition radiation monitor. In this device a thin tita-

nium, aluminum, or fluorescent ceramic foil, depending on the intensity of the

beam, is placed at a 45 degree angle with respect to the beam direction. Tran-

sition radiation produces light at 90 degrees to the beam direction. This light is

then collected after reflection through a series of mirrors in a region with lower

radiation levels, where a charge injection camera can then be used to produce an

image of the beam.

The beam then interacts with a graphite target, 1.9 interaction lengths long,

surrounded by a graphite tube and a titanium case. Helium gas flowing into the

gaps between the different components cools the target. Pions are produced from

the collision which are then focused along the beam direction by three magnetic

horns.

The horns are made of two coaxial aluminum alloy conductors encompassing

a closed volume. The first horn is primarily cylindrical, as shown in Fig. 1.8, and

11

Figure 1.8: A schematic showing a cross section of the target and the first magnetic

horn [?].

has the target inserted into its downstream end to increase pion containtment.

The second and third horns are parabolic in shape, and look like Fig. 1.9 [?].

As shown in Fig. 1.9, current moving in loops in the horn produces a magnetic

field. This magnetic field goes as ∼ 1

r, where r is the distance from the horn axis.

Secondary pions traversing the horn toward the axis are either focused or deflected,

depending on the direction of the current and their charge [?]. Having three horns

allows pions in a wide range of energy and angle to be focused, collecting them

with the first horn and focusing with the other two. The neutrino flux in the peak

energy region, 0.6 GeV, was increased by about a factor of 16 through the use of

these horns.

The majority of the produced pions decay in the decay volume to produce

muons and muon neutrinos. Other decays and contributions from kaons produced

in the target interaction are discussed in the following chapters. The decay vol-

ume is a 96 m long steel tunnel ending in the beam dump. The helium used

in the decay volume minimizes pion absorption and eliminates the production of

unwanted compounds such as tritium and NOx that would certainly result from

12

Figure 1.9: A cartoon showing the function of a parabolic horn. When current flows

in one direction, π− are deflected and π+ are focused. Reversing the current will reverse

which pion is focused and which is deflected [?].

beam interactions in air.

All hadrons and muons produced from pion decay with energy less than 5 GeV

are absorbed by the beam dump. The beam dump is composed of an inner core,

3.7 m deep, of graphite surrounded by fifteen iron plates comprising a total depth

of 2.4 m. The remaining muons are then measured by a succession of detectors in

order to characterize the neutrino beam.

1.3 Beam Monitors

Monitoring the beam is done by a series of detectors, starting with the muon

monitor, followed by an emulsion tracker, and finally by the INGRID detector

280 m from the target region. The muon monitor measures the direction and the

flux of high energy muons produced by secondary pion decay. It is necessary for

the experiment that the neutrino beam direction be known to within 0.25 mRad

and the intensity within 3%. For this purpose, two detector arrays are used, one

of PIN photodiodes 118.7 m from the target and one of ionization chambers 117.5

13

Figure 1.10: The muon monitor, with the photodiode detector on the right and the

ionization chamber on the left [?].

m from the target as shown in Fig. 1.10 [?].

The seven ionization chambers in the muon monitor are each made up of

seven sensors with active volume of 75x75x3 mm3 fitted inside aluminum tubes.

Depending on the beam intensity either argon with 2% nitrogen or helium with 1%

nitrogen are fed into the tubes, which are kept at constant temperature, pressure

and oxygen contamination.

For the PIN photodiodes, the active area is 10x10 mm2 with a thickness of 300

µm. The silicon layer is fully depleted by applying 80V. The distribution of charge

in the two detectors is used to reconstruct a 2D image of the muon distribution.

The resolution of the beam intensity from the muon monitor measurements is

0.1% and for the profile center is 0.3 cm.

The emulsion tracker is designed in a similar fashion to that used by the

OPERA experiment. Two separate modules are used. The first module is com-

posed of eight emulsion films, and measures the muon flux with a systematic

14

Figure 1.11: Left: The INGRID near Detector Right: A typical neutrino event in an

INGRID module [?].

uncertainty of 2%. For the other module 25 emulsion films are interleaved with

1 mm lead plates. For 2 GeV/c muons, this module can measure the momentum

with a precision of 28%. Interactions in the modules are analyzed by scanning

microscopes.

INGRID sits on the axis of the beam and is used to measure the direction, pro-

file, intensity and if possible, the energy of the neutrino beam [?]. It is composed

of 14 identical modules arranged in a cross shaped configuration as in Fig. 1.11.

Each of these modules is made up of 11 tracking scintillator planes, composed of

24 scintillator bars in the x and y direction read out by MPPCs, and nine 6.5 cm

iron plates.

These modules are surrounded on all sides by veto planes. These planes are

made of 22 scintillator bars segmented in the beam direction. Adjacent modules

can share a veto plane so that every module has either three or four associated

15

veto planes. A typical neutrino interaction event in an INGRID module is shown

in Fig. 1.11, where a particle, most likely a muon, interacts and traverse the

planes, leaving energy deposits whose magnitude is represented by the size of the

circle in the image. From these events INGRID can measure the beam center to

10 cm, which implies a beam angle precision of 0.4 mRad given its location with

respect to the beam.

Besides the 14 standard INGRID modules, two off-axis and one proton module

are also used. The off-axis modules are identical to the standard modules and are

used to check the axial symmetry of the beam. Also, the standard INGRID

modules cannot resolve the proton in charged current interactions. Therefore the

special proton module is constructed entirely of very fine grain scintillator, and

placed adjacent to the central modules in the INGRID cross. Then quasi-elastic

events, which consist of a lepton and a proton, can be detected. The quasi-elastic

cross section is important for comparing different models of beam neutrino Monte

Carlo, and this interaction will be discussed in detail in Chapter 4.

1.4 ND280

The off-axis near detector consists of the the pi-zero detector (also known as the

P0D), three time projection chambers (TPC), two fine grain detectors (FGD), the

electromagnetic calorimeter (ECal), and the side muon range detector (SMRD)

(See Fig. 1.12). The P0D, TPC, FGD and ECal sit inside a support struc-

ture known as the basket and are surrounded by a magnet with inner volume

of 7x3.5x3.6 m3. The SMRD is contained within the magnet yokes, and is used

primarily as a veto for the other detectors [?].

The purpose of ND280 is to provide information to quantify the neutrino flux

at Super-Kamiokande and to study neutrino interactions. Each detector is built

to make sure that the important parameters, such as the νµ and νe components of

16

Figure 1.12: The T2K near Detector [?].

the flux at the near detector and the rate of π0 production, are well understood.

Various neutrino event types such as charged and neutral current quasi-elastic,

resonant and inelastic reactions are all measured in the off-axis near detectors.

These detectors predominately sit at an angle of 2.5 degrees off the axis of

the beam, aligned with the direction to the far detector at Super-Kamiokande.

The T2K experiment measures neutrino oscillations at an off-axis angle based on

a design that was first proposed at Brookhaven National Laboratory in 1995 [?].

As previously discussed, neutrinos in the beam primarily come from the π+ →µ+ + νµ reaction. The kinematics of this reaction create neutrinos with energy

proportional to the pion energy in the direction of the beam.

However, the distribution of the neutrino energies at angles off-axis from the

beam are not proportional to the pion energy. As shown in Fig. 1.13, as the angle

increases, pions at a wide variety of energies begin to produce neutrinos that all

have the same momentum. Therefore, using an off-axis beam will both increase

17

Figure 1.13: Neutrino momentum from the decay of pions at various energies, with

each pion energy represented by a circle. Distributions for angles of 1.5 and 3 degrees

are marked. As the angle increases, all pions regardless of energy start to produce

neutrinos with the same momentum [?].

the flux of neutrinos at a given energy and produce a narrower neutrino energy

spectrum.

For the T2K experiment, the 2.5 degree off-axis angle was chosen to reduce

the high energy tail in the neutrino beam spectrum, reducing the size of the

expected backgrounds from neutral current processes. The distribution of events

in neutrino energy with various off-axis angles is shown in Fig. 1.14. At this angle

the neutrino spectrum peaks at an energy of about 650 MeV and this produces a

theoretical oscillation maximum at the far detector. [?].

18

E (GeV)v

v F

lux (

au)

μ

Figure 1.14: Energy spectra from an off-axis beam at: red line (2 degrees), green line

(2.5 degrees), and blue line (3 degrees) [?].

1.4.1 Tracker

The TPC and FGD make up the Tracker region of the near detector. Each TPC

uses low diffusion gas for momentum resolution of better than 10 percent for

particles with energy less than 1 GeV/c. It is designed to distinguish electron and

muon tracks with various momenta by measurement of dE/dx over a minimum

track length of 60 cm [?]. This is important for making precision measurements

of the νe component of the beam [?] [?].

The TPC have an inner box filled primarily with argon and an outer box filled

with carbon dioxide as shown in Fig. 1.15. Particle interactions ionize the gas

in the inner box and, due to the magnetic field, these ions drift toward readout

planes located on the side of the TPC. The pattern and arrival time of the signal

19

Figure 1.15: An image of the main components of the TPC [?].

can be used to produce a 3D image of the particle trajectory.

The FGD is composed of two targets. One of the two FGD targets is composed

of 30 layers of rectangular scintillator bars arranged in alternating x and y con-

figurations each containing 192 bars. A drawing of an FGD scintillator module is

shown in Fig. 1.16. The scintillator provides target mass for neutrino interactions,

and each is instrumented with MPPCs that measure the energy deposited by any

interacting particle. Fine segmentation is necessary to track low energy protons

in order to distinguish charged current quasi-elastic and non-elastic events.

The second FGD target contains water in order to provide a comparison of

the neutrino cross sections with Super-Kamiokande, a water Cherenkov detector.

Six 2.5 cm thick water targets alternate with seven modules of scintillator, where

each module consists of an x and a y layer. The water targets are made of thin

polycarbonate sealed with polyurethane. A vacuum pump system maintains the

pressure of the water targets, preventing water from spilling into the FGD.

20

Figure 1.16: The FGD with the front cover removed [?].

1.4.2 ECal and SMRD

Both the SMRD and the ECal are used to measure particles which either originate

outside the detector, or that escape the detector before they can be classified. In

its completed form, the ECal surrounds the P0D and Tracker and is used to

measure photons, primarily from π0 decay. It also helps differentiate electrons

and muons [?].

A total of 13 ECal modules of three different types are used. Barrel ECal

surrounds the tracker, P0D ECal surrounds the P0D and a single module called

the DSECal is located downstream of the tracker. Much of the data used in the

analysis described here was taken before the P0D and Barrel ECal were installed.

ECal modules are composed of scintillator and read out by MPPC, similar to

the FGD and INGRID. All of the modules contain scintillator layers combined

21

Figure 1.17: An ECal module [?].

with a lead layer. In the Barrel and DSECal the scintillator layers alternate

between two views separated by 90 and have lead layers that are 1.75 mm thick

to optimize detection of π0. In the P0D ECal the scintillator bars are all aligned

in the same direction and the lead layers are 4 mm thick because the P0D itself is

used for detection of π0. For the P0D ECal the main purpose is to track photons

or particles that leave the P0D and to act as a veto for interactions outside the

detector. An external view of an ECal module is shown in Fig. 1.17.

SMRD is used to detect muons which are at large angle with respect to the

beam which can not be measured in the TPCs and can also veto cosmic rays and

beam interactions in the sand. The magnet has 16 yokes, and in each of these

yokes there are 15 1.7 cm air gaps. SMRD scintillator modules are placed in these

gaps, with three layers of scintillator modules on the top and bottom for all yokes,

and both sides instrumented with three layers for yokes 1 through 5, four layers

for yoke 6 and six layers for yokes 7 and 8.

Each scintillator is read out by MPPCs as in the other scintillator detectors.

The SMRD has a position resolution for tracks, measured from relative timing

information, of 7 cm. It is able to provide a measurement of energy from detected

muons with a resolution less than 10 percent.

22

1.4.3 P0D

The P0D is the most upstream detector in ND280, and the detector measuring

neutrino cross sections with the greatest fiducial volume [?]. Its purpose is to

detect the π0 in neutral current νµ reactions that make up the largest reducible

background to detecting electron neutrinos at the far detector. The detector

dimensions are 2103 mm width, 2239 mm height and 2400 mm length and the

mass of the detector is 15,800 kg with water and 12,900 kg without.

The P0D contains alternating vertical and horizontal (Y and X) layers of

scintillator read out by MPPC much like the FGD, except that the scintillator

bars are co-extruded triangular polystyrene instead of rectangular [?]. Each bar

has a height of 17 mm and a width of 33 mm with a hole in the center with 2.6 mm

diameter which holds the fiber. The fibers are wavelength shifting fibers made by

Kuraray, doped with Y-11 and with a diameter of about 1 mm. Fig. 1.18 shows a

setup with several layers of the triangular scintillator instrumented with a similar

fiber.

The P0D, unlike previous scintillator based neutrino detectors, doesn’t use

photomultiplier tubes to detect light from the scintillator. Instead it uses Multi-

pixel photon counters, or MPPCs. MPPCs are ”avalanche photo-diodes with

metal resistor semiconductor layer like structure operating in the geiger mode” [?].

Basically this means MPPCs are detectors able to measure single photons using

special diodes with an avalanching property on a silicon substrate. Avalanche

photodiodes allow for the detection of single photons by multiplying the photon

into a many electron signal through a process called avalanching, effectively in-

creasing the gain. These have an advantage over photomultiplier tubes in that

they are much smaller and are not affected by magnetic fields.

The avalanching effect is caused by electrons in the semiconductor valence

band which, when reverse biased, are released into the conduction band due to

23

Figure 1.18: A photograph of a test setup for the scintillator. The fiber shown is only

used for the test, and is not the fiber used for T2K, but the holes for holding the fiber

are identical. However, the arrangement of the scintillator into overlapping triangles is

the same configuration used for T2K.

Figure 1.19: Left: A Multi-pixel photon counter. Right: The grid structure which is

composed of multiple photodiodes. Each photodiode section of the grid accepts photons

and then goes into an on state. Total photoelectron count is gotten by summing the

number of activated grid sites.

their thermal energy. If the voltage is high enough, these electrons have the ability

to knock out other electrons and form a high electric current in an effect called

impact ionization. In avalanching photodiodes, absorption of a photon causes the

original release of the electron which then causes the impact ionization.

Each pixel on an MPPC operates in a separate avalanche photodiode and resis-

tor combination [?]. They act as independent photon counters with a gain of the

24

Figure 1.20: The components of the P0D

same order as a photomultiplier. A pixel is activated when a photon causes impact

ionization, and the result is that a single photoelectron is registered. (See Fig.

1.19) These pixels are arranged on a grid, and the total number of photoelectrons

is determined by the total number of pixels activated in the grid.

The signal from an MPPC is read out by TriP-T based front end boards, or

TFBs. Each MPPC is read out by two channels on the TFB, in order to get both

a low and a high gain response to the same input. Therefore each 128 channel

TFB can be used to read out 64 MPPCs.

Charge is integrated in each channel by 23 capacitors. The capacitors integrate

consecutively, with each capacitor having a 480 ns integration window followed by

a 100 ns reset period. These integration windows are set to correspond with the

width of each beam bunch, which is 580 ns, such that charge from interactions

25

Figure 1.21: Read out chain for the P0D electronics. Information from MPPCs is

collected by TFBs, which are read out by RMMs. Data is sent from the RMMs to the

DAQ, and triggers and sychronization signals are sent from the clock modules to the

TFBs [?].

from each bunch are integrated by separate capacitors.

There are four main regions of the P0D, the downstream ECal, the downstream

target, the upstream target and the upstream ECal as shown in Fig. 1.20. The

ECal is composed of alternating podules with 4 mm lead radiator, to increase the

photon conversion probability. In the target region, the radiators are made of 1.3

mm brass and the podule and radiator also alternate with a 3 cm water target,

which is used to compare cross sections with the water target at the far detector.

In total the P0D contains 40 podules with 134 vertical (Y ) and 126 horizontal

(X) bars in each.

Unlike the FGD the water target contains HDPE water bladders which can be

filled or emptied at any time. Drip pans beneath the detector were installed to

catch any water that might leak out of the bags. The depth of the water in the

bags is also monitored with water depth sensors to in case of catastrophic leaks

and to provide information about the water mass.

The detector uses a total of 174 TFBs, with every 29 connected to the data

aquisition (DAQ) system by a read-out merger modules (RMM). Each of the

26

ECal regions is instrumented with 29 TFBs and each of the water target regions

is instrumented with 58 TFBs, so a total of 6 RMMs are used. The DAQ transfers

control commands, “clock” and “trigger” signals to the TFBs and the TFBs then

transfer data and cosmic triggers back to the DAQ through the RMMs as shown

in Fig. 1.21 [?].

“Clock” and ”trigger” signals are produced by the slave (SCM) and master

(MCM) clock modules. Information about the timing of the beam spills, the

“trigger” signals, and synchronization signals for the clocks of all the RMMs and

all the detectors, the “clock” signals, are received by the MCM for use by all of

ND280. The SCM then transfers these signals to the RMMs, keeping the P0D

timing separate from the other ND280 detectors. Other triggers, such as light

injection and pedestal taking triggers, can also be produced by the MCM and

transferred by the SCM to the RMMs.

The TFBs use trigger primitives based on coincidences of MPPCs, which could

indicate the interaction of cosmic rays, to create “cosmic” triggers which are then

combined with the other detectors through the cosmic trigger monitor, or CTM.

Front-end processing nodes (FPN) control and read out data from the TFBs.

Configuration and read out information comes from the read-out task (RXT), and

the data is converted into a readable format by the data processing task (DPT).

Finally, the MIDAS framework, developed by TRIUMF, provides an interface

between the electronics output and the users of the data. More details about the

P0D components, calibration and construction will be given in Chapter 2.

1.5 Super-Kamiokande

The detector at Kamioka has been running since 1996 [?]. It consists of large

cylindrical water Cherenkov detector with an inner (ID) and outer detector (OD)

region as shown in Fig. 1.22 [?]. Since the detector has been running for more

27

Figure 1.22: The far detector at Kamioka. It is a water Cherenkov detector located 1

km deep in Mount Ikenoyama [?].

than a decade, the behavior is very well understood. Calibration of the energy

and uncertainties in the modeling for the detector are both known to the percent

level [?].

In the ID, a 33.8 m diameter and 36.2 m tall cylinder, 11,129 inward-facing

50 cm diameter PMTs are used to detect Cherenkov radiation from interacting

particles. Cherenkov light from particles moving faster than the speed of light in

water form rings that are detected by the PMTs. Example interactions are shown

in Fig. 1.23.

The 2 m thick OD, which surrounds the ID, is used primarily to veto back-

ground events and contains 1885 20 cm PMT. A highly reflective material, Tyvek,

lines the OD and is used to reflect light off the surface of the OD walls and into

the PMT. For cosmic ray backgrounds the OD gives almost 100% rejection. Using

beam timing information, neutrino beam events that produce light in the OD can

be separated from other backgrounds.

Number of rings, ring thickness, energy deposited, timing, the OD veto and

other factors are used to discriminate between particle interaction types. For

28

Figure 1.23: An example of a muon (left) and an electron (right) interacting in the

Super-Kamiokande volume [?].

example, neutral pions are rejected by forcing two rings in the event, then using

information from the rings to calculate an invariant mass. Any event with an

invariant mass calculated to be above 105 MeV/c2 using this method is rejected

as shown in Fig. 1.24.

The T2K νµ → νe oscillation result has six cuts. It requires that the event be

fully contained in the inner detector fiducial volume, have only a single Cherenkov

ring, that the ring be electron-like, that no Michel electron be detected, that the

invariant mass previously described be below 105 MeV/c2 and that the total

energy deposited by less than 1250 GeV [?]. After all the cuts the current T2K

oscillation result finds a total of 11 events as shown in Fig. 1.25.

29

)2Invariant mass (MeV/c

0 100 200 300

Num

ber

of e

vent

s

0

5

10

RUN1-3 data)POT2010×(3.010

CCeνOsc. CCµν+µν CCeν+eν

NC=0.1)13θ22(MC w/ sin

Figure 1.24: In order to reject neutral pions two rings are forced and events with

invariant mass greater than 105 MeV/c2 are rejected

energy (MeV)νReconstructed

0 1000 2000 3000

Num

ber

of e

vent

s

0

2

4

6

RUN1-3 data)POT2010×(3.010

CCeνOsc. CCµν+µν CCeν+eν

NC=0.1)13θ22(MC w/ sin

Figure 1.25: Remaining events after all cuts have been applied in the most recent

T2K oscillation analysis.

30

2 P0D Construction and

Calibration

In the previous chapter, the components of the P0D detector were described. Each

of these components needs to be well understood to measure particle interactions.

The efficiency and time delay of photon transmission in the fiber and scintillator,

the measurement of these photons by MPPCs, and then the chain of electronics

that finally lead to a signal were all calibrated before the P0D was constructed.

Measurements were made of the dimensions and composition of all components

to increase the accuracy of the simulation.

In late 2009 the P0D was installed in the ND280 detector basket. After its

final construction, monitoring devices are used to keep constant updates on the

status of these processes and to monitor the water target, which has the highest

likelihood to change its composition over time. Finally online monitoring is used

to detect problems during data taking runs and to prevent damage to the detector.

2.1 The P0D Modules: P0Dule Calibration

Calibration of the P0Dules predominately involves calibration of the scintillator

and the fiber. For fiber, factors contributing to uncertainty are the time-walk,

photon loss, efficiency of photon detection by wavelength, mirror reflectivity and

31

Figure 2.1: Fiber time walk correction for the P0D and ECal

attenuation. The scintillator time-walk is negligible because of the short decay

times of the fluors, POPOP and PPO, that are responsible for light production in

the scintillator. However, other effects in scintillator are not negligible. Calibra-

tion for detection efficiency, and variation in light output with time is necessary [?].

In order to produce a “time stamp”, a measurement of the time the event

occurred, between 2.5-3.5 photoelectrons have to be detected by the TFB, where

a photoelectron is the energy needed to eject an electron by fluorescence in the

material. The fluors produce light through an exponential decay, and therefore

there is some time between the initial emission of light and detection by the

TFB. This “time walk” is probabilistic and depends on the decay constant, the

discriminator threshold and the total number of photoelectrons produced in the

interaction. Figure 2.1 shows the time walk correction for the P0D with corrections

for the effects of MPPC after pulsing.

Sometimes photons do not transmit fully through the fiber. Interactions with

particles in the fiber result in energy loss compared to the initial interaction.

Therefore the measured signal will be less than the actual amount of deposited

32

Figure 2.2: Left:Transmission loss in the Y-11 fiber versus wavelength according to

Kuraray for 3 lengths: 100, 150 and 200 mm

energy. This loss of photons is dependent on the length of the fiber, the wavelength

of the transmitted light and the radius of any bending in the fiber [?]. The

expected photon loss for the Y11 fiber is shown in Figure 2.2 and these values are

used to calibrate the measured photoelectrons.

MPPCs are very sensitive to the wavelength of the photons that are measured.

Some wavelengths are not detected as efficiently as others. Interactions in the

fiber alter the distribution of photon wavelengths. The spectrum of wavelengths

that are emitted by the Y11 is therefore dependent on its length, with longer

fibers having broader emission spectra with fewer photons at the most efficient

wavelength.

Therefore the total light measured at the MPPC in the preferred wavelength is

reduced as distance from the interaction increases, altering the nominal “photon

detection efficiency” or PDE of the MPPC. Patrick Masliah and Antonin Vacheret

measured the PDE for fibers of various lengths and the results are shown in Fig.

2.3. It can easily be seen that although there are differences in the PDE for various

lengths, the shift in wavelength is not large enough to make a very big difference.

Because the light is only read out on one end of the fiber, the other end is

polished and coated with sputtered aluminum to reflect light back to the sensor

33

Figure 2.3: Photon Detection Efficiency vs. Fiber Length measured by ND280 Cali-

bration Group and fitted with a line

end. The mirror is not perfectly reflective, and does absorb some of the light. In

order to determine what fraction of the light is reflected, a comparison was made

between the mirrored fibers and fibers that were cleaved at 45 degrees and painted

black [?]. The reflectivity was found to be 86% with a root mean square of 6%

measured over all fibers.

Attenuation is loss of light intensity over distance. The effect is modeled as

the sum of two exponentials as follows

a(x) = fe−x

Ll + (1− f)e−x

Ls , (2.1)

where x is the position of the signal, Ll is the long attenuation length, Ls is the

short attenuation length and f is the fraction of light in the long mode. The light

that is read out from the MPPC is then the sum of the attenuated signals from

the direct and reflected light

34

x(mm)

response

Figure 2.4: Examples of scanner response measurements as a function of scanner

position with pedestal subtracted. Every color represents a different scintillator bar.

r(x) = a(x) +Ra([l − x] + l), (2.2)

where R is the mirror reflectivity and l is the length of the bar. The parameters

Ls, Ll and f are not known so the attenuation in all bars has to be measured,

and then the truncated means are fitted to determine the unknowns.

One method that was used to determine the attenuation in each bar was

P0Dule scanning. A 60Co source was used to produce a signal at 11 different

positions in the X and Y directions [?]. A sample of the response of channels at

different positions is shown in Fig. 2.4. This method allowed all the planes to be

scanned for any problems before they were shipped to Japan, and gives a good

constraint on the attenuation.

Further attenuation data was taken in situ using “through going muons”.

Through going refers to the fact that they pass through the detector, but muons

for this study are produced specifically from atmospheric neutrino interactions

35

Distance to Sensor (mm) Distance to Sensor (mm)

Nom

alized R

esponse

Nom

alized R

esponse

Figure 2.5: Truncated mean responses (solid lines) for x and y bars, along with fits

(dashed lines). The left-hand plot compares the fits to the scanner data with the scanner

data itself, while the right-hand plot compares the scanner data with the fit function

from the through going muon data, with good agreement.

and interact in the detector uniformly with well understood properties. Measur-

ing the response of the muons in different parts of the detector, it is possible to

get information about the response at many more than 11 positions in each ori-

entation. It is also possible to take data from these muons at any time, and the

data that was used to calculate the attenuation parameters was taken after the

detector was installed. A comparison between the scanner data and the muon

data is shown in Fig 2.5, and the fits using the parameters calculated from the

muon data fit both results well.

After the detector had been installed for slightly over a year, it was discovered

that a variation with position still existed in the data. This difference is shown in

Fig. 2.6. It was determined that the difference was independent of the fit parame-

ters. In order to correct the difference, the detector was divided into sections and

each section was calibrated separately. The final result gives a consistent response

in all areas of the detector.

Because of the triangular shape of the scintillator bars, it is most likely that

36

Mea

n N

od

e E

nerg

y (

ph

oto

ele

ctr

on

s)

Figure 2.6: After attenuation correction, some variation is still seen in the response

as a function of distance from the MPPC. The detector is then split into sections, and

each section is calibrated seperately to a normalized response.

a through going muon will go through two bars in a layer as shown on the right

side of Fig. 2.7. In this case, a particle with very low energy may have its energy

deposit split between the two bars such that neither bar will pass minimum energy

cuts. It is also possible that it can go through the point, and therefore only travel

in one bar, as shown on the left side of Fig. 2.7.

To insure that the calibration was done properly it is important to understand

the effect of these different types of interactions on the muon detection effeciency.

This efficiency was studied, and the result is in Fig. 2.8. It was found that except

for some events that originated in the front of the P0D, all of the tracks were

detected in either one or two of the bars at every position in the detector.

The possibility that the transmission of light in the scintillator might become

less efficient over time was taken into account. About twenty different samples

were taken at equally spaced times using a radioactive source counting setup to

measure the light output with a reference piece of scintillator from the MINERvA

37

Figure 2.7: A cartoon of a minimum ionizing particle(MIP) interacting in the trian-

gular scintillator bars. The distribution of energy will be different depending on if the

particle interacts in one or two bars at a time.

production. No evidence was observed for variation in light output beyond the

uncertainties in the monitoring measurement, roughly 5%.

2.2 Construction

The scintillator for the P0D was the first component to be constructed. A fac-

tory at Fermilab was used, which was also used to produce scintillator for the

MINERvA experiment [?]. The fiber was delivered to FNAL in precut “canes”,

unspooled fiber 67 mm longer than the bar length, to avoid “memory effects”,

bending in the fiber caused by being wound on a spool [?].

The exterior coat of TiO2 is extruded simultaneously with the polystyrene

38

Figure 2.8: Detection efficiency in the P0D. The plots show the proportion of tracks

with 0 (green circles), 1 (blue triangles) and 2 or more (red inverted triangles) hits in a

layer, for both x and y.

scintillator bars, and then the end of the bars are painted with white paint. The

fiber readout ends were coated in epoxy, polished by a diamond and then the

mirror ends were coated in the Thin Films laboratory at FNAL. Each readout

end was then fitted with a ferrule sitting within 1 mm from the fiber end. These

ferrules were specifically designed for mounting into the MPPC housing.

Construction of the P0D began in the Fall of 2008 with P0Dule assembly.

After scintillator bars were glued together to form layers, these and the active

material layers were glued inside of a large 1.8 x 2.1 m P0Dule box made of

black polystyrene. The finalized P0Dule has a rigidity similar to a solid mass of

polystyrene with the same thickness. A PVC frame covers the edge of each P0Dule

and provides a structure to hold MPPCs that have been attached to ferrule fitted

fibers. These covers also provide support for the P0Dule weight when it is installed

in the detector basket.

The MPPCs were subjected to quality control tests at various values of over-

voltage. Those that passed inspection were tagged electronically and then inserted

39

into each scintillator bar by hand. Once all the fibers were installed, each P0Dule

was moved by crane into position in a super-P0Dule, which is the colloquial term

for the grouping of P0Dules into ECAL and target segments.

The water targets are constructed of HPDE bladders, based on designs used

in the Pierre Auger Observatory Cherenkov detector [?]. These bladders are

sandwiched between P0Dules which provide support in the water target super-

P0Dule. Two bladders are used in each water layer and separated by an HPDE

strut, in order to prevent deflections due to unbalanced pressure.

P0D installation began in September of 2009, and involved several steps. The

first step was lowering the super-P0Dules into the pit. Each super-P0Dule was

prefabricated with holes to allow installation with a very low tolerance of .5mm

on internal dimensions and 1mm on the thickness, and have dimensions of 2212

mm (x) by 2348 mm (y) 102 by 38.75 mm (z). Precise measurement of P0Dules

and super-P0Dules was required to fit the final P0D into its allocated space in the

basket. Small errors in positioning of the installed super-P0Dules were fixed by

sanding the aluminum support so that screws could be inserted.

The second step was installing the water cable used in cooling the P0D and

filling the water targets. The cables have to be run from the main water reservoir

at the south end of the pit to the bottom of the detector, where they are connected

to water pipes entering the detector from the bottom. The water is filtered tap

water and is mixed with a 0.25% solution of chlorine bleach to prevent contamina-

tion with living organisms. A pump rack was installed outside the magnet, which

contains 50 self-contained pumps, one to fill each of the water bags.

The third step was installing the power for the P0D. A cable tray had to be

build to hold the massive copper cables which are used to power the P0D. Then

these cables are connected at the P0D to four power boxes, which then connect

directly to the TFBs, and two floors below the location of the P0D are connected

to the central power station for the detector. The TFBs are thermally mounted

40

on plates attached to six rails on the sides of the detector.

Finally the RMMs (Readout Merger Modules) and all of the data taking cables

had to be installed. Each RMM has to be placed in the center of the P0D at the

top. Then, the TFBs are connected individually to each RMM. Finally, cables

are run from the central data processing unit two floors below the P0D up to the

top of the P0D using orange tubing as a protective covering.

2.3 MPPC and Electronics Calibration

Once the detector was built, the electronics were calibrated. The MPPC, as

described in Chapter 1, have 1.3 mm by 1.3 mm grids made up of photon counting

pixels. Each pixel is always in either an on or off state.

Therefore, when multiple photons activate the same pixel, only a single photon

is measured. This leads to a lower number of measured compared to actual pho-

toelectrons. This effect as well as noise caused by crosstalk (called avalanching)

create a need for studying and monitoring the output of the MPPCs. Calibration

efforts included measuring the pedestal, calibrating the gain using bias voltage,

monitoring pedestal and gain changes over time and corrections for saturation of

the MPPC pixels and the electronics.

The first calibration which was made was in measuring pedestal data. The

“pedestal” is a noise peak which exists even in the case that there are no excited

electrons in the photodiode. Therefore the location of the “pedestal peak” de-

termines the value of “zero” for each capacitor. A simple diagram of the MPPC

output, including the “pedestal” peak, is shown in Fig. 2.9.

Pedestal graphs are made up of the measurements taken with the electronics

activated, but without any cosmic rays or beam. In the analysis, some cosmic rays

do appear, but the pedestal events far outweigh the actual events. The MPPCs

have both high and low gain pedestals and each TFB has 64 MPPC channels. Each

41

Figure 2.9: A simple cartoon that shows the “pedestal”, one photoelectron and two

photoelectron peaks. The distance between the pedestal and the one photoelectron

peak gives the ADC count to one photoelectron conversion. The distance between the

one and two photoelectron peaks should be the same, and provides a cross check on the

ratio.

Integrated Charge (ADC Counts)

Res

po

nse

Integrated Charge (ADC Counts)

Res

po

nse

Figure 2.10: Left: One high gain channel of a TFB. Right: Low gain channel analyzed

in the same fashion as high gain, but only the pedestal is visible

channel has 23 capacitors, and each of these capacitors is calibrated separately.

The pedestal graph for high gain is typically a large zero peak, followed by a

smaller one photoelectron peak, and a much smaller two photoelectron peak. For

the low gain pedestal, usually only the pedestal peak is visible as shown in Fig.

2.10.

42

Integrated Charge (ADC Counts)

Res

pon

se

Figure 2.11: All the pedestal peak locations for all twenty nine TFBs

Figure 2.12: After subtracting the pedestal, the MPPC signal is a gaussian distributed

around a central value of zero, with higher order peaks from noise.

Once pedestal graphs have been made for all channels and all events, the data

can be analyzed. First, a graph is made of all of the pedestal peak locations for

all of the channels. This gives a good idea of how much the pedestal differs from

channel to channel as shown in Fig. 2.11.

In order to get the ADC count of a signal, it is necessary to subtract the

pedestal value from each capacitor. When the pedestal is subtracted from runs

43

Integrated Charge (ADC Counts)

Res

po

nse

Integrated Charge (ADC Counts)

Res

po

nse

Figure 2.13: Left: Distance from pedestal peak to one photoelectron peak. Right:

Distance from pedestal peak to two photoelectron peak

with no data being taken, the result is a gaussian distributed around a central

value of zero as shown in Fig. 2.12. Secondary peaks in the tail of the distribution

are caused by the higher order noise peaks.

The distance from the pedestal peak to the one photoelectron peak gives the

photoelectron to ADC (analog to digital conversion) gain. By the same logic, the

distance from the pedestal to the two photoelectron peak is the two photoelectron

to ADC gain. If the measurement is good, the two photoelectron gain should be

about twice as large as the one photoelectron gain. In general, this was seen to be

true. Most of the measured one photoelectron to ADC gains were between 12-15

ADC counts/photoelectrons as shown in Fig. 2.13.

The data can be used to give an estimate of the crosstalk. Assuming the

photoelectron peaks obey a poisson distribution, the number of events in the

pedestal as a fraction of the total number of events will give you an estimate of

the number of one and two photoelectron events that are expected. The poisson

distribution gives

f =µke−µ

k!, (2.3)

44

Res

po

nse

Expectation Value (photoelectrons/response)

Res

po

nse

Expectation Value (photoelectrons/response)

Figure 2.14: Left: Value of one photoelectron events over pedestal events gives ex-

pected photoelectrons per response. Right: Value of two photoelectron events over

pedestal events gives half square of expected photoelectron per response.

where µ is the photoelectron expectation value, k is the number of photoelectrons

seen, and f is the probability, or the fraction of events with that number of photo-

electrons in the total sample. It can be shown that the photoelectron expectation

value is equal to the natural log of the ratio of pedestal events to total events, and

also equal to the number of one photoelectron events divided by the number of

pedestal events. This value is around 0.15-0.18 when operating in pedestal mode.

The value that is measured is higher than the expectation value predicted by

the Poisson distribution. This is because of crosstalk. Crosstalk in the MPPCs is

caused by excess thermal electrons, excited either in adjacent pixels or along the

path of the thermal electron in the initial pixel, by the passage of thermal electrons

that were excited by the initial photon interaction. Some thermal electrons are

also produced continuously by energy from the environment, even when no photon

interaction occurs.

The integrated charge from these additional electrons then produces excesses

in the higher order peaks. Since the predicted amount represents what you expect

to see with no crosstalk, measuring the excess photoelectrons will give you a good

approximation of the crosstalk noise contribution. Knowing this value makes it

45

Run Number

Inte

gra

ted

Ch

arg

e (A

DC

Co

un

ts)

Run Number

Inte

gra

ted

Ch

arg

e (A

DC

Co

un

ts)

Figure 2.15: Left: Change in pedestal over time. X axis is run number, where runs

are spaced an hour apart. Y axis is change in pedestal from run 122 in ADC counts.

Right: Change in photoelectron/ADC gain over time.

possible to correct all measured photoelectron values by subtracting the measured

crosstalk. (See Fig. 2.14)

Another useful aspect of pedestal to study is how it changes over time. Factors

like temperature and overvoltage lead to fluctuation over the course of as little

as a few hours. Several data runs were taken to try and see what if any changes

occur in the pedestal data. These studies showed RMS of about 0.3 ADC over

the course of several days, or about 2 percent of the one photoelectron to ADC

gain.

Since the pedestals vary as previously described, corrections are made over

time to account for the shifts. When beam data is taken, pedestals are also

taken. Individual capacitor gains cannot be calculated during beam running as

only averages over all the channels are taken to reduce the necessary computer

memory. In order to calibrate each capacitor individually, data from previous

measurements of the channel and capacitor pedestals are used as follows

pcapt = pcapt0 + (pchant − pchant0), (2.4)

where pt is the new pedestal measurement and pt0 is the previous pedestal mea-

46

Comparator Level (DAC) Comparator Level (DAC)

Inte

gra

ted

Ch

arg

e (A

DC

Cou

nts

)

Inte

gra

ted

Ch

arg

e (A

DC

Cou

nts

)

Figure 2.16: Change in gain for high gain channels (left) and low gain channels (right)

between the January and November runs of 2010

surement, and the subscripts cap and chan stand for the capacitor and the channel

respectively.

Change in one photoelectron gain over time was also monitored. The one

photoelectron gain seems to change related to the change in the pedestal. Change

in two photoelectron gain is also monitored, but is about the same as change in

one photoelectron gain. (See Fig. 2.15) The variation in the one photoelectron

gain was also compared between the two data taking runs in 2010. The result of

this comparison is in Fig. 2.16.

Both the low and the high gain channels on the TFBs will saturate if enough

charge is injected. In Fig. 2.17 it shows the ADC count measurement compared

to the injected charge for both high and low gain. The high gain saturates at

much lower values of injected charge, so the low gain channel is only used above

that threshold, since the high gain channel is otherwise more accurate.

Since the response is non-linear, it is fitted with two cubic polynomials su-

perimposed using error functions. We consider the channels to be adequately

calibrated when the channel response is modeled with less than a 5% residual.

Currently P0D calibration has gotten a fit that has around a 2% residual.

47

Figure 2.17: A comparison of the ADC signal to the injected charge for the high and

low gain channels. At high levels of injected charge, the high gain channels saturate

and the low gain channel value is used.

A basic model of light entering the MPPC assumes that the light is all absorbed

at the same time, that the beam is larger than the MPPC, that the light is evenly

distributed on the surface of the MPPC and that the MPPC response is Poisson

distributed. A more realistic model needs to correct for the fact that none of these

assumptions are strictly true. The reponse and saturation of the MPPC can be

described as a function of the photon detection efficiency, PDE, and the number

of effective pixels with parameters p0 and p1 as follows

〈Npe〉 = p1 ×

1− e

−〈Nγ〉 × p0

p1

, (2.5)

48

Figure 2.18: Saturation curves for over-voltages of 0.95 V, 1.14 V, 1.34 V, 1.53 V,

1.73 V and 1.92 V fitted with a 2 parameter fit

where 〈Npe〉 is the number of photoelectrons read out by the detector and 〈Nγ〉is the number of incident photons. The result of fitting the data at various over-

voltages is shown in Fig. 2.18. The residual of these fits is mostly under 5% of

the fit value.

The response in photoelectrons in each bar varies due to individual properties

of the fiber, scintillator and MPPC readout. To account for this, the response

in each bar from through going muons was measured. The most probable value,

MPV, of 38.15 photoelectrons was used to normalize the response of the bars to

give a consistent response to particle interactions.

Through going muons were also used to calibrate the timing across TFBs on

and RMM and RMMs over the full P0D. Timing responses for the first and last

TFB are shown in Fig. 2.19. These gaussian distributions are fitted for all the

TFBs in an RMM, and the timing is normalized across the RMM by subtracting

the average value from the value from the individual TFB. Similarly, the RMMs

are offset from their measured value by the average of the TFB averages from

49

Time(ns) Time(ns)

Figure 2.19: Examples from TFB 0 and TFB 268 of timing distributions relative to

the trigger.

Figure 2.20: Timing distribution relative to trigger for all TFBs before and after

calibration.

all the other RMMs. TFB average times are stable to within 2.5 ns, but RMM

averages can vary by as much as ±10 ns, so the average of multiple measurements

is used to determine the final calibration constants. The result of this calibration

is shown in Fig. 2.20.

Finally, like the fiber, the electronics also have a time walk. The electronics

time walk is caused by the fact that the capacitor will charge more quickly and

hit the threshold for creating a time stamp if the signal is larger. The time it

takes for the threshold to be reached is dependent upon the decay constant of the

circuit τ , the threshold charge Qth and the signal charge Q0 as follows

50

tth = −τ × ln(1− Qth

Q0), (2.6)

Data taken by Imperial college [?] shows that this equation accurately models

the time walk behavior with residuals compared to the fit of less than 10% (apart

from a single outlier). In the P0D comparison between multiple measurements

has shown good agreement with the fit with variations on the order of 15%.

2.4 Light Injection

To monitor the P0Dule response over time, it is useful to have a system that can

be used to produce a well understood response. In the P0D light injection is used

for this purpose. The light injection system consists of 80 pairs of 400 nm LEDs

installed in 5 mm cavities in the P0Dule support [?].

The LEDs have the ability to expose the MPPCs to light intensities with

multiple orders of magnitude. This is necessary to simulate the expected range

of scintillator responses. These intensities are achieved by varying the height and

the width of the LED pulse, which in turn is caused by varying the current pulse

applied to the LED.

The electronics that are used to control the light injection were originally

created for the MINOS experiment. They consist of four pulser boxes, a control

box, a distribution box and a power supply. Special mounting was created to

affix the pulser boxes and the control box to the P0D itself, while the distribution

box and the power supply are on a crate outside the basket. Each LED is then

connected to the pulser boxes by a 60 cm long cable. The signal is transmitted

from the control box to the pulser box via ethernet link.

When beam data is not being taken, light injection runs can be taken. Pro-

grams with specific pulse height and width patterns are used to make specific

51

Figure 2.21: Light injection can be used to monitor photosensor variation. Here the

average signal in all photosensors from light injection measurements is shown over a

period of several weeks.

calibrations. These calibrations can be used to check the status of the electronics,

such as stability of the photosensors as in Fig. 2.21 and also to measure important

properties like timing variation between different bars.

2.5 Water Target Calibration

The water target needs to be continuously monitored because changes in the vol-

ume of the water or the configuration of the water bags can change the probability

of a neutrino interaction. Any time the water targets are filled or drained the

amount of water changes. Also, besides scheduled fills and emptying, sometimes

water is added to assure that the fiducial volume was completely filled, and also

water can leaks out of the detector for whatever reason. Because the detector is

not perfectly rigid, the bags can also settle over time, creating uncertainty in the

thickness[?].

52

Figure 2.22: Variation over the course of 40 minutes in pressure sensor readings on

full water targets.

Pressure sensors and wet-dry level sensors were used in both of the data taking

runs. In Run 1 a dipstick was used to check the levels of several of the bags, and the

results did not agree with the pressure sensors. Cross checks were also done with a

flow meter and by draining a few individual bags and measuring the final volume,

and in all cases the pressure sensor readings were different. For these reasons

pressure sensor data from Run 1 is considered unreliable, and the pressure sensors

were completely replaced for Run 2.

The water was completely drained and the volume measured after Run 1.

Even though the pressure sensors were faulty, the wet-dry level sensors continued

to be accurate within 50 mm for the entire run, and therefore it is known that the

fiducial region was always completely filled with water. To calculate the fiducial

volume the drained volume is used with the average of the levels measured by

the working pressure sensors just before the drain [?]. The drained volume was

found from the measurement of the depth sensor in the main water tank, which

53

measured a 2293±10 mm depth increase after the P0D was drained. For the 37

functioning pressure sensors the average depth for a water bag was 1880 ± 45 mm

compared to the total P0D height of 2239 mm.

In Run 2 more reliable pressure sensors were used. The variation of these

sensors over time is shown in Fig. 2.22. The residual is taken as ±1 mm with

a ±15 mm calibration offset which will be reduced by wet-dry sensor calibration

references in situ [?].

Since the water bags are made of thin plastic, it is possible for the water

to bulge. This bulging can lead to variations in the water levels as the bags

settle into their new bulging configuration, and therefore creates uncertainty in

measurements of the fiducial mass. In order to understand the magnitude of the

change in the levels, the water bags were monitored for one week after they were

filled. The result is shown in Fig. 2.23. This shows a variation of 2 cm for the

upstream bag and about 30 mm for the central water bag.

The average variation for all of the water bags over the course of a week

was 50 mm. In Fig. 2.24 the variation in the levels over the course of 19

days is shown. Bags on the upstream and the downstream end have the most

variation. Downstream water bags are affected especially badly because they are

not supported by the basket. More on the effects of the water level uncertainty

will be discussed in Chapter 6.

2.6 Online Monitoring

An important tool for P0D calibration as changes occur over time is online mon-

itoring. Some calibrations can only be taken when beam is down, like light in-

jection. Other things like pedestal data, electronics response and water target

measurements can be taken continuously.

54

Figure 2.23: Variation in water levels over 1 week due to settling for a)Upstream water

bag and b)Central water bag. Upstream bags are not supported as much by surrounding

P0Dules and therefore experience more settling.

The majority of the online monitoring that is done for the TriP-T detectors is

of the activity recorded from the beam events. Total response over the course of

the run from each of the capacitors is monitored globally. Also, a 3D display of

each event allows continuous visual checks. For example, if a MIP travels through

the detector but does not create activity in a P0D layer or a TPC chamber this

is cause for immediate concern[?].

Alarms are also set in case of major failures. The water targets will set off an

alarm if the water levels drop too low. Low water levels could mean that a major

leak has occurred, which has the potential to do severe damage to the detector

55

Figure 2.24: Total variation in water levels for all bags over the course of 19 day

observation period. Downstream bags show the largest variation because they are not

supported by the basket.

Time (ns) Time (ns)

Figure 2.25: Left: Hit Time with relation to Trigger for Pedestal Right: Hit time

relative to Trigger for Event data

electronics.

Before the current online monitoring for the P0D was designed, simple online

monitoring was used for testing the detector functioning. This was before the full

detector was installed, and therefore only about half the channels are included on

the plots. This simple online monitoring for the P0D originally consisted of an

56

126*(P0dule #) + Bar # 134*(P0dule #) + Bar #

23*(Chan #) + Cap #1920*(RMM#) + 64*(TFB #) + Chan#

Figure 2.26: Simple online monitoring tools used before the full detector was installed.

Top: A hit map by P0Dule and bar number in X and Y. Bottom: A hit map by RMM

number, TFB number and channel

electronics hit map, a detector hit map, and hit time for each event.

The electronics hit map was a map of the hits in each channel in a TFB in

order to monitor for the possible existence of empty channels. An empty or low

channel would mean that the electronics were never reading out, which indicates

a malfunction. For the detector hit map, each channel was converted to a location

in the P0D in x and y, so that it was possible to see exactly where each event was

happening in the detector (See Fig. 2.26). The hit time monitored the timing

of the event, to see if it is assigning time correctly, and to look at the timing

distribution (See Fig. 2.25).

Through going muon data from the beam is also taken. As described in pre-

vious sections, these interactions can be used to calibrate and recalibrate many

57

different components of the detector. In the next chapter, the implementation of

these calibrations in the software is described.

58

3 Software

In order to understand the data that is collected by the detector and compare it

with generated Monte Carlo, multiple steps have to be taken. First the raw data

or Monte Carlo is converted into “hits”, which have been corrected for electronics

effects. Once it is converted, methods are used to extract various signals. Once

“tracks” and large energy clusters have been differentiated from the hits, different

properties of each event can be investigated. This section includes only those parts

of the electronics simulation and reconstruction work that affect the analysis that

is detailed in the final section. The software chain for data and Monte Carlo is

illustrated in Fig. 3.1.

3.1 Electronics Simulation

To create simulated events first GEANT4 [?] objects are created from Monte

Carlo generated by NEUT, which is described in detail in in Chapter 4. These

generated events are then interpreted using the “nd280mc” package. The purpose

of the “nd280mc” package is to create a data structure, called a “digit”, with

the necessary information to perform calibration, such as information about the

charge deposited by the interacting particle.

59

Figure 3.1: Two different paths in software to process data and Monte Carlo for

reconstruction. Monte Carlo is generated by NEUT, becomes GEANT hits, is processed

by ND280MC, and gets effects from the electonics added by ElecSim. Data only needs

to be calibrated using OACalib before it enters reconstruction.

The ElecSim package then uses information from these “digits” to simulate

the effects of the scintillator, MPPC and electronics read-out [?]. Some effects,

like noise, are not simulated by the NEUT even generator and are therefore added

by the ElecSim package. After the “digit” is calibrated, the new structure that is

created is called a “hit”, and can be used for particle reconstruction,.

Effects in the MPPC described in Chapter 2, such as crosstalk, avalanching

and noise, are not simulated by the generator. In order to accurately compare

data and Monte Carlo, these noise events must be simulated by ElecSim. Noise

in the TriP-T electronics is similarly simulated by the ElecSim package.

MPPC noise is simulated uniformly in position and time. Light from the

generated event is either assumed to distribute uniformly across the face of the

MPPC or to have a Gaussian distribution as shown in Fig. 3.2. Information from

the noise hits are added to the generated event hits and the combination is sorted

in order of time.

60

Figure 3.2: Two different Gaussian light distribution models. The value of sigma in

the distribution dramatically affects the distribution of light.

For the purpose of the simulation, noise hits always cause afterpulsing, but

generated events will only create a response a certain fraction of the time, de-

pending on the photon detection efficiency. Pixel firing in the MPPC is simulated

in a binary fashion, with 1 representing a photon interaction or “on” state, and

0 representing the “off” state. In the case of signal photon interaction, the pixel

charge is given as 1 at the full voltage, smeared by the photoelectron resolution.

If the voltage is less than full, the response is reduced according to the measured

calibration as given in the Chapter 2. When no signal is provided, the pixels

default to their “off” setting of 0.

The probability of crosstalk and afterpulsing are determined by the instanta-

neous charge of the pixel. For both noise and generated events avalanching effects

are modeled probabilistically with a double exponential decay. Crosstalk is simu-

lated to occur at the measured rate. The position in the MPPC of the crosstalk

response is calculated as a function of the original pixel position and the time of

the event is set immediately after the initial pixel response.

For the TriP-T electronics noise is generated using a timestamp probability

method. Noise is generated only above the TriP-T TDC photoelectron threshold

value. Simulating noise below this threshold is unnecessary because noise de-

creases linearly as a function of photoelectrons on a log scale. The computational

61

Figure 3.3: Monte Carlo is calibrated to the data in ElecSim using data from through

going muons. The muon data is fitted with a Landau distribution convolved with a

Gaussian and corrected for photon detection efficiency based on overvoltage.

power required to simulate this noise is much larger than the benefit gained, so it

is ignored.

The response of the data and the Monte Carlo is normalized using information

from through going muon data and simulated muon events. A Landau distribution

convoluted with a Gaussian is fitted to the responses, and the most probable

value is extracted as in Fig. 3.3. The measured ratio of Monte Carlo to data was

1.34, and this parameter was used to calibrate the number of photons per MeV.

Unfortunately x and y bar difference caused by photon detection efficiency effects

were not taken into account, so the section by section calibration mentioned in

Chapter 2 was necessary to normalize the response of the two views.

Monte Carlo hits produced by ElecSim can be used for reconstruction with

after linearity corrections are applied. Raw data needs to be calibrated before it

can be used. In Chapter 2 the details of these calibrations were outlined. The

package created for this purpose is OACalib. After OACalib is run on raw data,

62

it can also be used in reconstruction.

3.2 P0D Reconstruction

Reconstruction takes the calibrated hits from the previously described stage and

uses pattern recognition algorithms to create basic structures for analyses. The

final products of this reconstruction chain are “track”, “vertex” and “node” ob-

jects that are used in particle identification. Unlike previous stages, it is important

to consistently treat data and Monte Carlo information equally in this stage to

prevent bias. A brief description of the methods is given, followed by a detailed

description broken into sections.

The first step in reconstruction is to separate data by time stamp into 23

cycles. These 23 cycles correspond to the 23 capacitors in each channel, and are

a result of the method of charge integration that is used. Each charge cycle is

about 480 ns and cycles are separated by 100ns.

Between six and and eight of the cycles will contain hits in data, but usually

only one cycle contains the interaction in Monte Carlo. In data the period where

interactions take place is dependent on the bunch structure of the beam as detailed

in Chapter 1. So, though it is simple to specify the cycle containing the interaction

in Monte Carlo, it is necessary to try to reconstruct events in every cycle in order

to treat Monte Carlo and data equally.

Then noise from the electronics and MPPCs, which make up the majority of

hits, must be removed as best as possible. Reconstructing the correct total energy

of a particle, or having 100% “energy completeness”, is the ideal goal. However,

including too many noise events will reduce the efficiency of the reconstruction. In

order to maximize the energy completeness of the event it is important to balance

noise reduction with keeping as many true event hits as possible.

63

After that, a “road following” algorithm is used to create “track” objects.

“Road following” describes the basic method of using a line segment found from

a simple algorithm to add other hits that are likely to belong to the same object.

Thetrack objects created by “road following” may or may not be minimum ionizing

particles (MIPs). To increase the chance of discriminating between MIP and

shower events, hits outside the identified track are added. Also, showers can

produce high energy hits separated by enough distance to be identified as separate

tracks, so track objects are added to other tracks based on proximity to produce

a final “track”.

Because of the geometry of the P0D, these final “tracks” are created sepa-

rately in the X and Y views and then combined. The final 3D object is fitted

to determine a likely “vertex” where the event originated, under the assumption

that the particle traveled from upstream to downstream. Multiple vertices can be

identified in each event.

These vertices can then be looped over in an analysis. Properties of the vertex

or track can be used to identify the event as a shower or a MIP, and to reduce

background processes in an analysis. The cuts that were used in the νe analysis

work will be described in a later chapter.

3.2.1 Noise Cleaning

The first step after hits are separated into cycles is “cleaning” the hits. Cleaning is

the process of trying to eliminate noise hits using charge, timing and proximity to

other hits. Any hit with a charge greater than 15 photoelectrons is automatically

a “clean” hit.

In order to determine whether a hit with a charge less than 15 photoelectrons

is “clean”, the hits are sorted using Delaunay triangulation [?]. Delaunay triangu-

lation is an algorithm which creates triangles from the position of all of the hits.

64

Figure 3.4: Delaunay triangulation groups hits into triangles. Triangles are then

surrounded by circles, and if more than three points exist in the circle, new triangles

are formed until all points are formed into circles with no more than three points.

In each iteration of the algorithm, circles are drawn around the current triangles.

If any of these circles contains more than three points, new smaller triangles are

formed and the process is repeated until all the hits are contained in circles with

no more than three points as in Fig. 3.4. Any pair of points in the triangle is

called an “edge”.

The difference in position and time between the two points in every edge is

determined. If the charge of the hit is greater than 7 photoelectrons and its edge

partner is within 30 ns in time and 10cm, about three podules or bars, in space

then it is considered a likely particle interaction product. Any particle with less

than 7 photoelectrons must have an edge partner within 30 ns in time and 3.5

mm in space to be considered. All other hits are eliminated as noise. The hit

distribution before and after the cleaning process is shown in Fig. 3.5. If a cycle

does not contain at least five hits after cleaning, no further reconstruction is done.

65

Figure 3.5: Distribution of hits before (blue) and after (red) cleaning. All hits with

charge greater than 15 photoelectrons are kept, and hits below that charge are kept

only if they meet minimum criteria.

3.2.2 Creating Track Seeds

To differentiate particle interactions the first step is to look for “tracks”, which

appear as energy deposited following a line. Fig. 3.6 shows the basic “track”

construction steps. In the P0D this is done separately for the X and Y views.

These “track” candidates are expanded in the next step to allow for showering

events which do not deposit energy following a line.

A linear pattern can be detected using an algorithm called a Hough trans-

form [?]. This algorithm assumes a line with an equation ρ = xcosθ + ysinθ with

ρ and θ as shown in Fig. 3.7. Every “clean” hit has an X or Y and Z position. In

the ρθ space these points form curves. Points in ρθ space where the most curves

intersect describe likely lines in the XZ or Y Z coordinate space.

The curves may not precisely intersect, so it is important to define the size

of the ρ and θ bins. For the P0D the angular bins are 1.8 and the radial bins

are 25mm. Also at least four curves must intersect in order to be considered a

66

Figure 3.6: Steps in creating a track seed. Energy deposits in the detector (a) are

fitted with a simple line using a Hough Transform(b). Hits included in the Hough line

are then refitted using PCA to determine the track direction and the endpoints and hits

near the end of the newly fitted line are added(c).

Figure 3.7: Points in XY space (left) are transformed into curves in ρθ space (right).

When curves on the right intersect, the ρθ coordinate of the intersection describes a line

in the XY space.

candidate for a line. Linear “tracks” found using this method are called “seeds”.

After the seeds are created, a “road following” algorithm is used to add any

remaining hits. In this particular version, hits are added to nearby seeds starting

with the seed that has the largest number of hits and then cycling over all other

seeds in order of size. This is based on the hypothesis that the largest seed is

more likely to be the origin of nearby hits than other nearby smaller seeds.

67

Figure 3.8: Two basis vectors with the greatest variance for the given distribution of

points. Principal component analysis transforms hits from the original basis into these

new bases for any data set.

Before adding hits, information about the track seed is found using principal

component analysis, or PCA. PCA is a mathematical method of transforming

hits from the original basis into a new basis that is a linear combination of the

original basis vectors. Minimizing redundancy and maximizing the variance in

the new basis produces principal components, or vectors aligned with the natural

coordinate system of the distribution, as shown in Fig. 3.8. To determine the

basis with the maximal variance the matrix of eigenvectors, P , of the covariance

matrix, C = XXT , is used, where X is the vector of the hit positions with the

mean hit position subtracted [?]. The positions Y in the new basis, are calculated

as Y = PX.

The information from PCA that is used in the road following are the end point

positions and the direction of the seed. Hits are first added to the upstream end

of the seed and then to the downstream end. Only one hit is added at a time,

with the added hit being the hit that is determined to be closest to the end point

and still passes the necessary criteria.

68

Figure 3.9: A graphic of the Kalman filter process.

To focus on adding hits in the forward going direction, the dot product of the

distance between the end position and the candidate hit with the PCA direction

is required to be less than 30 mm. Also, hits further than 8cm in the Z or 60mm

in the X or Y direction if the hit is in the same layer as the end point, are not

added. Finally, any hit within the road width but outside an opening angle of

0.15 rad is not considered.

Hits are added to the track until no hits are found that meet the necessary

criteria. After hits are added, any nearby hits in the same layer are also added,

up to a maximum of three additional hits.

Seeds are not allowed to share any hits added in the previous steps. However,

in the next step hits near the vertex are allowed to be shared between multiple

seeds. At the vertex it is very difficult to determine what hits belong with what

seed, so we allow them to be in any nearby seed. Hits added in this way must

we within 40 mm in the X or Y directions, and a maximum of four hits can be

added to a seed with this method.

The final “track” candidates are then fitted using a Kalman filter. Kalman

69

filters can provide fits even for distributions that change stochastically along a

path. Predictions from Bayesian probability of subsequent points on the path

from previous predictions compared with actual measurements produce precise

fits [?]. It is able to do this by using information about the error covariance P ,

and assuming the process, for some value of A and B, approximately obeys

xk = Axk−1 +Buk−1, (3.1)

where x is an estimated position and u is an optional control input. If this can be

assumed then measurements, denoted as z, can be compared at each point using

the Kalman gain K and the projection matrix H , which must be determined

independently for each data set, as shown in Fig. 3.9. Updated information for

P and K from the comparison with measurements are then used to continue the

process of prediction until all points are fitted.

For many systems the errors can be taken initially to be normally distributed,

with process error covariance Q and measurement error covariance R. In the

case of MIP tracks process noise is determined from multiple scattering. Multiple

scattering can be calculated from the momentum of the particle p, radiation length

l, and the width of the region w as

Cms =

(

13.6

p

)2

× w

l(1 + 0.038 ∗ lnw

l)2. (3.2)

The filter uses a fit to a line as the initial assumption. It is run first in

reverse, from downstream to upstream, and then forward. This creates a fit that

is accurate at both ends of the track candidate. A collection of hits in a P0Dule

layer fitted in this way is called a “node”.

70

Angle(rad) Angle(rad)

Figure 3.10: Angle of secondary tracks with respect to most upstream track for Left:

Electrons and Right: All other particles. Secondary tracks are found primarily within

0.2 rad in the electron case, but over a wider angle otherwise.

3.2.3 Seed Merging and Expansion

The previously described algorithm works well for tracks that are approximately

linear, such as MIPs. For showering tracks, like electrons or gammas, multiple

track seeds are often found in a single particle interaction. It is useful for the

purpose of particle identification to group as many associated seeds into a single

track object as possible, and also to gather nearby hits that would be noise in a

MIP event but could shower deposits.

It is important to only merge seeds that are likely to come from the same par-

ticle interaction. For example, the decay of a neutral pion produces two photons.

These two photons are most likely to interact in different areas of the detector,

and the products of their interaction will be separated from each other in both

distance and angle. In contrast, when an electron interacts, the products will all

be in the same direction as the initial interaction. A simple drawing of the two

cases is shown in Fig. 3.11.

The angle between the most upstream seed direction and the direction of

any downstream seeds, where direction is found from the Kalman fit of the node,

71

Figure 3.11: A cartoon showing the general energy deposit of a)electron and b)neutral

pion tracks. It is important for particle identification to avoid merging the two photon

tracks from neutral pion decay into a single track like the electron.

discriminates between seeds belonging to electron tracks, which were usually found

within 0.2 radians from the upstream track, and all other particle interactions,

which are more widely distributed, as shown in Fig. 3.10. Also it was found that

requiring that the merging candidate seed be within 100 mm in the XY direction

from the upstream seed minimized incorrect merging.

Track merging is done iteratively. Seeds are first merged with the most up-

stream seed, which is considered to be the likely location of the interaction vertex,

if more than 50% of their nodes are within the necessary angle. Once the upstream

seed is expanded and refit, any unmerged seeds are rerun through the merging

algorithm and added if they meet the necessary criteria with respect to the up-

stream seed. Fig. 3.12 shows a set of seeds from a shower event before and after

the initial merging procedure. A second iteration of the algorithm will add the

green seed shown to the red upstream seed.

Once the seed merging procedure is finished unassociated hits are added. To

add as little noise as possible the allowed XY separation between the seed and

the hit is required to be less than 40 mm, or slightly more than two bar widths.

Hits may also be added even if the hit is downstream of the track end as long as

72

Y Position (mm)

Z P

osi

tio

n (

mm

)

Z P

osi

tion

(m

m)

Y Position (mm)

Figure 3.12: Left: Before and Right: After initial track merging. Some tracks frag-

ments like the one shown in green may be rejected initially for being too far from the

upstream track, but will be added in subsequent iterations

Y Position (mm) 500

Z P

osi

tion (

mm

)5

00

Figure 3.13: A cartoon to represent the method of adding hits to an existing track

object. Hits in black are from the original track seed, hits in red are added, and hits in

purple are either too far to the side or downstream to be added.

the XY separation is less than 40 mm and the Z separation between the hit and

the track end is no greater than 200 mm. This is done to allow the possibility of

small secondary showers which are not large enough or energetic enough to form

seeds. This process is illustrated in Fig. 3.13.

73

3.2.4 Track Matching and Vertexing

Because the scintillator in each P0Dule is divided into two views, ”XZ” and

”Y Z”, the previous algorithms are all done independently in each 2D view and

then combined. The method of matching 2D XZ and Y Z tracks into a single 3D

object is fairly simple. Tracks are matched as long as they overlap with another

track in enough Z layers.

A numerical score is calculated for each possible combination, where an overlap

increases the score by one and a non-overlapping point decreases the score by

one. If a pair of tracks does not share any overlaps, the pair is penalized with

a large negative score. The ratio of the charge separation to the total charge of

overlapping nodes is subtracted from the score to penalize overlapping nodes with

widely varying charge deposits.

The pairs with the highest scores are kept as the final 3D “track” candidates.

Any 2D tracks that do not achieve a high enough total score are left unmatched.

Any new 3D tracks are refitted with the Kalman filter to make 3D nodes. Also,

attenuation corrections done in situ are applied at this stage.

Once the 3D “track” candidates are constructed, all the 2D and 3D objects are

passed to an algorithm which determines the interaction vertices. Every “track”

object, 2D or 3D, is paired with every other track object, including itself, except

for the case of two 2D tracks in different views. Vertices are determined from

each pair by either extrapolating backwards from the track direction to the most

upstream point for a track with itself, or looking for the likely intersection point

for two separate tracks. These constructed vertices are kept as long as the time

difference between the two tracks is less than 40 ns, the X , Y or Z position

uncertainty is greater than 50 cm.

Once vertices have been constructed for every possible combination, the ver-

tices are clustered as long as they are within a 40 ns time window and are within

74

Z Position (mm)

X P

osi

tion

(m

m)

Figure 3.14: Result of vertex finding algorithm. The vertices are marked with crosses.

Often multiple vertices are identified (blue and yellow) even if the majority of the “track”

objects are associated with one (red).

20 cm in distance. This process is iterated until all vertices are clustered with

their neighbors, reducing the number of vertices as much as possible. The combi-

nation of tracks into vertices is shown in Fig. 3.14, with a few leftover unclustered

vertices at the downstream end of the detector.

3.3 Electron Energy Calibration

The primary signature of CCQE νe events is an electron shower. An analysis of

simulated data was performed in 2009 to develop an algorithm for electron energy

reconstruction. The first step in this was to construct a Monte Carlo program to

find the relationship between photoelectrons in the detector and energy deposited

by showering objects in MeV.

Since the P0D is made up of several sections that have very different charac-

teristics, it was necessary to construct several extra geometries containing only

these sections. Currently we have a P0D geometry which contains all ECAL, one

that contains all water targets, one containing all water targets with empty water

bags, and a geometry with only scintillator.

75

Figure 3.15: Left: Ratio of PE/MeV in Water Target between 100-165 MeV Right:

Same ratio in ECAL target between 165-270 MeV

The Monte Carlo particle gun generated electrons in an energy range from 0

to 1000 MeV with semi-logarithmic binning. Then, the energy deposited in the

detector, and the photoelectrons in the detector were compared for each energy

as seen in Fig. 3.15

The ratio of PE/MeV created a Gaussian shape with a left-side tail. This

shape was fitted with a Gaussian with a varying width using the equation

Cex−µ2

2(σmax(1,1+a(x−µ)))2 . (3.3)

where µ is the mean of the Gaussian and σ is the width. The width of the Gaussian

is related to the error in measuring photoelectrons. Statistically this was modelled

as [?]

B√E

+ C, (3.4)

where B√Ecomes from photostatistics where

√

Nphot∼=

√E ∗ constant, with Nphot

is the number of photons, E is the energy and C is a constant term from sampling.

Using this equation to fit the width of the Gaussian at various energies produced

results in agreement with what was seen in the integrated energy distribution as

seen in Fig. 3.16.

76

Figure 3.16: Left: Width of Energy Ratio Gaussian for Water Target Right: Width

for ECAL Target

Electron Energy(MeV)0 200 400 600 800 1000 1200

(pe

/MeV

)tr

ueQ

/ E

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

Electron Energy(MeV)0 200 400 600 800 1000 1200

(pe

/MeV

)tr

ueQ

/ E

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

Figure 3.17: Left: Fitted Ratio of PE/MeV in Water Target for various energies with

uncertainty from plot RMS Right: Fitted Ratio of PE/MEV in ECAL target

We expect that the value of the mean of the Gaussian fit of the PE/MeV

ratio for all energies ought to be approximately the same, and give the conversion

from deposited photoelectron to actual energy in MeV. Therefore, the mean vs.

weighted average energy was plotted for each bin. The result is fairly linear for

the scintillator only, ECAL and water target geometries as shown in Fig. 3.17.

Here the errors are given by the RMS of the width of the Gaussian, and not the

fitted value.

The average value of the mean of the Gaussian for each geometry was then

found. Using this, the photoelectron to MeV conversion was found by plotting the

reconstructed MeV to true MeV ratio in the pure geometries. This is illustrated

77

Figure 3.18: Left: Normalization for Water Target Right: Normalization for ECAL

Target

Figure 3.19: Normalization for Full Detector

in Fig 3.18 where the calbrated reconstructed energy over Monte Carlo energy are

distributed as Gaussian random variables with a mean of 1. This conversion works

very well for all energies in the water target, ECAL and scintillator geometries.

The normalization data was used to reconstruct the energy in the full detector

geometry. The various constants are applied in their respective geometry, and

then the total deposited energy was calculated. Figure 3.19 shows the result,

which is a Gaussian nicely centered around a mean of around 1.

Fluctuations over time in the electronics performance and improvements in

MC geometry caused a mostly linear change in the photoelectron to MeV ratio

for shower deposits [?]. Since the change is mostly linear, it can be corrected for

78

Constant 700.2

Mean 1.07

Sigma 0.09896

Reconstructed/True Energy0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

100

200

300

400

500

600

700

Constant 700.2

Mean 1.07

Sigma 0.09896

Constant 495.7

Mean 1.053

Sigma 0.07098

Reconstructed/True Energy0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

100

200

300

400

500

Constant 495.7

Mean 1.053

Sigma 0.07098

Constant 550.7Mean 1.057Sigma 0.05418

Reconstructed/True Energy0.6 0.8 1 1.2 1.4 1.60

100

200

300

400

500

600

Constant 550.7Mean 1.057Sigma 0.05418

Figure 3.20: Ereco/Etrue for single electron particle gun events. The particles are

produced at the upstream end of the water target region, and represent three energies

relevant to this analysis; 1, 2 and 4 GeV.

without redoing the previously discussed studies. Instead in 2011, Monte Carlo

electrons were produced with energies of 1,2 and 4 GeV. The reconstructed and

true energy were compared, and the result is shown in Fig. 3.20. The average

ratio of reconstructed energy to true energy was 1.06, so this scaling factor is

applied to all reconstructed tracks in the νe analysis.

79

4 Electron Neutrinos at T2K

and Simulation

4.1 Intrinsic Electron Neutrinos

There are several backgrounds to the signal processes which have to be well under-

stood in order for T2K to make precision measurements. Neutral current single

π0 events are a background for both the electron neutrino measurement and the

sterile neutrino measurement. Since T2K is searching for νe appearance at the

far detector, it is also very important to understand the intrinsic νe of the beam,

which is estimated to make up about 0.4 percent at peak energy as can be seen in

the neutrino flux calculations shown in Fig. 4.1. The most recent T2K analysis

found 11 signal events with an estimated contribution of 1.7 events from electron

neutrinos produced by the beam. Being able to calculate the actual electron neu-

trinos in the beam, as well as producing a Monte Carlo approximation for the

electron neutrino interactions at the near detector are both necessary steps to

reduce the uncertainty on this background.

A major focus of study is searching for charged current quasi-elastic inter-

actions of the beam electron neutrinos in the pi-zero detector(P0D), where the

Feynman diagram is shown in Fig. 4.2. Intrinsic νe in the beam comes predom-

inately from three sources: pion, kaon (K+, KL), and µ decay as shown in Fig.

80

(GeV)νE0 1 2 3 4 5 6 7 8 9 10

PO

T)

21/5

0MeV

/10

2F

lux

(/cm

710

810

910

1010

1110

1210 at ND280µν at ND280µν at ND280eν at ND280eν

Figure 4.1: Electron Neutrino flux at off-axis near detector from the various neutrino

types. The parent particles that dominantly contribute to the nuµ and νe flux are shown

in Fig. 4.3.

Figure 4.2: An electron neutrino charged current quasi-elastic event

4.3. It is important to measure the electron neutrinos explicitly because, although

the K+ contribution is well understood, KL and µ contributions are not. The pro-

portion of KL and KS that makes up the total K0 production is not known, and

low energy muons can decay before they reach the muon monitor, and therefore

cannot be measured.

81

(GeV)νE0 1 2 3 4 5 6 7 8 9 10

PO

T)

21/5

0MeV

/10

2F

lux

(/cm

510

610

710

810

910

1010 allpion parents

kaon parentsmuon parents

(GeV)νE0 1 2 3 4 5 6 7 8 9 10

PO

T)

21/5

0MeV

/10

2F

lux

(/cm

610

710

810

910

1010

1110

1210 allpion parents

kaon parentsmuon parents

Figure 4.3: Left: Electron Neutrino flux from various parents at off-axis near detector

(ND280) Right: Muon Neutrino flux from various parents at off-axis near detector

(ND280).

4.2 Electron Neutrino CCQE Cross Section

In order to constrain backgrounds to the oscillation results, electron neutrino

interactions are measured in the near detector. The expectation is that any de-

viation between the simulation and the data will be caused by backgrounds from

the beam that are not well understood. It is also possible that there could be

some uncertainty in the cross section for the electron neutrino interaction itself,

due to various factors.

To calculate a cross section Monte Carlo simulations based on models and data

from other experiments are used. The T2K experiment officially uses the NEUT

generator [?] to simulate particle interactions. This generator uses the Llewellyn-

Smith approximation as the basis of its simulation. However, this approximation

is based on many simplistic assumptions which do not hold for all values of energy

and four-momentum transfer. Several attempts have been made to parameterize

the difference, but still there are many questions.

Also this approximation is only valid for neutrino interactions with a single

nucleon, not with complex nuclei like those of the P0D. To compensate for this

fact, T2K uses a modified form of the Fermi gas model to estimate the effect of

82

the complex nuclei. The Fermi gas model gives a description of the arrangement

of the nucleons inside the atom.

Then, final state interactions within the nuclei must be considered. Final state

interactions refer to interactions between particles in the nuclei with particles

that interact with or are created by the incident neutrino. These interactions can

produce various experimental signals and must be well understood to distinguish

between quasi-elastic events and their backgrounds. T2K models these effects

with a cascade model and various studies on the production of final state particles

in resonance and deep inelastic scattering reactions.

4.2.1 Llewellyn-Smith Approximation

The Llewellyn-Smith cross section is determined from the well known lepton cur-

rent and a hadron current that can be written in terms of a vector and an axial

component as follows

JH = JV + JA. (4.1)

JV contains three terms related to the vector form factors F 1V , F

2V , and F 3

V

and JA respectively contains three related to the axial form factors FA, F3A and

Fp. A description the the bilinear covariant structure of the currents is given by

several authors [?] [?], and the total sum is given in Llewellyn-Smith’s paper as

Eq. 3.13[?].

Using this hadron current, Llewellyn-Smith calculates the quasi-elastic cross

section to be

dσ

dq2(νn→l−pνp→l+n) =

M2G2cos2θc8πE2

ν

[

A(q2)∓B(q2)s− u

M2+ C(q2)

(s− u)2

M4

]

, (4.2)

83

where q is the invariant four-momentum transfer, M is the mass of the nucleon, G

is the Fermi coupling constant, θc is the Cabibbo angle, Eν is the neutrino energy,

and

s− u = 4MEν + q2 −m2, (4.3)

where m is the mass of the lepton. The functions A(q2), B(q2) and C(q2) are

written in terms of the form factors and ξ, the difference between the anomalous

magnetic moment of the proton and the neutron, as follows

A(q2) =m2 − q2

4M2

[(

4− q2

M2

)

|F 2A| −

(

4 +q2

M2

)

|F 1V |2 −

q2

M2ξ|F 2

V |2(

1 +q2

4M2

)

−4q2ReF 1∗V ξF 2

V

M2+

q2

M2

(

4− q2

M2

)

|F 3A|2 −

m2

M2

(

|F 1V + ξF 2

V |2 + |FA + 2Fp|2

+

(

q2

M2− 4

)

(

|F 3V |2 + |Fp|2

)

)]

,

(4.4)

B(q2) =−q2

M2ReF ∗

A

(

F 1V + ξF 2

V

)

− m2

M2Re

[(

F 1V +

q2

4M2ξF 2

V

)∗F 3V

−(

FA +q2Fp

2M2

)∗F 3A

]

and

(4.5)

C(q2) =1

4

(

|FA|2 + |F 1V |2 −

q2

M2

∣

∣

∣

∣

ξF 2V

2

∣

∣

∣

∣

2

− q2

M2|F 3

A|2)

. (4.6)

F 1V and F 2

V are the vector and FA and Fp the axial form factors of the first class

currents. First class currents have the property of conserving both time and

charge symmetry as well as signs following those of the leading term in their

current under a transformation from neutron to proton. The terms associated

with F 1V and FA are considered the leading terms in the hadron current since

they have no dependence on the four-momentum transfer besides that of the form

factors.

From electron scattering experiments F 1V and F 2

V have been measured, and the

best representation of the result is the BBBA07 parametrization [?]. However,

84

early experiments showed that for low values of four-momentum transfer, the form

factors are approximately dipoles with the following form

1

(1 + Q2

m2V

)2. (4.7)

Since the form of FA was initially unknown, it was considered reasonable to esti-

mate that it would also be approximately a dipole. The value mA, the axial mass

corresponding to the mV variable in the vector dipole approximation, has been

measured by many neutrino scattering experiments at various energies and various

nuclei. None of these experiments have currently tried to make any corrections to

the dipole form of FA similar to the corrections done for the vector form factors

at values of high four momentum transfer.

F 3V and F 3

A are form factors associated with the second class current (SCC).

The existence of such currents requires charge or time symmetry violation, and

current measurements show the size of these violations to be small. Additionally

a nonzero F 3V term would violate conservation of the vector current (CVC). Both

F 3V (0) and F 3

A(0) can be limited experimentally in studies of beta decay. Almost

all current analyses of neutrino data assume that the SCCs are zero. The vector

SCCs only enter the cross-section in terms suppressed by m2/M2, but there are

unsuppressed terms involving the axial SCC form factor.

In many analyses, the term Fp is ignored because it is only involved in terms

∼ m2

M2 , and therefore contributes little to the cross section. If this term is included,

the form factor is determined from PCAC which states (if the residual operator

is considered to be small)

δµJA = Cφ, (4.8)

where φ is the renormalized field operator that creates the π+ and the value of C

can be calculated [?] at q2 = 0. Using this value and the Goldberger-Treiman

85

relation [?], which is given as

gπNNFπ = FAMN , (4.9)

where gπNN is the pion strong coupling constant and Fπ is the pion decay constant.

PCAC gives the following relation between Fp and the pion nucleon form factor

gπnn

Fp(q2) =

2M2FA(0)

q2(−FA(q

2)

FA(0)+

gπnn(q2)

gπnn(0)

1

(1− q2

M2π)). (4.10)

Under the assumption that the Goldberger-Treiman relation holds for all values

of q2, then Fp is given as

Fp(q2) =

2M2FA(q2)

M2π − q2

, (4.11)

where Mπ is the pion mass. This is the relationship that is used in all modern

neutrino generators.

4.3 Quasi-Elastic Cross Section Comparison

The theory of lepton universality would mean that the structure of the cross

section should be the same as in the muon case, and therefore that the Llewellyn-

Smith approximation could also be used. Both kinematic limits and lepton mass

dependent terms in the approximation contribute to the difference in the cross

section. Here we look at the differences in terms of the neutrino energy and the

square of the four-momentum transfer Q2.

As metrics, we define the fractional differences between the muon and electron

86

neutrino CCQE cross-sections

δ(Eν , Q2) ≡

dσµ

dQ2 − dσe

dQ2

∫

dQ2 dσe

dQ2

(4.12)

∆(Eν) ≡∫

dQ2 dσµ

dQ2 −∫

dQ2 dσe

dQ2

∫

dQ2 dσe

dQ2

. (4.13)

The integrals over Q2 in Eqs. 4.12 and 4.13 are taken within the kinematic limits

of each process, and those limits depend on lepton mass as discussed in the next

section.

Another useful metric is the difference between a cross-section in a model with

a varied assumption from that of a reference model. Our reference model derives

F 1V and F 2

V from the electric and magnetic vector Sachs form factors which follow

the dipole form of Eq. 4.7 with C = c2M2V = (0.84) (GeV/c)2, and it assumes

FA is a dipole with C = c2M2A = (1.1) (GeV/c)2. The reference model uses the

derived FP from Eq. 4.11, and assumes that F 3V = F 3

A = 0 at all Q2. We then

define

∆ℓ(Eν) ≡∫

dQ2 dσℓ

dQ2 −∫

dQ2 dσrefℓ

dQ2

∫

dQ2 dσrefℓ

dQ2

, (4.14)

where σrefℓ is the reference model for νℓn → ℓ−p or its anti-neutrino analogue and

σℓ is the model to be compared to the reference.

Both the neutrino and anti-neutrino cross sections are restricted by a maximum

and minimum allowed region in four-momentum transfer. These limits are written

in terms of the center of mass energy El and momentum pl of the lepton and the

neutrino energy Eν as

Q2min = −m2

l + 2Eν (El − |pl|) and (4.15)

Q2max = −m2

l + 2Eν (El + |pl|) . (4.16)

87

Energy(GeV)0.5 1 1.5 2 2.5 3

(N

o K

Lim

s)∆-

-310

-210

-110 Minimum2 Qν

Maximum2 Qν

Energy(GeV)0.5 1 1.5 2 2.5 3

(N

o K

Lim

s)∆-

-310

-210

-110 Minimum2 Qν

Maximum2 Qν

Figure 4.4: The total charged-current quasi-elastic cross-section difference for neutri-

nos (top) and anti-neutrinos (bottom) due to the kinematic limits in Q2. This difference

is −∆ defined in Eq. 4.13, meaning that the electron neutrino cross-section is larger than

the muon neutrino cross-section.

88

Energy(GeV)0.5 1 1.5 2 2.5 3

)2=

1.1

GeV

/cA

(m∆(m

odifi

ed))

-

A(m∆

-0.03

-0.02

-0.01

0

0.01

0.02

0.03=0.9 A mν=0.9 A mν=1.4 A mν=1.4 A mν

Figure 4.5: The change in the fractional difference of muon CCQE cross-section and

electron CCQE when mA is changed from a reference value of 1.1 GeV/c2 in a range

generously consistent with current experimental data.

Figure 4.4 shows the effect of the kinematic limits. Not surprisingly, the effect

is very large near the threshold for the muon neutrino and anti-neutrino reaction.

These effects are accounted for in the description of the quasi-elastic process in

all commonly used neutrino generators. However, it is worth noting that the

difference in Q2 spanned by the two reactions can lead to large effects in varying

form factors that significantly affect either the small or large Q2 parts of the

cross-section.

As previously stated, the differences between the muon and the electron neu-

trino cross section that do not come from kinematic limits come from the depen-

dence on the lepton mass in the form factor approximation. Since the term C(q2)

does not contain a lepton mass term, it has no effect on the difference.

In the anti-neutrino case, the B(q2) term is modified. Going from the neutrino

to the anti-neutrino case is equivalent to exchanging s and u. Since the A(q2) and

C(q2) terms are multiplied by even powers of (s − u) they are not affected. The

effect on the B(q2) term is then to change sign to -B(q2).

As noted above, the vector form factors F 1V and F 2

V are precisely measured

in charged lepton scattering [?]; however, the axial form factor is still uncertain

because neutrino experiments that measure it do not agree amongst themselves or

89

with determinations in pion electroproduction as discussed above. Therefore the

axial form factor will dominate any differences in the electron and muon cross-

sections due to uncertainties in leading form factors.

Figure 4.5 illustrates the change in the fractional difference of muon and elec-

tron neutrino CCQE cross-sections when the axial form factor is varied by chang-

ing the assumed dipole mass in a range consistent with experimental measure-

ments. The size of the effect is of order 1% at very low energy and drops with

increasing energy. This difference in cross-section may be accounted for in varia-

tions of the axial form factor within the analysis of an experiment using a modern

neutrino interaction generator.

At low Q2, the pseudoscalar form factor does have a significant contribution

to the muon neutrino CCQE cross-section, of nearly the same order of the leading

terms. However, Eq. 4.11 shows that the contribution will be suppressed for Q2 >∼M2

π , and all terms involving FP are suppressed by m/M and so the contribution

to the cross-section is negligible for electron neutrinos. At low neutrino energies,

the pseudoscalar form factor effect on the cross-section difference, ∆(Eν) is nearly

as large as that of the kinematic limits. The effect of the form factor as a function

of neutrino energy and Q2 is different for neutrinos and anti-neutrinos.

Current neutrino interaction generators [?; ?; ?; ?] include the effect of FP

shown in Eq. 4.11 under the assumptions of PCAC and that the Goldberger-

Treiman relation holds for all Q2. Experimental tests of the Goldberger-Treiman

relation have identified small discrepancies which imply that the left hand side of

Eq. 4.9 is between 1% and 6% less than the right-hand side [?; ?]. Guidance from

models suggests that this effect is likely to disappear at high Q2 [?]. We examine

the effect of varying FP (0) by 3% of itself as a reasonable approximation to the

possible difference due to this effect. A more significant difference may arise due

to violations of PCAC. This has been directly checked in pion electroproduction

studies [?] which can directly measure FP (Q2) in the range of 0.05 to 0.2 GeV/c2.

90

Uncertainties in this data limit the reasonable range of pole masses in Eq. 4.10

to be between 0.6Mπ and 1.5Mπ. Effects due to these possible deviations from

PCAC and the Goldberger-Treiman relation are shown in Fig. 4.6 along with the

effect of assuming FP = 0 for comparison.

As noted previously, non-zero second class currents violate a number of sym-

metries and hypotheses, and are therefore normally assumed to be zero in analysis

of neutrino reaction data and in neutrino interaction generators. We take a data

driven approach and look at the effect of the largest possible second-class current

form factors, F 3V and F 3

A that do not violate constraints from this data.

Vector second-class currents enter the cross-sections for neutrino quasi-elastic

scattering always suppressed by m/M and therefore only appear practically in

muon neutrino scattering cross-sections. Both vector and axial vector form factors

give large contributions to the B(Q2) term given in Eqs. 4.2 and 4.5, and therefore

typically have very different effects, often even different in sign, for neutrino and

anti-neutrino scattering.

The vector second-class currents are difficult to detect in most weak processes

involving electrons because the process is generally suppressed by powers ofme/M .

Therefore even very precise beta decay measurements have difficulty limiting the

size of F 3V (0) to less than several times the magnitude of the regular vector form

factors [?]. The best limits from beta decays currently limit F 3V (0)/F

1V (0) to be

(0.0011±0.0013)mN

me≈ 2.0±2.4 [?]. Studies of muon capture on nuclei can provide

modestly better limits, but at the expense of assuming there are no axial second

class currents [?]. An analysis of anti-muon neutrino quasi-elastic scattering has

been used to place limits of similar strength, but again under the assumption of

no axial second class currents and with an assumed Q2 dependence, F 3V (Q

2) =

F 3V (0)/(Q

2 +M23V )

2 with a fixed M3V of 1.0 GeV/c2 [?]. From the preponderance

of the data, we choose to parameterize the maximum size of the allowed vector

second class current as F 3V (Q

2) = 4.4F 1V (Q

2), which is not excluded by the results

91

Energy(GeV)0.5 1 1.5 2 2.5 3

mod

ified

|∆-no

min

al|∆

-510

-410

-310

-210

-110π>0 0.6mPF

π>0 0.6mP Fν

G-T Violations

G-T Violationsν

Energy(GeV)0.5 1 1.5 2 2.5 3

nom

inal

|∆-m

odifi

ed|∆

-510

-410

-310

-210

-110=0pF

=0P Fν

π>0 1.5mPF

π>0 1.5mP Fν

Figure 4.6: The effect of variations of FP from the reference model which assumes

PCAC and the Goldberger-Treiman relation. The plots illustrate the change cross-

section difference, ∆(Eν), between a varied model and the reference model. Possible

violations of the G-T relation produce a negligibly small effect, even at low energy. The

range of violations from PCAC allowed by current data would allow significantly larger

changes. The effect of setting FP to zero is shown for comparison.

92

2Q0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

δ

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

V 200 MeV SCCν 200 MeV No SCC ν 200 MeV No SCC ν

V 200 MeV SCCν

2Q0.1 0.2 0.3 0.4 0.5 0.6

δ

-0.4

-0.3

-0.2

-0.1

0

0.1

V 600 MeV SCCν 600 MeV No SCC ν 600 MeV No SCC ν

V 600 MeV SCCν

2Q0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

δ

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

V 1500 MeV SCCν 1500 MeV No SCC ν 1500 MeV No SCC ν

V 1500 MeV SCCν

Figure 4.7: δ(Eν , Q2), defined in Eq. 4.12, as a function of Q2 for several selected Eν .

The difference between including and not including the maximum allowed second class

vector current (“SCCV”), F3V (Q

2) = 4.4F 1V (Q

2), is shown.

93

Energy(GeV)0.5 1 1.5 2 2.5 3

=0)

V3(F∆

>0)

-V3

(F∆

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

V SCCν

V SCCν

Figure 4.8: Changes in the difference between the muon and electron neutrino cross

sections due to including F 3V .

of any of the above studies. The effect of this is significant, particularly at low

neutrino energies and is shown in Figs. 4.7 and 4.8. Recall that the effect on the

electron neutrino cross-section from F 3V is negligible, so this effect occurs almost

entirely in the muon neutrino cross-section.

In order to examine the effects of the second class current F 3A first we need an

approximation for its four-momentum dependence. It seems reasonable to assume

that, like F 1V , F

2V and FA, F

3A should also be approximately a dipole as in Eq. 4.7.

Since it is an axial current form factor, it seems reasonable to assume that it would

also depend on the same mA that FA depends on. The full form of the form factor

F 3A using the dipole approximation is

F 3A(0)

(1 + Q2

m2a)2, (4.17)

where F 3A(0) is dependent on the constraint that is chosen, and with our default

choice being the Wilkinson calculation.

To fully constrain the behavior, it is necessary to understand the behavior at

Q2=0. Our method is to use constraints on the form factor imposed by the KDR

parameters of Kubodera et al [?]. Several experiments [?] [?] [?] [?] have been

done to constrain the value of the KDR parameters. Using Wilkinson’s method

94

Constraint1 2 3 4 5 6

(0)

A(0

) / F

A3F

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 4.9: Constraints on the ratio F 3A/FA with errors from 1)Wilkinson 2)Wilkin-

son with Short Range Effects 3)Wilkinson calculation using A=20 KDR parameters

4)Wilkinson calculation using A=20 KDR parameters with Short Range Effects 5)A=12

data 6)A=20 data. The value used in simulation is the maximum magnitude of the re-

sult combined with the error. A red dashed line marks the value that is used as the

base model for the second class currents.

of calculating the magnitude of the form factor from the KDR parameters, F 3A is

constrained to be less than 10% of the value of F 2V at at Q2=0. Figure 4.9 shows

these experimental constraints and the effect we allow in this study.

Figure 4.10 shows the effect of including this allowed axial second class current

on both the difference of electron and muon neutrino cross-sections and on the

muon neutrino cross-section itself. It is significantly smaller than the effect of the

vector second class current because the limits on these currents are more stringent.

4.3.1 Radiative Corrections

To calculate the effect of radiative corrections on the total quasi-elastic cross-

section, we follow the approximate approach of calculating the leading log correc-

tion to order logQ/m, where Q is the energy scale of the interaction process [?].

This approach has a calculational advantage in investigating the differences due to

the lepton mass, m because the lepton leg leading log only involves sub-processes

where photons attach to leptons. The key result from this approach is that the

95

Energy(GeV)0.5 1 1.5 2 2.5 3

=0)

A3(F∆

>0)

-A3

(F∆

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

A SCCν

A SCCν

A SCCν

A SCCν

Energy(GeV)0.5 1 1.5 2 2.5 3

µ∆

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

A SCCµν

A SCCµν

Figure 4.10: Top: Changes in the difference between the muon and electron neutrino

cross sections due to including F 3A; Bottom: the change in muon neutrino cross-sections

due to including F 3A.

96

Energy(GeV)0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

(No

Rad

Cor

r)∆

(Rad

Cor

r)-

∆

-0.22

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

ν

ν

ν

ν

ν

ν

ν

ν

Figure 4.11: Our estimate of the fractional difference between the electron and muon

neutrino total charged-current quasi-elastic cross-sections, ∆ as defined in Eq. 4.13, as

a function of neutrino energy. The negative difference means that the electron neutrino

cross-section is larger than the muon neutrino cross-section.

97

cross-section which allows for the presence of radiated photons, σLLL is related to

the Born level cross-section, σB, by

dσLLL

dEℓdΩ≈ dσB

dEℓdΩ+

αEM

2πlog

4E∗ℓ

m2

∫ 1

0

dz1 + z2

1− z

×(

1

z

dσB

dEℓdΩ

∣

∣

∣Eℓ=Eℓ/z− dσB

dEℓdΩ

)

, (4.18)

where E∗ℓ is the center-of-mass frame lepton energy.

In the case of elastic scattering, the relationship in σB between Eℓ and the

scattering angle, θℓ simplifies the calculation because there is at most one z in the

integrand for which the cross-section does not vanish for a particular lepton angle

z =[

2Eℓ (M + Eν)(

m2 + 2MEν

)

− 2 cos2 θℓEℓEν

×√

m4 + 4E2ν

(

M2 −m2 sin2 θℓ)

− 4m2M2 − 4m2MEν

]

/[

m4 + 4Eν

(

Eν

(

m2 cos2 θℓ +M2)

+m2M)]

. (4.19)

We then obtain the remaining cross-section by integrating Eq. 4.18 over the final

state lepton energy. Note that this procedure only gives a prescription for eval-

uating dσ(Eν,true)/dQ2true; however, the radiation of real photons means that the

relationship between lepton energy and angle and Eν and Q2 in elastic scattering

will no longer be valid. The effect of this distortion of the elastic kinematics will

depend on the details of the experimental reconstruction and the neutrino flux

seen by the experiment, so the effect must be evaluated in the context of a neu-

trino interaction generator and full simulation of the reconstruction for a given

experiment.

The difference of the effect on the total cross-sections as a function of neutrino

energy is shown in Fig. 4.11. We estimate a difference of approximately 10% over

the energies of interest in oscillation experiments. The magnitude of the lepton leg

correction to the muon neutrino total cross-section is smaller, roughly 0.4 times

this difference, so the larger effect is on the electron neutrino cross-section.

98

Our estimation of the effect is surprisingly large at the relevant energies for

oscillation experiments. Although the leading log correction in the lepton mass

may accurately estimate the difference between corrections to electron and muon

neutrino induced reactions, this is only an approximate treatment which should

be confirmed in a full calculation implemented inside a generator. This difference

in cross-sections due to radiative corrections is not included in the commonly used

neutrino interaction generators [?; ?; ?; ?].

4.3.2 Summary of Quasi-Elastic Cross Section Effects

Large differences between the electron and muon neutrino quasi-elastic cross-

sections exist at low neutrino energies from the presence of different kinematic

limits due to the final state lepton mass and due to the presence of the pseu-

doscalar form factor, FP , derived from PCAC and the Goldberger-Treiman rela-

tion. These differences are typically accounted for in modern neutrino interaction

generators.

There are also significant differences due to radiative corrections, particularly

in diagrams that involve photon radiation attached to the outgoing lepton leg

which are proportional to logQ/m. These differences are calculable, but are

typically not included in neutrino interaction generators employed by neutrino

oscillation experiments. If our estimate of these differences, of order 10%, is

confirmed by more complete analyses, then this is a correction that needs to be

included as it is comparable to the size of current systematic uncertainties at

accelerator experiments [?; ?].

Modifications of the assumed FP from PCAC and the Goldberger-Treiman

relation and the effect of the form factors F 3V and F 3

A corresponding to second class

vector and axial currents, respectively, are not included in neutrino interaction

generators. A summary of the possible size of these effects, as we have estimated

99

Energy(GeV)0.5 1 1.5 2 2.5 3

|no

min

al∆-

mod

ified

∆|

-410

-310

-210

-110 Non-StandardPF Non-ZeroV

3F Non-ZeroA

3F

ν

Energy(GeV)0.5 1 1.5 2 2.5 3

|no

min

al∆-

mod

ified

∆|

-410

-310

-210

-110 Non-StandardPF Non-ZeroV

3F Non-ZeroA

3F

ν

Energy(GeV)0.5 1 1.5 2 2.5 3

| ν)no

min

al∆-

mod

ified

∆-( ν)

nom

inal

∆-m

odifi

ed∆|(

-410

-310

-210

-110 Non-StandardPF

Non-ZeroV3F

Non-ZeroA3F

Non-StandardPF

Non-ZeroV3F

Non-ZeroA3F

ν-ν

Figure 4.12: Top and Middle: For the form factors not well constrained and not

accounted for in neutrino generators, a summary of the magnitude of the fractional size

of differences in the total charged-current quasi-elastic cross-sections between electron

and muon neutrinos and anti-neutrinos as a function of neutrino energy. For FP the

average of the magnitude of the PCAC violating effects are summed linearly with the

magnitude of the Goldberger-Treiman violation effect. Bottom: The magnitude of the

difference between ν and ν of the fractional differences which illustrates the size of

apparent CP violating asymmetries in oscillation experiments.

100

them, is shown in Fig. 4.12.

These differences, particularly from the second class vector currents, may be

significant for current [?; ?; ?] and future[?] neutrino oscillation experiments

which seek precision measurements of νµ → νe and its anti-neutrino counterpart

at low neutrino energies. Previous work [?] has demonstrated sensitivity to these

second class currents in neutrino and anti-neutrino quasi-elastic muon neutrino

scattering, and future work with more recent data [?; ?] and newly analyzed

data[?] may help to further limit uncertainties on possible second class currents.

4.3.3 Fermi Gas Model

In atoms with multiple nucleons, the momentum distribution of the nucleons

within the nucleus has a large effect on the cross section for neutrino interactions.

One way of describing this is the Fermi Gas model. This model describes the

distribution of a collection of weakly interacting fermions. Current nuclear theory

says that protons and neutrons move semi-freely inside the nucleus [?], and so the

model can be applied for this situation.

This model describes fermions as existing in rectangular wells, with neutrons

and protons in separate wells. At a temperature of zero, the number of states

allowed for the particle can be found in terms of the particle momentum from the

relation

dn =4πp2V dp

(2πh)3. (4.20)

For a nucleus in its ground state, the lowest states will be filled up to a limiting

momentum pf , called the Fermi momentum. Therefore, the total number of states

can be found by integrating from zero to pf . From this you can get a value for

the quantization volume of an atom with a certain number of nucleons. The value

101

Figure 4.13: Protons and neutrons in their rectangular wells according to the Fermi

Gas Model. The energy Ef is calculated from the Fermi momentum pf and the mass

of the nucleon. Particles inside the well are part of the “Fermi sea”.

of the Fermi momentum is different for the proton and the neutron, so you get

respectively,

Vi =3π2h3Ni

p3fi, (4.21)

where Vi, Ni and pfi are the volume, number and Fermi momentum of the re-

spective nucleon. In NEUT the value of pf is taken to be 225 MeV/c. These set

of assumptions are considered the “pure” or “relativistic” form of the Fermi Gas

model.

NEUT uses an implementation of the “relativistic” Fermi Gas model created

by Smith and Moniz [?]. In order to calculate the total hadron current tensor

component of the cross section Wµν , they sum over all the nucleon momentum

states

Wµν =

∫

d~kf(~k, ~q, ω)Tµν. (4.22)

The tensor terms Tµν are the hadron current tensors calculated for different values

of nucleon energy and momentum. Smith and Moniz give the form of the Tµν terms

102

Figure 4.14: A fit to data of the Smith and Moniz Fermi Gas model [?]. Note poor

fit at high energy transfer.

for the Llewellyn-Smith hadron currents in the 1971 paper. The function f(~k, ~q, ω)

is used to describe the distribution of the nucleons and is given as [?]

f(~k, ~q, ω) =mTΩ

2π3

δ(ǫk − ǫk−q + ω)

ǫkǫk−qni(|~k|)(1− nf (|~k − ~q|). (4.23)

Ω is the quantization volume, like that calculated previously, mT is the target

mass, and ω is the energy transfer from the neutrino. The energy ǫk and ǫk−q and

the number of states as a function of momentum ni(|~k|) and nf |~k − ~q) are the

values for the target before and after the interaction. In the case of the relativistic

model, the n(|~k|) are equivalent to θ(pf − |~k − ~q|).

(1-nf(|~k−~q|)) is the Pauli Blocking parameter. This is included to insure that

the recoil nucleon is outside of the Fermi sea, which means that the nucleon state

is not occupied and therefore forbidden by Pauli exclusion. If the state is already

occupied, the interaction cannot occur and the interaction probability is zero.

After Wµν is calculated, the cross section can be determined in the same way

as described previously. This model works well for lower values of energy loss

103

ω but does not account for the tail at higher values [?]. Some generators make

attempts to correct the tail region, but NEUT does not [?].

4.3.4 Final State Interactions

When a neutrino interaction occurs in complex nuclei, there is a large probability

that there will be further interactions inside the nucleus. The simplest case is when

the struck nucleon then interacts with other nucleons. There is also a possibility

that particles like deltas, kaons, etas or pions are created in the collision and then

go on to interact inside the nucleus as well. The kinds of secondary interactions

inside the nucleus are called final state interactions.

The basic method for simulating the final state particle interactions is called

the cascade model. First, the location of the neutrino-nucleon interaction is de-

termined. To do this, it is necessary to simulate the density of the nucleus.

For atoms with mass number less than seven, the density is considered to be

approximately Gaussian. Since oxygen is the primary target in the T2K exper-

iment and has a mass number of sixteen, this approximation cannot be used.

Instead, NEUT models the nuclear density using a Woods-Saxon potential [?],

which has the following form

ρ(~r) =Z

AρA

1

1 + e|~r|−c

a

, (4.24)

where ρA is the average nuclear density, Z is the atomic number, A is the mass

number, ~r is the radial distance, c describes the size and a describes the width of

the nuclear surface.

Once the initial position is determined, the final state particles are moved a

unit length from the origin and the probability of an interaction is calculated.

If the particle interacts, the products of that interaction, if any exist, are then

followed. If there is no interaction, the original particle is then followed for another

104

unit length and the probability of interaction is calculated again. This process

continues until either the particle is absorbed or is calculated to have left the

nucleus.

Therefore, understanding the probability of interaction inside the nucleus for

different particles is very important. Each of the particles can also interact in

a variety of ways, and the probability of each of these modes must be known.

In NEUT, well tested models and information from various nuclear scattering

experiments is used to predict the interaction probabilities.

Pions can interact in three ways, inelastic scattering, charge exchange and ab-

sorption. High energy pions in these interactions can produce additional particles

which will then be followed separately. For these three modes, NEUT separates

the interaction probability into two categories, pions with momentum greater and

less than 500 MeV/c.

For pions with momentum less than 500 MeV/c a model created by L.L Sal-

cedo et al. is used [?]. This model takes into account many effects including

Fermi motion and Pauli blocking (like in the Fermi Gas model), but also includes

effects like the ∆ width and renormalization corrections. Delta pole dominance

is assumed, but Kroll Ruderman, pion pole, and direct and crossed nucleon pole

loop diagrams are also considered.

It uses a method for determining particle interaction properties called partial

wave scattering. This is a method of describing a plane wave as a series of spherical

waves. Scattering is considered to cause a phase shift in these waves, δ, which can

then be measured experimentally. In the absorption mode, both two body s-wave

absorption and three body p-wave absorption are considered.

Absorption of pions is a major problem in analyses. If a pion is produced and

absorbed, pion production events will look like other signals. In the case of a

charged current quasi-elastic reaction, ν+p → l−+p+π− or ν+n → l−+n+π+,

the signal is a proton and electron in the final state. If a π− is produced in the

105

Figure 4.15: Data for various nuclei of pions produced in photon-nucleon interactions

compared with prediction by L.L. Salcedo et al. [?] with (solid line) and without (dashed

line) pions with energy ≤ 40 MeV in order to compare to data.

nucleus and absorbed, a proton and an electron are the only particles in the final

state, exactly the same signal of the charged current quasi-elastic reaction ν+n →l− + p, but the true reaction is pion production. These kinds of events are called

“CCQE-like” and are a major background for a CCQE cross section measurement.

Therefore simulating absorption correctly is one of the most important aspects of

a final state interaction model.

The Fermi momentum in this model is described as a function of the nuclear

density as follows

pf (~r) =

[

3

2π2ρ(~r)

]−13

, (4.25)

106

Figure 4.16: Probability calculated from model and pion-nucleon scattering data for

inelastic scattering (white), charge exchange (blue) and absorption (green). Black re-

gions represent probability of no interaction.

where ρ(~r) is given by the Woods-Saxon potential as before. A comparison of the

model predictions with data from photon induced pion production is shown in

Fig. 4.15.

Since the density dependence causes a dependence on the pion position and

momentum, these must be modeled precisely. Direction and momentum of the

pion are determined using the average of the phase shifts from previous pion nu-

cleon scattering experiments and uncertainties in phase shift from data and Monte

Carlo comparison of models of the effective nuclear density for pion interactions

[?] [?].

For pions with momentum greater than 500 MeV/c, the interaction probability

is only dependent on the momentum of the pion. NEUT uses pion-nucleon scat-

tering information at these momentums to determine the interaction probability.

The calculated probability values for the three modes are shown in Fig. 4.16.

Kaon nucleon interactions are handled similarly to high momentum pions.

107

Figure 4.17: Interaction probabilities for a nucleon in 16O as a function of nucleon

momentum [?]. The solid curve, the dashed curve, the dotted curve and the dash-dotted

curve correspond to no interaction, elastic scattering, single pion production and double

pion production respectively.

Information about the cross section at various energies is stored from multiple

kaon scattering experiments [?] [?] [?]. The kinematics of the particles produced

in the kaon interactions are also stored and used to predict the momentum and

angle of particles created in the collision.

η absorption through the ηN → N∗ → π(π)N channel is simulated [?]. This

process is considered to be likely to contribute to nucleon decay into η. The cross

section is estimated by the following equation

σ =π

k2(J +

1

2)

ΓηNΓπ(π)N

(W −M∗)2 + Γtot

4

, (4.26)

where k is the momentum of the η in the center of mass system, J is the spin of

the resonance, Γ is the width of the resonance, W is the invariant mass of the ηN

system and M∗ is the mass of the resonance.

In the case of a nucleon interacting with another nucleon, the quasi-elastic

scattering, single and double pion production cases are considered. If a nucleon

scatters quasi-elastically then the particle is followed until it either produces a

pion or exits the nucleus. The possibility of nucleon absorption is not considered.

108

Measurements from nucleon-nucleon scattering experiments are used to predict

the probability of pion production. Like in the high energy pion and kaon cases,

this information is taken from averages of multiple experiments and not from

any particular model. NEUT does consider the case of pions created with and

without a delta resonance separately. Without a delta resonance, it uses the same

information as GCALOR [?], and with a delta resonance it uses a model by

Lindenbaum et Al [?]. The resulting probabilities of each interaction are shown

in figure Fig. 4.17.

4.4 Modeling Backgrounds

When making cross section measurements from data, it is important to understand

all the processes that are contributing. Even if the signal process is well modeled,

poor modeling of the background could lead to data and Monte Carlo differences

in the final result. NEUT models background interactions in the quasi-elastic,

resonance and deep inelastic scattering energy regions.

4.4.1 Resonance

The resonance energy region is dominated by interactions where there is a baryon

resonance that decays to another particle. NEUT considers the possibility of decay

into a single pion, single photon, single kaon and single η (and a nucleon). The

model of Rein and Sehgal [?] is used to predict the cross section for the eighteen

known partial wave resonances with invariant mass (W) less than 2 GeV/c2.

For single pion resonance production, Rein and Sehgal consider fourteen dif-

ferent pion final states. The basic description of these interactions is

ν +N → l +N∗ → l + π +N ′, (4.27)

109

where ν is the neutrino, N and N ′ are the nucleons, π are the pions, l is the final

state lepton and N∗ is the baryon resonance. Rein and Sehgal do not consider

the photon, kaon or η final states, but NEUT uses their method to calculate their

decay amplitudes.

In order to calculate the amplitude for producing each resonance, a modified

Feynman-Kislinger-Ravendal (FKR) model is used. This is a harmonic oscillator

quark model that can be used to calculate the charged and neutral current induced

transition matrix elements from ground state nucleons to the excited resonance

state. The matrix elements are completely specified by the SU6 multiplet, which

describes the wave function of the constituent quarks, and by the radial excitation

mode.

To calculate the amplitude to decay into a certain final state, three things are

needed: the probability distribution, the branching ratio of the state, and the

sign of the decay. The probability distribution is determined using a normalized

Breit-Wigner factor ηνBW (W ), which can be calculated from the width of the

resonance and the kinematics of the interaction. An “elasticity” factor xνE is used

to modify the amplitude based on the branching ratio of the single pion final state

for the decay. The value of the branching ratio is determined from experimental

measurements. The sign of the decay sgn(N∗ν) is calculated, with the requirement

that the isospin Clebsch-Gordon coefficient of the P33 resonance be positive, from

the FKR model previously described. These three factors are combined to form

the decay amplitude as follows

ην =√

xνE · ηνBW (W ) · sgn(N∗ν). (4.28)

The total cross section for each of the final states is then calculated by multiplying

the decay and the resonance amplitudes. The Rein Sehgal model also considers

the affect of interference of the resonances in this region. This is done using a

density matrix which is a sum of all the amplitudes of all the interfering resonances

110

Figure 4.18: Cross-sections of (a) νµp → µ−pπ+ (b) νµn → µ−pπ0 (c) νµn → µ−nπ+

. Solid lines show the calculated cross-sections.

over their spins, which can then be used to describe the angular distribution of

decay products caused by the interference.

NEUT uses this method in the case of the P33 resonance, but not the other

seventeen resonances. For all other resonances, NEUT generates the final momen-

tum of the decay products isotropically in the resonance rest frame. This method

ignores the effects of the interference completely, but still gives reasonable agree-

ment with the data (Fig. 4.18).

4.4.2 Deep Inelastic Scattering

At higher energies, the dominant process is deep inelastic scattering. Deep in-

elastic scattering is different from lower energy scattering processes in that the

neutrino begins to interact with the individual quarks instead of the nucleons.

SLAC in the late 1960s was the first experiment to see this interaction and con-

firm the existence of the quarks, which had previously been only a mathematical

concept.

111

Constructing the cross section for deep inelastic scattering is similar to con-

structing the cross section for quasi-elastic scattering. At the higher energies, some

of the terms can be ignored. NEUT eliminates non-dominant structure functions,

those with a Ml/MN prefactor (with Ml the lepton mass and MN the nucleon

mass), in its method. Also, it is possible to approximately relate the structure

functions F1 and F2 in the following way, in a method called the Callan-Gross

approximation [?]

F2 = 2xF1, (4.29)

where x is −q2/2Mν and ν is (Eν − El), with EN and El the energy in the

laboratory frame of the nucleon and the lepton respectively. This approximation

is only valid for leading order terms in QCD [?]. Higher order corrections exist

but are not used in NEUT [?] [?].

After making all of these approximations, the final form of the cross section

used for W ≥ 1.3GeV/c2 is

d2σ

dxdy=

G2fMNEν

π

(

(1− y +1

2y2 + C1)F2(x, q

2)± y(1− 1

2y + C2)xF3(x, q

2))

)

,

(4.30)

C1 =yM2

l

4MNEνx− xyMN

2Eν

− M2l

4E2ν

− M2l

2MNEνxand (4.31)

C2 = − M2l

4MNEνx, (4.32)

where y = ν/Eν .

To model the form factors F2 and F3 a parton distribution function is used.

These functions cannot be computed by using perturbative QCD, and so they

are constructed from data. NEUT uses information from the GRV98 [?] parton

112

distribution function with corrections to improve fits at lower q2 by Bodek and

Yang [?].

In the region where W ≥ 2GeV/c2 PYTHIA/JetSet is used to generate the

deep inelastic scattering events. For W < 2GeV/c2 PYTHIA does not work as

well, and the single pion production is already being simulated from the resonance

production. For this reason, a separate method is used to generate events in the

low W region. This method uses KNO scaling [?], which relates the probability

P(n) for a certain particle multiplicity n to the average pion multiplicity for that

value of energy in the laboratory frame 〈n〉 as follows

P (n) =1

〈n〉φ(n

〈n〉). (4.33)

Both 〈n〉 and the function φ( n〈n〉) are dependent on the interaction and must be

determined from data. For the pion multiplicity, NEUT uses the value 〈nπ〉 =

0.09 ± 1.83 lnW 2, which is derived from a hydrogen bubble chamber experiment

at Fermilab [?]. The function φ( n〈n〉) is derived from data from BEBC [?]. Using

this combination, all pion multiplicities can be generated in the low W region.

Pion production does also have a forward backward asymmetry which is ac-

counted for by using an empirical fit to data from the BEBC experiment [?]

〈nπf 〉〈nπb〉

=0.35± 0.41lnW 2

0.5± 0.09lnW 2. (4.34)

Finally the location of the deep inelastic scattering interaction is determined by

a formation length. This formation length is the distance required for hadroniza-

tion to occur. The formation length L is the ratio of the momentum of the hadron

and a parameter µ2 which is determined from experiment. In NEUT µ is set to

0.08 GeV 2 based on results from the SKAT experiment.

113

4.4.3 Coherent Pion Production

The final background that is considered is a poorly understood process called co-

herent pion production. This is caused by the neutrino interacting with a complex

nucleus, such as oxygen, instead of one of the constituent nuclei. Current fits are

based on very limited amounts of data, and therefore the uncertainty for this type

of background is very high.

The usual model used for this process is a PCAC approximation by Rein and

Sehgal [?]. The cross section for pion-nucleon interactions has been studied in

detail and has been shown to be fairly well modeled by the PCAC approach.

Therefore, in order to predict the cross section for the coherent pion production,

it is necessary to have a relationship between the pion-nucleon interaction and the

coherent pion interaction. Rein and Sehgal predict the following relationship

dσ(π0ℵ → π0ℵ)|dt| = A2|Fℵ|2

dσ(π0N → π0N)

|dt| |t=0, (4.35)

where ℵ is the complex nucleus, A is the number of nucleons in the nucleus, N

is a single nucleon, π0 is a neutral pion and Fℵ is the nuclear form factor. Fℵ

is broken into a piece representing the absorption of the pion Fabs, and a factor

related to the square of the four-momentum transferred to the nucleus t, like so

|Fℵ|2 = Fabse−b|t|, (4.36)

where b is one third of the square of the nuclear radius, which in the case of oxygen

is 80 GeV −2. With these relationships, the cross section can be determined from

PCAC methods to be

dσ

dxdyd|t| =G2MNf

2πA

2Eν

32π3(1− y)

[

σπ0Ntot

]2

(1 + r2)m2

A

m2A +Q2

Fabse−b|t|, (4.37)

114

where G is the weak coupling constant, r = Re(fπN )/Im(fπN), mA is the axial

vector mass, fπ = .93 mπ, MN is the mass of the nucleon, and y = (Eν − El)/Eν

with Eν and El the energy of the neutrino and the lepton respectively. Fabs is

given by

Fabs = e−〈x〉ρσπNinel , (4.38)

where 〈x〉 is the mean path length, ρ is the nuclear density, and σπNinel is the average

inelastic pion-nucleon cross section.

Like in the quasi-elastic case, there are limitations on the four-momentum

transfer because the lepton in the interaction has mass. NEUT uses a correction

suggested by Adler and implemented by Rein and Sehgal [?]. This correction

factor is multiplied by the previously calculated cross section, and has the form

C =

(

1− Q2min

2(Q2 +m2π)

)2

+y

4

Q2min(Q

2 −Q2min)

(Q2 +m2π)

2, (4.39)

where C is the correction factor, and Q2min = m2

ly

1−y.

115

5 Selection Cuts

5.1 Cut Descriptions

To measure the intrinsic νe content of the beam, νe interactions in the detector

have to be separated from the various background interactions. First data is

reconstructed into track objects. Then algorithms extract properties from the

track objects that are used for discriminating between various particle types and

interactions.

Many methods of discriminating based on different observables are used, such

as log likelihoods and neural net algorithms. In this analysis, a simple cut method

is used. For each discriminating observable, a single value is chosen. Events on

the wrong side of that value are characterized as background candidates.

These cuts were based on many considerations. Where the reconstruction was

known to have problems, such as at large angles with respect to the beam direction,

cuts were made to minimize the uncertainty from these problems. When possible

cuts were made in order to maximize the purity and efficiency of extracting νe

events.

116

5.1.1 Fiducial and Single 3D Track Cuts

Most activity in the detector comes from particles that are created outside the

detector. Since the P0D is not very deep underground, particles created by cosmic

ray interactions in the atmosphere can sometimes be detected. Also, neutrinos

in the beam can interact in the rock and sand that surround the detector. This

latter category provides the majority of the background from the environment.

To limit these backgrounds, only vertices created inside the detector volume

are considered in the analysis. The region inside the detector where vertices

are considered valid candidates is called the fiducial volume. Fiducial volume

dimensions in the P0D are given in Table 5.1.

Min (mm) Max (mm)

x −829.0 771.0

y −846.0 894.0

z −2997.5 −1272.2

Table 5.1: Boundaries of the P0D νe fiducial volume, in terms of ND280 coordinates.

The origin is the center of the basket, as defined in Chapter 1; the center of the P0D is

offset in x and y from the origin. This is the reason for the asymmetric values of the x

and y cut.

For the upstream and downstream definition the edge of the water target is

used. Interactions in the water region can be compared directly to interactions

at the Super-Kamiokande water Cherenkov detector, where ECal regions are pre-

dominately intended for veto and energy containment. Requiring that the track be

within 250 mm of the sides was also determined to provide optimal containment

and background reduction. These boundaries are shown schematically relative to

the different detector components in Fig. 5.1.

A study was done using a simple cut requiring a single 3D track, exiting the

117

Figure 5.1: A schematic showing the approximate location of the fiducial cut in the

P0D. Interaction is restricted to within the water target region and 250 mm from the

side of the detector.

P0D through the back, not the sides. This cut produced a sample that is more

than 90% muons. From this sample the distribution of vertices in data and Monte

Carlo, normalized by POT, can be compared as in Fig. 5.2. This shows that the

current fiducial definition contains the area where the event rate is approximately

linearly distributed in x,y and z. This means there are no obvious excesses to

suggest events are leaking in, or regions where the rate of event reconstruction is

anomalously low.

Particles that exit out the side of the detector, determined by having energy

deposited in the two outermost bars, are automatically vetoed in the νe analysis.

Such tracks were shown to often have poor energy resolution, and sometimes could

not be fit with a Kalman filter. Tracks that exit out the back of the detector how-

ever generally have good energy containment however, because of the downstream

ECal, and are not rejected.

This analysis considers every vertex found in the reconstruction step as a

candidate νe event. However, vertice must have an X , Y and Z position in order

to properly apply the fiducial cut, and therefore must be 3D. Therefore the fiducial

118

(m)vtxReconstructed x-1000 -500 0 500 1000

# of

Eve

nts

0

100

200

300

400

500

600

700

(m)vtx

Reconstructed y-1000 -500 0 500 1000

# of

Eve

nts

0

100

200

300

400

500

600

700

(m)vtxReconstructed z-3000 -2500 -2000 -1500 -1000

# of

Eve

nts

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 5.2: Distribution of vertices for single track vertices selected from muon events

in x, y and z. MC is in red and is scaled by pot, data events are represented by black

circles. The blue lines represent the location of the fiducial volume for the νe analysis.

The distribution in z is truncated, not showing a massive data excess in the second bin;

this excess is from sand muon events entering theP0D, which are not simulated in the

MC.

119

Number of 3D tracks0 1 2 3 4 5 6 7 8 9 10

0

10

20

30

40

50

310×

Signal0π w/ µ0π no µ0π, µno

0π no µno Out of P0DData

Figure 5.3: Number of 3D tracks for vertices passing the fiducial volume cut. Vertices

with exactly one 3D track pass the cut, as shown by the dashed blue lines.

cut removes vertices that do not contain any 3D tracks.

Due to the effectiveness of the track merging algorithm, electron showers are

likely to be reconstructed as a single track. To reduce background from particles

that produce multiple tracks, like pions, a requirement is made that the vertex

contain only a single 3D track. A comparison of data and Monte Carlo for this

cut is shown in Fig 5.3 and shows reasonable agreement.

5.1.2 Median Width Cut

The beam is primarily composed of νµ, and therefore the most common particle

produced is a muon. Muons are minimally ionizing particles, and the tracks they

produce tend to be narrow. In the P0D, these particles predominately deposit

energy entirely in one bar per layer, or split their energy over two adjacent bars.

Fig. 5.4 shows the typical MIP interactions in comparison with a typical shower

interaction.

The P0D contains layers of high Z material, brass in the water region and

120

Figure 5.4: A cartoon showing the typical energy deposit mode of MIPs compared

to electrons. The dashed line shows the initial angle of the particle that produced

the interaction (parent particle), and the solid lines show the path of the subsequent

interactions in the scintillator caused by the parent particle. To reduce the calculated

width of MIP interactions, charge in adjacent bars is merged.

lead in the ECal, which create the electron “showers”, or electron-positron pairs

created from bremsstrahlung radiation. Therefore, a useful variable for separating

muon and electron events in the P0D is the width of the track. The algorithm

that is used to calculate the width calculates the median of the energy weighted

standard deviation of all the node positions in the track.

To calculate the width, first the bars in each node are ordered by the amount

of charge deposited in each. If the two bars with the highest charge in the node

are adjacent, the position from the two bars is averaged, and treated as a single

bar. This is done in order to reduce the width that is reported in the case a MIP

deposits energy in two triangular scintillator bars. Otherwise information from

each hit in a node is used to calculate the median width.

Then the median width for each node, wi is calculated as follows

wi =

√

∑

j Ej(xj − µ′)2∑

j Ej, (5.1)

where Ej is the energy of one of the j hits in the node, xj is the position of the

121

Median width (mm)0 5 10 15 20 25 30

# of

Eve

nts

0

5

10

15

20

25

30

35

40Signal

0π w/ µ0π no µ0π, µno

0π no µno Out of P0DData

Figure 5.5: Distribution of median width with all other cuts applied. Signal and

background are shown stacked, and the data is shown as points with statistical errors.

The dashed line shows the cut position, and the arrow indicates the region passing the

cut. The highest bin is an overflow.

hit, and µ′ is the average of all the positions in the node. Using this method, the

width of MIP tracks will be predominately below 1 mm. The decision to cut at

1 mm was also the only cut in the analysis chosen specifically to maximize the

purity and the efficiency.

The distribution of widths for different interactions, after all other cuts are

applied to maximize discrimination, is shown in Fig. 5.5. It can be seen that

backgrounds with pions are predominately above 20 mm. So, it can be seen that

computing the width in this way is a strong method for eliminating backgrounds.

5.1.3 Kinematic Cuts

Previously the methods for determining the energy and angle of a track were

discussed. Cuts based on this information are performed predominately to reduce

uncertainty due to these methods. For instance, tracks at high angles cannot be

properly fitted with a Kalman filter. This combined with the fact that νe electrons

122

zθcos 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

# of

Eve

nts

0

10

20

30

40

50

60

70Signal

0π w/ µ0π no µ0π, µno

0π no µno Out of P0DData

Figure 5.6: Distribution of cos θz, where θz is angle between the track and the z axis,

after all cuts have been applied. Signal and background are shown stacked, and the

data is shown as points with statistical errors. The dashed line shows the cut position,

and the arrow indicates the region passing the cut. Other cuts, including requiring a

single track and high Eν , as well as the high CCQE content after those cuts, cause the

distribution to be very forward going.

tend to be forward going, motivate a cut at 45% from the beam direction. The

result of this cut is shown in Fig. 5.6.

Because the analysis requires a single 3D track in the vertex, quasi-elastic νe

events are favored over other νe reactions. For this reason, neutrino energy is

determined from a CCQE approximation as follows

Eν =m′

nEe +(

mp2 −m′

n2 −me

2)

/2

m′n −Ee + pe cos θ

, (5.2)

where Eν and Ee are the neutrino and electron energies, m′n is the neutron mass

modified by the binding energy, 34 MeV, mp, and me are the masses proton and

electron, θ is the track angle and pe is the electron momentum.

The deviation of the true energy from the reconstructed energy for νe events

was studied and is shown in Fig. 5.7. At higher energy where the reaction is less

likely to be CCQE the approximation is more likely to underestimate the neutrino

123

True Neutrino Energy(GeV)1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

), T

ruth

ν)/

(E, T

ruth

ν -

E, R

eco

ν(E

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

), Truthν

)/(E, Truthν - E, Recoν

(E-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

a.u

.

0

2

4

6

8

101 - 2 GeV

2 - 6 GeV

Figure 5.7: Fractional uncertainty in neutrino energy reconstruction for νe events

taken from νe sample Monte Carlo after requiring exactly one 3D track in the fiducial

volume. Each column is normalized to 1, to best illustrate the spread. No energy cut

is applied. The second plot is a profile, split between the 1-2 GeV and 2-6 GeV energy

ranges (without the column normalization used in the left plot).

energy. This shift is shown clearly in the associated profile plot, which shows the

region from 1-2 GeV and 2-6 GeV separately. Other possible causes of energy loss

are energy from the electron leaking out the back of the detector and failure to

reconstruct all the deposited energy into a single track object.

The current analysis does not have a good ability to discriminate νe from back-

grounds at low energies. In Fig. 5.8 it can be seen that events with neutral pions

and low energy muons dominate. For this reason, and also to look predominately

at νe events from kaon decays, a cut was made in energy at 1.5 GeV. Future

analyses will work to improve the discrimination at the lower energies.

5.1.4 Secondary Vertex Cut

For the analysis, every vertex in a cycle is considered as a possible νe candidate

separately. Information from secondary vertices, those vertices in the cycle that

are not the vertex currently being considered, can help to reduce potential back-

124

(GeV)νReconstructed E0 1 2 3 4 5 6

# of

Eve

nts

0

10

20

30

40

50 Signal0π w/ µ 0π no µ0π, µno

0π no µno Out of P0DData

Figure 5.8: Reconstructed quasi-elastic neutrino energy distribution of events passing

all cuts with no energy cut applied, but with weighting factors that are discussed in

Chapter 6. The last bin is an overflow.

ground contamination. Currently the energy and angle of secondary vertices is

used for discrimination purposes, in a method similar to calculating the transverse

momentum, or pT . For this reason it is referred to as the “pT” cut.

Figure 5.9 shows a cartoon of an electron event with a secondary vertex. Re-

construction most often creates secondary vertices in electron events from lower

energy hits near the far end of the track, but within a small angle from the track

direction. Backgrounds, like neutral pions, create secondary vertices that are at

a higher angle from the track direction and deposit more energy on average.

For this cut, all events with only a single reconstructed vertex pass automat-

ically. Electron events are much more likely to have only a single reconstructed

vertex in a cycle than the backgrounds. For events with multiple vertices in a

cycle, for each node of the secondary vertex the angle θi from the direction of the

candidate vertex and energy Ei are summed as follows

pT =∑

i

Eiθi. (5.3)

125

Figure 5.9: A cartoon showing the likely location of secondary vertices (red) for an

electron shower. Pion events are more likely to create secondary vertices from large

energy deposits at higher angles.

This creates a pT distribution as shown in Fig. 5.10. Signal was found to have

a pT value less than 100 MeV rad for 3D secondary vertices and 30 MeV rad for

2D secondary vertices. Because the electron signal is more likely to reconstruct

only a single vertex in a cycle, this cut has a very high efficiency for retaining νe

events.

126

(MeV rad)T

Maximum 3D p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

310×

# of

Eve

nts

0

20

40

60

80

100

120

140

160 Signal0π w/ µ0π no µ0π, µno

0π no µno Out of P0DData

Figure 5.10: Distribution of the maximum pT in the cycle, after all other cuts (in-

cluding Eν > 1.5 GeV) have been applied. Signal and background are shown stacked,

and the data is shown as points with statistical errors. The dashed line shows the cut

position, and the arrow indicates the region passing the cut. Vertices from cycles in

which there is only one vertex appear in the zero bin, and the highest bin is an overflow.

127

6 Systematic Uncertainties

In previous chapters the methods for simulating the detector, reconstructing

events, modeling cross sections, and finally selecting an electron neutrino charged

current quasi-elastic sample have been described. It is important to understand

the differences between the models that are used and what is actually seen in

data. This chapter deals with trying to understand and quantify these systematic

uncertainties.

6.1 Beam Systematics

Previously the T2K beam line was described in detail. Understanding the beam

is important for understanding the neutrino flux, and then subsequently for pre-

dicting an expected number of neutrino interactions in the detector.

Systematic uncertainty from the neutrino beam can be broken into two basic

categories. The first category are uncertainties in the production of particles

in the initial collision between the proton and the target and any subsequent

interactions that produce particles which contribute to the neutrino flux. To

estimate the uncertainty in this category, interaction models are compared to

data from outside experiments like NA61, as described in Chapter 1.

128

Figure 6.1: Ratio of NA61 to FLUKA for pion multiplicity in bins of pion momentum

p and proton direction θ.

The second category are uncertainties in the properties of the beam, like the

position, angle, focusing and others. Information from the beam monitors is used

to determine the changes in these properties. Information about the stability of

the beam over time is also measured using the muon monitor and INGRID.

6.1.1 Particle Production Uncertainty

Uncertainty in particle production comes from multiple sources. Officially the

pion multiplicity, kaon multiplicity, secondary nucleon multiplicity, tertiary pion

scaling, and beam cross section uncertainty are quantified. Wherever NA61 data

is used it is from the most recent finalized result [?].

Predictions from FLUKA and results from NA61 for pion multiplicity are

compared in bins of pion momentum p and proton direction θ for π+ and π−

separately (Fig. 6.1). The uncertainty is calculated for each bin, and is generally

between 5-10%. In regions where no data is available from NA61, an uncertainty

of 50% was assigned.

Uncertainty for charged kaon multiplicity is primarily calculated using data

from T. Eichten et al [?]. This experiment does not use a T2K replica target and

129

Figure 6.2: Ratio of Eichten data to FLUKA for charged kaon multiplicity in bins of

transverse momentum and xF .

uses protons with 24 GeV/c instead of 30 GeV. The differences caused by using a

Be target instead of a C target are taken into account by doing A scaling, which

accounts for the differences in the kaon absorption in different materials [?]. This

scaling has the approximate form

Ed3σ

dp3= Aα, (6.1)

where E is the proton energy, p is the kaon momentum, A is the atomic number

and α is a function of the scaling variable, found by fitting to data. Comparisons

between Be that is scaled to Al and actual data from the same experiment by

Eichten et al. on Al give about a 10% uncertainty from this scaling method.

Differences caused by the different proton momenta are accounted for by using

Feynman scaling. This type of scaling is used to parameterize the interaction

of particles using the center of mass energy s, the energy, longitudinal and the

transverse momentum of the kaon. An important parameter for this scaling is xF ,

or Feynman x, which is 2pL/√s.

FLUKA at 24 GeV/c and the Eichten data are compared, and then the differ-

ence is converted into an uncertainty on the kaon multiplicity using the Feynman

130

Figure 6.3: Comparison of FLUKA and NA61 for kaon cross section at different

momenta.

scaling. These uncertainties are not in terms of Eν but in terms of the scaling

variables xF and transverse momentum as in Fig. 6.2. The total uncertainty on

the kaon multiplicity is the sum in quadrature of the A scaling uncertainty, the

difference between the FLUKA and the Eichten predictions, and the systematic

uncertainty of the Eichten data itself.

No data exists to compare neutral kaon production for T2K, so the information

from the Eichten study is used with a simple quark parton model assumption to

make a prediction. With isospin symmetry the expected number of valence and

sea quarks in the proton is n = uv/dv = 2, us = us = ds = ds and ds = ds. From

this assumption, a relation between the number of K0 and the number of K± can

be constructed

N(K0L) = N(K0

S) =N(K+) + (2n− 1)N(K−)

2n=

N(K+) + 3N(K−)

4. (6.2)

This model has been shown to agree within 15% with data in the range of xF for

the T2K beam. The relation between the Eichten data and the FLUKA model are

then scaled the same as the charged kaon case (Fig. 6.4). The total uncertainty

131

Figure 6.4: Ratio of data to FLUKA for neutral kaon multiplicity in bins of transverse

momentum and xF .

Figure 6.5: Ratio of NA61 to FLUKA for second nucleon production in bins of trans-

verse momentum and xF .

for neutral kaons is then the sum in quadrature of the simple quark parton model

uncertainty, the Eichten data uncertainty and the scaling uncertainty.

Secondary nucleon multiplicity is studied by comparisons to data from Eichten,

as in the kaon multiplicity case, and Allaby et al. [?].These studies include data

132

from secondary protons and secondary neutrons, but the data is split into regions

of phase space by the Feynman scaling factor. For protons the regions with xF ≥.9

and xF ≤.9 are treated separately and for neutrons only the region with xF ≤.9

is covered.

In the xF ≤.9 region, the production uncertainty is only dependent on the

ratio of the FLUKA result to the data converted by the Feynman scaling. The

result is shown in Fig. 6.5. Outside the region covered by the data, uncertainties

are determined by the nearest comparable data point. In the region with with

.99 ≥ xF ≥.9 production is scaled by an arbitrary factor of 2 and in the region

xF ≥.99 a factor of .944 is used.

Tertiary pion scaling uncertainty is the uncertainty on the “tertiary pion”

production, pions produced from secondary protons and neutrons. Tertiary pion

production uncertainty is calculated using NA61 data compared to FLUKAMonte

Carlo using the Feynman scaling [?]. Because of questions about the accuracy of

this method, a second scaling variable, xR = E ∗ /E∗max, where E∗ is the energy

of the produced pion and E∗max is the maximum available center of mass energy,

is also used and the difference between the two results is compared [?]. The

difference between these two methods gives about a 1% uncertainty on the νµ

flux, which is then used as the tertiary pion production uncertainty.

Finally, the uncertainty on the inelastic production cross sections are calcu-

lated. Data from proton interactions in carbon in multiple experiments is used [?].

There is a large discrepancy between the measured cross section in the Denisov

result [?] compared to the other data sets that are used to calculate these cross

sections as shown in Fig. 6.6. This discrepancy is equal to the proton-nucleon

quasi-elastic cross section, and the belief is that unlike the other data sets, the

quasi-elastic component has not been subtracted.

The difference between the Denisov result and the other data sets dominates

the uncertainty, and cannot be ignored because the theory that the quasi-elastic

133

Figure 6.6: Measured inelastic nucleon production cross sections from several experi-

ments. Results from Denisov [?] are clearly anomalous, and the discrepancy is though

to be from not subtracting the quasi-elastic cross section [?].

cross section is not subtracted is only speculation. Therefore the quasi-elastic cross

section for each of the produced particles is taken to be the uncertainty on the

production cross section for that particle. To see the effect of these uncertainties on

the flux, Monte Carlo is run for multiple “throws”. A “throw” involves assigning

a rate which is chosen randomly from a Gaussian distribution around the mean

with a standard deviation equal to the uncertainty. For each of multiple throws,

with each throw having a different rate, the flux predictions will be different. The

variation in the flux from these throws is then used as the uncertainty from the

production cross section.

6.1.2 Uncertainty in Beam Properties

Beam monitors as described in Chapter 1 provide an estimate for the beam center

and angle of the beam. Alignment uncertainty of the beam monitors and for

the beamline, as well as systematic uncertainties in the monitor measurements

contribute to the total uncertainty on these values. Effects such as uncertainty in

134

Figure 6.7: Variations in the beam position from the muon monitor and INGRID

the beam monitor width measurements, effects of the momentum dispersion and

uncertainties in the quadrapole magnet model also contribute.

Uncertainty in the beam direction is calculated using information from IN-

GRID and the muon monitors. The variation in beam direction for various runs

is shown in Fig 6.7. The total uncertainty on the beam direction is the sum of

the systematic uncertainty of the INGRID and muon monitor measurements, the

actual measured deviation of the beam position, and the alignment uncertainties

for the near detector and Super-Kamiokande. For both the beam center and angle

and the beam direction cases, the uncertainty on the flux is calculated by rerun-

ning the Monte Carlo using new values of these parameters that are modified by

the magnitude of the uncertainty.

Since the three horns focus the beam, horn misalignment can also have an

effect on the neutrino flux. Studies were done to determine the effect, and it was

concluded from this study that only a misalignment in the Y, and not in the X,

directions significantly affected the νµ flux. Horn 1 was aligned with the beam

position monitors, and therefore the uncertainty in its alignment is considered as

part of the beam position monitor uncertainty. For Horn 2 and 3 the effects of

moving the horn in the positive and negative Y direction by 5 mm was investigated,

and the difference in the flux that was caused was used as the uncertainty from

135

Figure 6.8: Ratio of νe flux at near detector with and without horn alignment changes

the horn alignment. The calculated effect of these changes on the νe flux at the

near detector can be seen in Fig 6.8.

The alignment of the target is another important consideration. Beam Monte

Carlo samples were generated with the target rotated by 1.3 mRad in the hor-

izontal direction and 0.1 mRad in the vertical direction. The changes in the νe

flux at the near detector that were caused by this modification are shown in Fig.

6.9.

Finally, the uncertainty on the horn field asymmetry and current are mea-

sured. The current is measured using Rogowski coils, which are toroidal coils of

wire. The manufacturer of the horns gave the uncertainty for the coil calibration

and setting. During the run, the current was continually measured, and the max-

imum difference in the value over that time was taken as the monitor stability

uncertainty. Radial dependence of the magnetic field varies approximately as 1/r.

However measurements show a difference from the prediction, and the difference

is taken as the current-field relation uncertainty. The changes in the νe flux at the

136

Figure 6.9: Ratio of νe flux at near detector with and without target alignment changes

Figure 6.10: Ratio of νe flux at near detector with and without horn current changes

near detector that were caused by horn current uncertainties are shown in Fig.

6.10.

137

The field asymmetry is thought to be caused by a difference in the path length

of the striplines that provide current to the upper and lower parts of the horn. To

test the affect of this asymmetry, a magnetic field that is modified azimuthally is

simulated. Measurements were then taken in both Horn 2 and 3 of the actual field

asymmetry, and the deviation from the simulation were taken as the uncertainty

from the field asymmetry.

6.2 Cross Section Uncertainty

The Monte Carlo simulation program NEUT is based on models constructed to

fit the available data as accurately as possible as described in Chapter 4. However

some of the assumptions used in NEUT are overly simplistic or outdated. Com-

parisons between NEUT predictions and newer data sets and models give an idea

of the uncertainty in the Monte Carlo predictions [?].

Table 6.1shows the systematic uncertainties that were calculated for the dif-

ferent simulated interactions in NEUT.

Process Systematic uncertainty (comment)

CCQE energy dependent (< 1% at 2 GeV)

CC 1π 30% (Eν < 2 GeV) – 20% (Eν > 2 GeV)

CC coherent π± 100%

CC other 30% (Eν < 2 GeV) – 25% (Eν > 2 GeV)

NC 1π0 30% (Eν < 1 GeV) – 20% (Eν > 1 GeV)

NC coherent π 30%

NC other π 30%

Table 6.1: Summary of systematic uncertainties for the relative rate of different

charged-current (CC) and neutral-current (NC) reactions to the rate for CCQE based

on NIWG guideline.

138

Figure 6.11: Results of MiniBooNE CCQE study [?]. This favors an abnormally high

value of the axial mass MA and a large normalization factor of 10%. Uncertainties

from fits to this data are large.

The CCQE interaction study by MiniBooNE is shown in Fig. 6.11. The large

discrepancies at low Q2 with axial mass MA=1.03 GeV, or near the current world

average measurement for that parameter, have been explained by many theorists

as problems with the Relativistic Fermi Gas (RFG) model [?] [?]. Therefore,

systematic uncertainties in the CCQE cross section from nuclear modeling are

given by the difference between the RFG predictions and the prediction of spectral

function models used by the NuWro [?] generator.

For the charged current single pion reaction, NEUT with unmodified cross

sections is compared to MiniBooNE data with FSI effects taken into account.

This is done by comparing the ratio of the CC1π cross section to the CCQE cross

section to limit experiment dependent effects such as uncertainties in the beam

flux. The result is shown in Fig. 6.12. The uncertainty on the data is 20% and

the difference between the NEUT prediction and the MiniBooNE result is 10%

so the overall uncertainty is set to be 30% below 2 GeV.

139

E [GeV]vμ

Fra

ctio

nal

Unce

rtai

nti

es

Figure 6.12: Comparison of the NEUT νµ CC1π+/CCQE cross section ratio to

the FSI corrected MiniBooNE data. Fractional uncertainty in the data (black) and

NEUT/data discrepancy (red) [?]. Error bars include statistical and systematic uncer-

tainties.

For the neutral current single pi-zero measurement MiniBooNE data is com-

pared to the NEUT neutral currents that produce the same final state, a single

pion with no visible charged particles, without requiring that the true reaction be

NC1π0 [?]. The cross section for the reaction was then measured in bins of pion

angle and momentum, and for neutrino energy of 808 MeV. The total uncertainty

for the NC1π0 reaction is taken as the sum of the systematic uncertainty of the

data and the difference between the NEUT and MiniBooNE values as shown in

Fig. 6.2.

Measuring the charged current coherent cross section is challenging. SciBooNE

has several results [?] [?] that set upper bounds, as shown in Fig. 6.13. NEUT

clearly overestimates the CC coherent cross section, but due to the nature of the

current experimental limits a 100% uncertainty is assigned for this interaction.

140

σ [×10−40 cm2/nucleon] Frac. Err. or Diff. [%]

MiniBooNE data 4.56 ± 0.72 ± 15.8

NEUT MC 4.25 -6.8

Table 6.2: Total MiniBooNE flux-averaged cross section for inclusive NC1π0 produc-

tion, including fractional uncertainty in the data (first row) and NEUT/data difference

(second row)[?].

Figure 6.13: Left: Comparison of the NEUT bare νµ CC (red) and NC (blue) coherent

π cross sections compared to the SciBooNE ratios, normalized to the NEUT total CC

cross section. The CC points are 90% CL upper limits. Right: Uncertainty in NC

Coherent cross section from M cohA parameter variation

The neutral current coherent result is a comparison between the measured bare

cross section normalized to the NEUT total CC cross section. The data here has

a 20% uncertainty and the difference between the SciBooNE data and the NEUT

prediction is 15%. This along with the effects in the parameter M cohA as shown in

Fig. 6.13 give the 30% uncertainty for this interaction.

141

6.3 Detector Systematics

As discussed in Chapters 1 and 2, the P0D is made up of multiple components,

each with their own models and calibrations. Uncertainties in these can affect

the event selection by shifting the vertex location, energy, interaction rate, or cut

efficiency. Also, the difference between the assumption that the majority of the

energy in the reconstructed νe events came from the electron and the measured

energy contributions give some systematic uncertainty.

6.3.1 Fiducial Definition

Previously a simple selection requiring a single 3D track exiting the P0D through

the back of the detector was described. The distribution of the vertices for these

tracks, which are predominately muons, show good agreement with data. There-

fore, to see the effect of varying the fiducial volume, the number of selected events

in this sample was compared for different x, y and z boundaries.

These variations are done separately for the +z and -z directions. Interactions

can be produced in either the active material or the scintillator. The reconstruc-

tion however does not distinguish between vertices in brass and vertices in water,

which are adjacent layers, and instead locates all non-scintillator vertices in the

center of the water target. This misplacement causes a discrepancy in the vertex

distribution in the upstream and downstream parts of the detector. This problem

is illustrated in Fig. 6.14, where the difference between the true and reconstructed

vertex position for νe events is plotted for x,y and z. Systematically moving the

vertices in the +z direction results in a higher uncertainty in the vertex position

in the +z than in the −z direction.

To calculate the systematic, the boundaries are varied by the νe vertex res-

olution as determined from the plots in 6.14. For x, y and z this resolution is

approximately 30 mm, or two bar widths. The distributions have long tails, but

142

Entries 126428Mean -0.424RMS 29.91

Reconstructed-True Position(mm)-100 -80 -60 -40 -20 0 20 40 60 80 1000

500

1000

1500

2000

2500

3000

3500

Entries 126428Mean -0.424RMS 29.91

Entries 126428Mean 0.06147RMS 29.59

Reconstructed-True Position(mm)-100 -80 -60 -40 -20 0 20 40 60 80 1000

500

1000

1500

2000

2500

3000Entries 126428Mean 0.06147RMS 29.59

Entries 126428Mean -12.54RMS 32.41

Reconstructed-True Position(mm)-100 -80 -60 -40 -20 0 20 40 60 80 1000

500

1000

1500

2000

2500

Entries 126428Mean -12.54RMS 32.41

Recon P0Dule - True P0Dule-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Fra

ctio

n of

Ver

tices

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 P0Dule difference between true and recon’d vertex

Figure 6.14: Difference between true and reconstructed vertex position in x, y, and

z, for true νe Monte Carlo events.

these were determined to be caused primarily by the reconstruction of incorrect

secondary vertices, which are predominately eliminated by the pT cut. We choose

to ignore the contribution from these tails to the resolution, since the purpose of

using the resolution is just to get a rough measure of likely variations in vertex

position from reconstruction uncertainties.

The fractional difference between data and Monte Carlo is calculated with the

following equation

V =D′/M ′

D/M, (6.3)

where D and M are the selected data and Monte Carlo events in the simple cut

sample with the original fiducial volume and D′ and M ′ are the data and Monte

143

−2σ −1σ +1σ +2σ

xy 0.995 ± 0.004 0.994 ± 0.003 0.998 ± 0.003 1.002 ± 0.004

−z 0.999 ± 0.001 0.999 ± 0.001 1.002 ± 0.001 1.004 ± 0.002

+z 0.979 ± 0.004 0.979 ± 0.004 1.000 ± 0.001 1.006 ± 0.004

Table 6.3: Data/MC percent difference in event rate per volume ratio. The value of

σ is determined from the vertex resolution for each direction.

Uncertainty (%)

xy 0.6

−z 0.2

+z 2.1

Total 2.2

Table 6.4: Systematic uncertainty in event rate from fiducial volume choice. The total

shown is the sum in quadrature of the three individual uncertainties.

Carlo using the modified boundaries. These fractions are given in Table 6.3.

The systematic uncertainty is taken to be the largest variation in the fractional

difference from one, U , or mathematically U = |V − 1|, in each direction. These

maximum variations and their sum in quadrature, the total systematic uncertainty

for the fiducial volume cut, are given in Table 6.4.

6.3.2 Energy Scale

Uncertainty in the energy scale can come from electronics, MPPC or detector

material modeling. Each of these components was investigated individually. Many

of these parameters are shown to have no significant variation between data and

Monte Carlo, and therefore are ignored in the systematic uncertainty calculation.

For the electronics, known uncertainties exist from variations in bar response,

144

Node E (path length corrected)0 10 20 30 40 50 60 70 80 90 100

Are

a no

rmal

ized

0

10

20

30

40

50

60

70

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No smearing10% smearing15% smearing20% smearingData

Node E (path length corrected)0 10 20 30 40 50 60 70 80 90 100

Rat

io M

C/D

ata

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

No smearing10% smearing15% smearing20% smearing

Figure 6.15: Left: Node energy spectrum in through-going muons for data (dashed

black line) and Monte Carlo with different levels of channel-to-channel response varia-

tion. The node energies are corrected for the path length in the scintillator by a factor

cos θz. Right: Data/MC ratio for each value of the response variation, showing that

σ = 15% best reproduces the data.

and changes in electronics response over time. Variations in the measured response

from the electronics between different scintillator bars is calibrated as discussed

in Chapter 2. However, some residual variation remains. Also, variations in light

production within each individual bar is not accounted for in calibrations.

The effects of random variations between various bars are investigated by vary-

ing the response of each bar. This variation is chosen randomly from a Gaussian

distribution with a mean of zero deviation and various widths. The value of the

variance is determined by comparing the node energy distribution from through

going muon data to models with smearing of 10,15 and 20 %. In Fig. 6.15 the

effect of the bar to bar variation and the ratio of data to Monte Carlo is shown.

The Monte Carlo used in the analysis was then varied randomly using the same

Gaussian with both a width of 0.15/√NHits, where NHits is the number of hits

in the track, and with the full 0.15.

Changes in the electronics response over time are due to changes in over-

voltage from tunings and changes in temperature. Many of these changes have

been studied and corrected for, but still large variations can be seen. The response

145

MPV32 33 34 35 36 37 38 39 40

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Region AEntries 22Mean 36.44RMS 0.2368

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Region BEntries 32Mean 34.96RMS 0.1225

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Region BEntries 32Mean 34.96RMS 0.1225

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Region DEntries 33Mean 33.34RMS 0.1048

Region DEntries 33Mean 33.34RMS 0.1048

MPV32 33 34 35 36 37 38 39 40

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Region BEntries 32Mean 34.96RMS 0.1225

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Region DEntries 33Mean 33.34RMS 0.1048

Region DEntries 33Mean 33.34RMS 0.1048

Region CEntries 43Mean 34.06RMS 0.09862

Region DEntries 33Mean 33.34RMS 0.1048

Region BEntries 32Mean 34.96RMS 0.1225

Region CEntries 43Mean 34.06RMS 0.09862

Region DEntries 33Mean 33.34RMS 0.1048

Region BEntries 32Mean 34.96RMS 0.1225

Region CEntries 43Mean 34.06RMS 0.09862

Region DEntries 33Mean 33.34RMS 0.1048

Figure 6.16: Response histograms for four time periods in which known variations

occurred. Each entry in the histogram is weighted by the p.o.t. for the contributing

runs. The mean of each histogram is used to derive the calibration constant for the

time period.

of through going muons at different times in the data taking run is fitted with

a Landau distribution convolved with a Gaussian. The results for four different

periods are shown in Fig. 6.16. The variation in response over time from these

studies is 10% and since deviation in time averaged over space can be expected to

be approximately the same as the deviation in space averaged over time, it gives

good agreement with the 15% smearing that was calculated.

The peaks found from these plots are uncorrected by the currently used calibra-

tion constants. After the calibration constants have been applied, the distribution

of MIP peaks forms a narrower peak as shown in Fig. 6.17. The width of this

distribution is taken as the systematic uncertainty, and is approximately 3%.

For MPPCs, the noise rate is known to be significantly off. In Monte Carlo

a sample of 1 GeV electrons was created. In Fig. 6.18 the reconstructed energy

for the sample for different noise levels is compared. No large change is observed,

and the systematic uncertainty is taken to be zero.

Another known uncertainty in the MPPCs is the saturation. As described in

146

MPV35 35.5 36 36.5 37 37.5 38 38.5 39

PO

T-w

eigh

ted

0

5

10

15

20

25

1810×

Figure 6.17: Through-going sand muon responses after correction by the calibration

factors, with each entry weighted by p.o.t.

Reconstructed Energy (MeV)0 200 400 600 800 1000 1200 1400

0

50

100

150

200

250

300

350

400 Noise Level

MC Default

5×

10×

20×

Figure 6.18: The reconstructed energy of 1 GeV electrons. Increasing the simulated

noise rate has no discernible effect on the energy scale.

Chapter 2, saturation is simulated using data from muon interactions, and the

saturation model assumes a uniform light distribution across the fiber. For this

study, the photon detection efficiency and the light distribution were varied, and

the effect on the reconstructed energy for a Monte Carlo distribution of electrons

is taken as the systematic uncertainty.

The electrons are produced at 500 MeV, 1,2 and 4 GeV, and are distributed in

147

Figure 6.19: A measurement of PDE for various trigger times in the integration

window with an overvoltage of 1.34 V. This overvoltage is higher than the overvoltage

used in the P0D data taking, but the figure clearly shows that an error of almost 50%

on the PDE is clearly too large [?].

the upstream portion of the detector. Since modifications in the photon detection

efficiency and light distribution effect the MIP peak, it is also necessary to produce

a sample of muons for each configuration. Once the MIP peak is measured from

the muons, it and the recalibrated parameters are propagated through the entire

reconstruction and calibration chain.

In the UK saturation study, a Gaussian distribution with sigma varying be-

tween 0.15 and 0.3 were considered, with a value of 0.25 giving an improvement

in data and Monte Carlo comparison. We vary this parameter by ± 0.5 and look

at the variation in the reconstructed energy in the electron distribution.

Photon detection efficiency variation was also measured. The fit result was

0.26 ± 0.13, compared to the value used in the analysis which is 0.29. From [?] it

is obvious that an uncertainty of 0.13 on this parameter is unreasonably large, as

can be seen in Fig. 6.19. Therefore the difference between the measured value of

0.26 and the analysis value of 0.29 is taken as a reasonable variation. The results

148

500 MeV 1 GeV 2 GeV 4 GeV

% % % %

Light Model

σ = 0.20mm −3.91 ± 0.18 −5.59 ± 0.15 −7.36 ± 0.14 −10.97 ± 0.19

σ = 0.25mm −2.16 ± 0.17 −2.83 ± 0.16 −4.07 ± 0.13 −6.52 ± 0.17

σ = 0.30mm −0.52 ± 0.18 −1.14 ± 0.15 −1.79 ± 0.13 −3.08 ± 0.18

PDE

0.26 0.88 ± 0.18 0.80 ± 0.15 0.86 ± 0.13 0.47 ± 0.18

Table 6.5: The percentage change in the reconstructed energy of mono-energetic elec-

trons, for different MPPC sensor configurations. The 1 GeV values are used to estimate

the potential variation in the energy scale, as these electrons are closest in energy to

those produced by 1.5 GeV neutrinos, the energy of the kinematic cut.

of these variations is shown in Table 6.5.

One source of possible variation between data and Monte Carlo from detector

material is in the bar attenuation. As discussed in Chapter 2, the attenuation was

measured with through going muons and the P0Dule scanner to within 2% of the

fit prediction. The attenuation function that is derived from these measurements

agrees in data and Monte Carlo, so no systematic uncertainty is assigned from

this source.

The density and thickness of the detector material also introduces some pos-

sible data and Monte Carlo differences. The properties of the lead and the steel

in the detector have uncertainties in their densities, but the default thickness is

correct. Varying the density by ±1σ, from the maximum to the minimum value

shown in Table 6.6, the uncertainties from the density are calculated.

For the brass and the Ti02 known uncertainties in the thickness exist. In both

cases the mean value of the thickness is modified to the correct value and then

the ±1σ variation is taken around that value. For the brass, the total uncertainty

149

is calculated by modifying the Monte Carlo values of the density, as shown in ??,

and thickness separately. The thickness of the brass in the P0D was measured to

be 1.28 with an uncertainty of 0.03 mm [?]. The total uncertainty for brass is then

the sum in quadrature of the two measured variations. For Ti02 the uncertainty

comes from the thickness alone.

Material Default Minimum Maximum

Brass 8.50 g/cm3 8.13 g/cm3 8.87 g/cm3

Steel 8.00 g/cm3 7.72 g/cm3 8.28 g/cm3

Lead 11.35 g/cm3 11.30 g/cm3 11.40 g/cm3

TiO2 0.10 mm 0.17 mm 0.24 mm

Table 6.6: Variation of geometry parameters, to study the effect on the energy scale.

The ‘default’ values were all taken directly from the Monte Carlo.

To see the effect on the energy reconstruction, the same sample of electrons

used to calculate the MPPC saturation effect is used. The values in the Monte

Carlo, given as default in Table 6.6, are changed to the ±σ values, and the change

for each energy is found. For the purpose of the systematic, the variation of the

1 GeV electrons is used, since it is closest to the energy cut value of 1.5 GeV.

6.3.3 Rate and Mass Normalization Weightings

The Monte Carlo is normalized to the data based on several measurements. For

the inclusive νe analysis, an overall rate normalization is done in the same manner

as the Run I-II νe appearance paper [?], based on a mostly charged current quasi-

elastic sample of muon neutrino interactions in the tracker. The ratio of data to

Monte Carlo that they found was

Rµ,DataND /Rµ,MC

ND = 1.04± 0.028(stat)+0.044−0.037(det.syst.) ± 0.038(phys.syst.).

150

Material Variation 500 MeV 1 GeV 2 GeV 4 GeV

% % % %

Brass −1 σ 0.68 ± 0.50 1.10 ± 0.44 0.65 ± 0.48 1.30 ± 0.85

+1 σ −0.52 ± 0.52 −0.57 ± 0.43 0.12 ± 0.47 0.50 ± 0.86

Steel −1 σ 0.86 ± 0.51 0.31 ± 0.44 0.55 ± 0.49 1.09 ± 0.84

+1 σ 0.44 ± 0.51 0.00 ± 0.45 0.50 ± 0.48 1.12 ± 0.83

Lead −1 σ 1.13 ± 0.50 0.86 ± 0.43 1.07 ± 0.47 0.61 ± 0.92

+1 σ 1.26 ± 0.50 0.74 ± 0.43 0.80 ± 0.47 2.08 ± 0.82

TiO2 −1 σ 0.10 ± 0.51 −0.53 ± 0.46 0.34 ± 0.49 0.04 ± 0.86

+1 σ 0.42 ± 0.50 0.31 ± 0.42 0.63 ± 0.49 1.25 ± 0.84

Table 6.7: The percentage change in the reconstructed energy of mono-energetic elec-

trons, as the detector geometry is varied. In each case, the geometry is changed to

the current best estimate, and then an individual parameter is varied by 1σ. The 1

GeV values are used to estimate the potential variation in the energy scale, as these

electrons are closest in energy to those produced by 1.5 GeV neutrinos, the energy of

the kinematic cut.

This result implies a 6% uncertainty from the rate normalization.

For the CCQE-like study, the rate is normalized by 1 and the uncertainty on

this normalization is calculated from the previously mentioned beam systematics.

These systematics are combined into a 160×160 bin covariance matrix as shown in

Fig 6.20. The entries are separated by bins of energy, neutrino type, and detector

to account for the correlations between the different parameters. For instance, the

νµ and νe fluxes are correlated since both are dependent on the rate of secondary

particle production in the beam.

To get the uncertainties from the covariance matrix, Cholesky decomposition

is used. The portion of the n × n matrix corresponding to the parent neutrino

151

Figure 6.20: 160×160 bin covariance matrix of beam flux uncertainties. The first 80

bins are the near detector and the last 80 bins are the far detector, ordered by neutrino

type and energy.

and detector for the event is selected for decomposition. A variation in the flux is

generated for each of the n bins by multiplying the decomposed covariance matrix

by a randomly sampled value from a Gaussian with mean of zero and a width of

one.

Ten thousand of these variations form a Gaussian distribution as shown on

the left side of Fig. 6.21. The width for this distribution is then taken as the

systematic uncertainty for that bin. For each bin, the ratio of the width and the

mean in each bin is plotted. The average uncertainty from all bins of this plot is

10.8%.

Another normalization that is used is the mass uncertainty normalization.

Measurements were made of the P0D fiducial mass for Run I and Run II [?]. The

definition of the fiducial region is an area with an X width of 1600 mm and a Y

width of 1740 mm, with the center at the center of the P0D and within the water

target region.

Currently there is no known change in the detector mass between Run I and

Run II, and malfunctions in the water depth sensors in Run I, as described in

152

/ ndf 2χ 130.5 / 131Constant 2.4± 195.2 Mean 0.02± 18.91 Sigma 0.015± 2.019

10 15 20 25 300

20

40

60

80

100

120

140

160

180

200

220

/ ndf 2χ 130.5 / 131Constant 2.4± 195.2 Mean 0.02± 18.91 Sigma 0.015± 2.019

Fractional Variation0.08 0.09 0.1 0.11 0.12 0.13 0.140

2

4

6

8

10

12

14

Figure 6.21: Left: An example set of ten thousand throws. The result is a Gaussian

with a sigma equal to the systematic uncertainty from the flux measurement for that

bin. Right: Sigma of the fitted gaussion as a fraction of the mean.

Chapter 2, lead to a higher uncertainty in the water mass measurement. For this

reason, we use the Run II measurement, which is known with greater confidence.

The uncertainties calculated in this measurement take into account the total un-

certainty from the water mass measurements and other detector materials such

as brass, lead, scintillator, and even the p0dule covers and epoxy that hold the

detector together.

The Run II measurement for the period when the detector was filled with

water was 5484 ± 44 kg compared to the Monte Carlo value of 5799 kg. The

deviation from the measured mass is 4.3 ± 0.8 % [?]. This uncertainty of 0.8 %

is taken as a systematic uncertainty on the Monte Carlo predicted rates.

6.3.4 Muon Rejection

The ability of the width cut to reject muons depends on the agreement between

data and Monte Carlo of the reconstructed width. In order to do this comparison,

“sand muons”, or muons produced by neutrino interactions in the sand surround-

ing the detector hall, were selected from data. This selection required that there

be a single track in an interaction cycle that passes through the upstream ECal

153

Track length (m)0 0.5 1 1.5 2 2.5 3

0

0.5

1

1.5

2

2.5

3

3.5

310×

Particle gun MC

Data

Figure 6.22: Length of tracks in sand muon particle gun MC (red) and data (black),

used as a proxy for muon energy. The agreement is generally good, except for short

tracks. The MC is normalized to the same number of events as the data.

of the P0D and stop inside the water target or downstream ECal, with no associ-

ated reconstructed shower. Since no Monte Carlo predictions exist for the exact

distribution of sand muon interactions, a sample was created with the above re-

quirements, and distributed such that the angle and energy of the tracks closely

matched that of the selected data events, as shown for track length in Fig 6.22.

The width is calculated using the same algorithm as the width cut, as discussed

in Chapter 5, but only for nodes that are downstream of the upstream ECal, since

that region is excluded in the analysis. A comparison of the results for data

and Monte Carlo is shown in Fig. 6.23. In order to calculate the systematic

uncertainty, the ratio of data to Monte Carlo above the cut width, as given in

Table 6.8, is used to scale up the background that is composed of muons with no

associated neutral pions.

The large disparity between data and Monte Carlo is believed to be caused by

the factor of four difference in the noise rate and a mis-modelling of the charge

distribution of the noise. In Fig. 6.24 it can be seen that the large discrepancy

just above the cut width disappears if the contributing hits are required to have

a charge of no less than 10 photoelectrons. The mechanism of the width increase

154

Median width (mm)

0 1 2 3 4 5 6 7 8 9 10

Are

a n

orm

aliz

ed

-410

-310

-210

-110

1

Particle gun MC

Data

Figure 6.23: Median width distribution of stopping sand muons in data (black) and

particle gun Monte Carlo (red) with median width cut shown(blue). The selection

criteria are described in the text.

Selected fraction (%)

Data 1.4

MC 1.2

Ratio Data/MC 1.18

Table 6.8: Fractions of stopping muons selected by the width cut in data and Monte

Carlo, and their ratio. The ratio is used in the analysis to scale up selected MC events

without a π0, and 100% of the correction is included as a systematic on this effect.

from the excess of high charge noise is that noise hits are added to nodes that

would otherwise contain only a single hit, or two hits that would be merged based

on the width algorithm criteria. The separation between the noise hit and the true

MIP hits is then recorded as an anomalously high width, creating the discrepancy.

6.3.5 Angular Resolution

Reconstruction of the track angle is used to calculate the kinematics of the recon-

structed tracks. Variations between the reconstructed angle in data and Monte

155

Node width (mm)0 5 10 15 20 25 30

1

10

210

310

Node width (mm)0 5 10 15 20 25 30

1

10

210

310

Figure 6.24: Distribution of node widths in data (black) and particle gun sand muon

MC (red), with the width cut also shown(blue). Left: with default reconstruction

parameters. Right: with all hits below 10 photoelectrons removed before reconstruction.

In each case, the MC histogram is scaled to the same number of events as the data.

Carlo could therefore affect the reconstructed energy and Q2 distributions. To

simulate the effect of an incorrect angular resolution in MC on an event-by-event

basis, the unit vectors representing the true electron direction t and the recon-

structed track direction r are used to construct a new track direction r’ as follows

r′ =t+ α(r− t)∣

∣t+ α(r− t)∣

∣

. (6.4)

This has the approximate effect of increasing the angular resolution by a factor of

α if r is close to t. After the new direction r’ is calculated, the result is modified

and the difference between the original result and the new result with the modified

angle is taken as the systematic uncertainty. For a range of values of α between

0.5 and 1.5, the fractional change in number of selected events is less than 0.5%.

This uncertainty is small and therefore is not included in the total systematic

uncertainty.

156

Charge Deposit (p.e.)0 100 200 300 400 500 600

# of

Eve

nts

-110

1

10

210Side DepositSide Deposit

Figure 6.25: The side charge deposit of events passing all cuts other than the side

exiting cut.

6.4 Additional Checks

6.4.1 Side Exiting Events

As previously noted, the noise rate in the P0D is about four times the simulated

value. This might cause more events to be reconstructed as having energy deposits

in the side of the P0D in data than in Monte Carlo. These events would then be

classified as “side exiting” and be removed by the analysis cuts.

Noise hits are known to predominately have energies in the 0 to 10 photoelec-

tron range as discussed in Chapter 2. In Fig. 6.25 the side deposit charge for all

events that pass all cuts except the side exiting cut are shown. For clarity the

plot has been shifted down by a small fraction of a photoelectron and all of the

events which pass the side exiting cut, which make up the majority of the events,

are moved into the -20 to 0 bin. It can be seen that the 6 remaining data events

which are rejected by the side exiting cut all have higher energy than the expected

noise. Therefore, no systematic uncertainty is deemed necessary for this cut.

157

MC Data

Scanner Ntot Nmerged Fraction (%) Ntot Nmerged Fraction (%)

1 64 8 12± 5 119 19 16± 3

2 63 5 8± 3 119 6 5± 2

3 64 4 6± 3 119 10 8± 2

Table 6.9: Results of hand scan of selected events. The total number of events scanned

Ntot, and the fraction classified by the scanner as “merged” Nmerged, are shown, along

with the fraction including statistical uncertainty. )

6.4.2 Hand Scan

The track merging stage of the P0D reconstruction can cause multiple MIP-like

tracks to be merged, forming one track with high width. These events are then

likely to pass the width cut despite being composed entirely of MIP-like tracks.

Since it is difficult to determine for certain if components of merged tracks in data

are actually MIPs, one way to compare the rate of merging in data and Monte

Carlo was by using human event scanning. Three scanners looked at all data

events events passing all cuts, and a common set of MC events passing the same

selection, noting events which they believed contained a set of merged tracks.

The results are shown in Table 6.9. For each scanner, there is no statistically-

significant difference in the fraction identified as merged between data and Monte

Carlo, so this systematic is taken to be negligible.

6.4.3 Proton Reconstruction

The most likely particle in a νe interaction to be reconstructed as a single track

is the electron. In some cases however the proton is identified instead. Protons

misidentified as signal can also come from background interactions.

The P0D reconstruction does not have a dedicated particle identification method

158

Figure 6.26: Left: Efficiency of reconstructing a track, for single particle gun protons,

gener- ated with uniform energy and isotropic, but downstream, angular distributions.

The dominant effect is the number of hits passing the cleaning thresholds, leading to

a strong energy dependence. Right: Kinetic energy distribution of protons in events

passing all selection criteria.

for protons. Therefore the efficiency for selecting protons with the current selec-

tion methods was studied using Monte Carlo particle gun protons. In Fig. 6.26

the distribution of energies for protons selected by the analysis and the efficiency

for selecting them at each energy from the particle gun study are plotted. Below

150 MeV few protons are reconstructed because the energy deposit is so low in

the detector that it is vetoed as a noise signal.

The effect of incorrect proton identification is greatest near the reconstruction

threshold, at 150 MeV, and in the high energy tail. For the energy threshold, a

20% variation in the proton detection efficiency was considered plausible due to

the high discrepancy between the noise rate in data and Monte Carlo. In the high

energy tail 20% was considered plausible due to consensus from NIWG studies of

the CCQE cross section as a function of Q2. As was previously discussed, there

currently exist discrepancies between data and Monte Carlo that are large enough

to justify the 20% uncertainty.

159

7 Sidebands, Final Analysis and

Results

All analyses and sidebands that will be discussed use the full Run I and Run II

data in which the P0D was filled with water. Only data passing quality checks in

the P0D are used, ultimately amounting to 8.6×1019 p.o.t. divided between Run I

and Run II as shown in Table 7.1. In Table 7.2 the subrun and run identification

for the data is given. All data comes from P0D Production 4B with corrections

specified previously for known saturation mis-modelling.

p.o.t. / 1019

Run I Run II

Data 2.9 5.7

MC 49.9 109.9

Table 7.1: p.o.t. used in data and Monte Carlo, by run period. The Run I and Run II

MCs differ by detector geometry (the latter includes with the full ECal installed between

the P0D and the magnet), and by simulated beam intensity and number of bunches.

Each MC sample is scaled to the relevant data sample, and summed after scaling.

Before looking at the effects of the full set of cuts on data and Monte Carlo,

sidebands are created from events failing the width and pT cut. These sidebands

are used to estimate the effectiveness of the cuts and the validity of the systemat-

160

ND280 Run Number Date

Start End Start End

Run I 4165 5115 2010-03-18 2010-06-25

Run II 6462 7663 2010-11-18 2011-02-14

Table 7.2: ND280 run numbers and dates for the data sample used for this analysis.

ics. Because these cuts predominately eliminate background from specific particle

interactions, muons in the case of the width and π0 for pT , they can be used to

constrain the backgrounds in the νe analyses.

Two separate νe analyses were performed. The first is done as a crosscheck

on the νe flux to assure that the beam modeling was reasonable for the 2011

oscillation analysis. In the second, the νe CCQE-like signal is compared for data

and Monte Carlo as a function of Q2.

The two analyses use two different sets of flux weights. Flux weights were

described in Chapter 6, and the relevant weights for these analyses are called the

“11av1” and “11av2” weights. The primary difference between the two is that the

11av1 weights do not include kaon tuning, which was added in 11av2.

The analysis that uses the 11av1 weights was done as a crosscheck for the

νe oscillation analysis and uses the flux weights from the TPC measurement of

the νµ flux. Therefore the TPC measurement, the oscillation measurement and

the νe crosscheck are all consistent. In the second analysis the 11av2 weights are

used, since it is a stand alone analysis and the kaon tuning decreases the flux

uncertainties.

For a better understanding of the relative size of the systematic effects, the

fractional uncertainty in the number of selected signal and background MC events

for the rate analysis are shown in Table 7.3. From the table it is clear that the

largest systematic errors come from the cross section and energy scale uncertain-

161

Systematic Uncertainty Signal (%) Background (%)

EM Scale 7 16

Cross Sections 0 25

Rate Normalization 6 6

Fiducial Volume 2 2

Muon Rejection 0 4

MC statistics 3 4

Mass uncertainty 1 1

Total 10 31

Table 7.3: The fractional uncertainty in total number of selected signal and background

MC events for each systematic. The total is a sum in quadrature of all errors. Errors

with the same value, and the EM scale, are 100% correlated. (This is taken into account

in the final result.)

ties. The uncertainty on the background is especially useful for understanding the

size of reasonable variations in the sideband studies.

7.1 Sidebands

The largest backgrounds for the νe analysis are from events with muons and

neutral pions. Because the beam is primarily νµ, muons are produced far more

frequently than the electrons that are the expected signal. Even if 99% of the

muons are eliminated, the number of muon events remaining in the sample will

still far outnumber the νe events. The muon background is dramatically reduced

by the existing cuts, but is most dramatically targeted by the width cut.

Therefore an “anti-width” cut is done as a sideband. In Fig. 7.1 it is shown

that events that fail the width cut are predominately muon events with no as-

sociated neutral pion. Flux weights, along with the FV mass and tracker result

162

(GeV)νReconstructed E1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

# of

Eve

nts

1

10

210Signal

0π w/ µ0π no µ0π, µno

0π no µno Out of P0DData

Figure 7.1: Data and Monte Carlo comparison for events that fail the width cut but

pass all other cuts (the range covers events below the Eν threshold, but this is marked

in blue at 1.5 GeV).

MC scaling factors are applied, but muon rejection scaling is not applied, since

it applies only to events passing the width cut, while this sample contains events

which fail the cut. An example of an event that fails the width cut, likely a muon,

is shown in Fig. 7.2.

In the analysis region, to the right of the blue line in the figure, the data and

Monte Carlo agree well. Below this line the agreement is visibly worse. Above 1.5

GeV the Monte Carlo predicts 26 events predicted and data predicts 23 events for

a 0.6σ difference (with statistical errors only). Between 1 and 1.5GeV the most

significant discrepancy occurs, where there are 330 data events with a prediction

of 365 events. This still gives a difference of 10%, which is within the background

systematic errors of 25%. Overall there are 13844 data events with a prediction

of 14340, an agreement at the 4% level.

Neutral pions are not produced at as high a rate as muons. However the

two photons that are produced from neutral pion decay produce electromagnetic

showers similar to those of the electron. If one of the photons is too low energy

163

-300 -250 -200 -150 -100

-100

-50

0

50

100

Top (X-Z)

-300 -250 -200 -150 -100

-100

-50

0

50

100

Side (Y-Z)

Figure 7.2: An example of an event (Run 4542, event 44384) failing the “Median

Width” cut. Boxes indicate detector hits, with size proportional to hit charge. Hits

not associated with any reconstruction object are drawn in black, and those associated

with a track are drawn in red. The red line indicates the reconstructed track position

at each layer as found by the Kalman filter, and the cross indicates the reconstructed

vertex position with an ellipse indicating its uncertainty.

-300 -250 -200 -150 -100

-100

-50

0

50

100

Top (X-Z)

-300 -250 -200 -150 -100

-100

-50

0

50

100

Side (Y-Z)

Figure 7.3: An example of an event (Run 4408, event 18642) failing the pT cut. See

Figure 7.2 for details of the display. Each track is drawn in a different color.

to be detected or if the two photons overlap then the problem is especially bad.

Ideally the neutral pion background would be measured in the P0D and provide

164

(GeV)νReconstructed E1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

# of

Eve

nts

0

20

40

60

80

100

Signal0π w/ µ0π no µ0π, µno

0π no µno Out of P0DData

Figure 7.4: Data and Monte Carlo comparison for events that fail the pT cut but pass

all other cuts (the range covers events below the Eν threshold, but this is marked in

blue at 1.5 GeV). Flux weights and the MC scaling factors are applied. The highest bin

is an overflow.

some constraints for this effect. However, when the analyses were done neutral

pion production in the P0D had not been measured. The “anti-pT” sideband

predominately selects events containing a neutral pion, either with or without a

muon. An example of an event rejected by this cut is shown in Fig. 7.3. In Fig.

7.4 it is shown that there is good agreement between data and Monte Carlo for

this sideband. Above 1.5 GeV 363 events are predicted by the MC compared with

376 events in data, for a difference of 0.7σ [?].

7.2 Final Analyses and Results

7.2.1 Rate Analysis

The purpose of the first analysis is to constrain the νe background in the T2K

neutrino beam above 1.5 GeV. Cutting above 1.5 GeV serves two purposes. The

first is that the current P0D reconstruction and cut methods produce the cleanest

165

True neutrino energy (GeV)0 1 2 3 4 5 6

Effi

cie

ncy

(%

)

0

5

10

15

20

25

30

35

νAll Reco E

>1.5 GeVνReco E

Reconstructed neutrino energy (GeV)0 1 2 3 4 5 6

Pur

ity (

%)

0

10

20

30

40

50

60

70

80

90

Figure 7.5: Efficiency (left) and purity (right) as a function of neutrino energy. The er-

ror bars shown are from MC statistics. Efficiency is shown as a function of true neutrino

energy (since unreconstructed events included in the denominator do not have a recon-

structed energy) both with and without the Eν > 1.5 GeV cut applied in reconstructed

neutrino energy.

sample of electron neutrino events in this energy range.

This is also the region where νe from kaon decay are most likely to be found.

Kaon decay was a major source of uncertainty in the 2010a oscillation analysis

because kaon data from NA61 had not yet been used to tune the beam Monte

Carlo.

Applying all of the previously described cuts in Monte Carlo gives Nsel =

114.9 ± 2.7 (stat) selected events. N selνe = 75.0 ± 2.2 (stat) of those events are

Signal (CC νe). The total number of predicted CC νe interactions in the P0D

fiducial volume with Eν > 1.5 GeV in MC is Nνe = 621 ± 8. From this the

efficiency, ǫ, and purity, p, is calculated as follows

ǫ =N sel

νe

Nνe

= (12.1± 0.4 (stat))% (7.1)

p =N sel

νe

Nsel

= (65± 2 (stat))%, (7.2)

where the error shown is statistical.

166

The efficiency and purity as functions of energy are shown in Figure 7.5. At

lower energies the efficiency is lower because the width cut eliminates many elec-

tron tracks that do not have sufficient energy to produce wide showers. This

reinforces the previous statement that the efficiency of this analysis is best for

events with energy greater than 1.5 GeV.

Event Type NEUT Reaction Codes Background (%) Signal (%)

CC NC

Elastic ±1,51,52 0.8 0.2 60.8

1 π± ±11,13,33,34 4.6 1.2 23.1

1 π0 ±12,31,32 2.7 8.7 5.0

Coherent π ±16,36 1.6 10.9 3.4

Multi π ±21,41 5.1 3.6 6.2

Other Resonant ±22,23,42,43,43,45 0.7 1.0 0.6

DIS ±26,46 30.0 27.0 0.8

Outside P0D n/a 0.6 1.4 0.0

Table 7.4: Signal and background breakdown by interaction type, as predicted

by the NEUT MC (See http://www.hep.lancs.ac.uk/nd280Doc/nd280mc/v4r42/-

classND280NeutKinematicsGenerator.html for a complete list of reaction codes.).

The background percentages are relative to the total predicted background, and the

signal percentages relative to the total predicted signal.

The dominant background after all cuts (75%) are events that contain a π0.

Table 7.4 shows the selected backgrounds broken down by interaction type, with

the main contributions coming from νµ-induced deep inelastic scattering events

and from νµ-induced NC coherent and resonant π0 production.

About 61% of the selected signal CC νe was found to be quasi-elastic. This is

taken as confirmation of the reasonable use of quasi-elastic kinematics in recon-

structing the neutrino energy. The comparison between true neutrino energy and

167

(GeV)νTrue E0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

(G

eV)

νR

econ

stru

cted

E

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Figure 7.6: Comparison between true and reconstructed neutrino energy.

-300 -250 -200 -150 -100

-100

-50

0

50

100

Top (X-Z)

-300 -250 -200 -150 -100

-100

-50

0

50

100

Side (Y-Z)

Figure 7.7: One of the 129 signal events (Run 4477, event 2453) selected from the

Run I and Run II data. See Figure 7.2 for details of the display.

the quasi-elastic approximation is shown in Fig. 7.6. Each column is normalized

to one, so the figure shows the smearing due to the reconstruction. All cuts have

been applied, except for the reconstructed neutrino energy cut, which is marked

in blue. Note that compared to the energy completeness from events with a single

3D track in Chapter 5, the tail at low reconstructed energy has been largely re-

moved by the pT cut removing events with secondary vertices far from the primary

vertex containing large amounts of energy. The red line marks Ereco = Etrue. The

last row and column are overflows.

168

Systematic shift R′ −Rnom

+ 1σ − 1σ

EM Scale −0.13 0.21

Cross Sections −0.13 0.13

Rate Normalization −0.10 0.11

Fiducial Volume −0.03 0.04

Muon Rejection −0.03 0.02

Monte Carlo Statistics −0.04 0.04

Proton Reconstruction −0.07 0.07

Total 0.26

Table 7.5: Contribution to the systematic uncertainty on R in the first analysis from

each source. R′ is the value of R calculated with the ±1σ systematic shift applied, and

Rnom is the nominal value of R. The method used to compute the total systematic shift

is described in the text.

169

19Accumulated pot / 100 1 2 3 4 5 6 7 8

Sel

ecte

d ev

ents

0

20

40

60

80

100

120

Figure 7.8: Cumulative number of selected events as a function of total p.o.t. collected.

The data distribution is shown in black, with the expected distribution for a constant

rate of events/p.o.t. in red.

(GeV)νReconstructed E1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

# of

Eve

nts

0

5

10

15

20

25

30

35

40

45 Signal0π w/ µ 0π no µ0π, µno

0π no µno Out of P0DData

Figure 7.9: Reconstructed neutrino energy distribution of events passing all cuts. All

MC scaling factors are applied, along with the flux weights. The last bin is an overflow.

In data, after all selection cuts are applied 129 events were selected. An

example of a selected event is shown in Fig. 7.7. Fig. 7.8 shows the event rate

compared to the number of protons on target in data. Using a Kolmogorov-

Smirnov test returns a distance of 0.05, for a p-value of 0.86, indicating that the

rate of events is constant as is expected. Finally, the general agreement between

170

Data and Monte Carlo within statistical errors is shown in Fig. 7.9.

We form a ratio, R, that should be one if data and Monte Carlo simulation

agree. R is defined as

R =D − B

S= 1.19± 0.15(stat)± 0.26(syst), (7.3)

where D is the number of data events, and S and B are the numbers of signal

and background events predicted by the Monte Carlo, respectively. Within the

statistical and systematic errors this result agrees with one. The total effects

of the previously described systematics on R are given in Table 7.5. The errors

are assumed to be uncorrelated and therefore summed in quadrature. With no

significant excess no evidence is found from this measurement of mis-modelling of

the kaon decay produced νe background.

7.2.2 Q2 Analysis

The purpose of the Q2 analysis is to use the improved beam systematics to make

an estimate of the CCQE-like component of the selected events as a function of

Q2. CCQE cross sections are often used to normalize other reactions, and are

therefore very important to understand. For muon neutrinos the CCQE cross

section is well measured but for electron neutrinos currently it is not.

The CCQE-like sample contains all events that have the same final state as

a CCQE event. From particle gun Monte Carlo it was shown that charged pions

with energy less than 50 MeV cannot be identified in the P0D. Therefore the

definition of CCQE-like is taken to be a CC νe event with no mesons except for

charged pions with energy less than 50 MeV, and no baryons besides protons and

neutrons.

Utilizing the updated flux tuning alters the composition of the signal and back-

ground reactions. Changing the definition of signal to be CCQE-like also increases

171

the background in categories like single charged pion, since νe interactions con-

taining a pion are no longer considered signal. The composition of the selected

events in Monte Carlo after all these changes is shown in Table 7.6.

Event Type NEUT Reaction Codes Background (%) Signal (%)

CC NC

Elastic ±1,51,52 1.9 0.1 76.3

1 π± ±11,13,33,34 17.1 0.9 17.5

1 π0 ±12,31,32 4.8 6.4 3.3

Coherent ±16,36 5.4 8.1 0.3

Multi π ±21,41 9.1 2.5 2.3

Other Resonant ±22,23,42,43,43,45 1.1 1.0 0.3

DIS ±26,46 21.9 18.7 0.0

Outside P0D NA 0.2 0.1 0.0

Table 7.6: Signal and background breakdown by interaction type for the second anal-

ysis. The conventions are the same as Table 7.4.

With this new definition of signal and all of the previously described cuts, as

well as the effects of using the updated flux tuning, Nsel = 130.7 ± 2.9 (stat)

selected events are found with N selνe = 66.4 ± 2.0 (stat) of those identified as

CCQE-like signal. The total number of selected events in data is unchanged by

the change in the flux tuning or the signal definition. Therefore, the new ratio

RQE is found to be

RQE =D − B

S= 0.97± 0.17(stat)± 0.40(syst), (7.4)

This ratio agrees with 1 within the uncertainties. The calculated value of the

systematic error on RQE from all sources is shown in Table 7.7. In Fig. 7.10

the Q2 distribution of signal and background events in data and Monte Carlo is

shown.

172

Systematic shift R′QE −RQEnom

+ 1σ − 1σ

EM Scale −0.14 0.25

Cross Sections −0.24 0.24

Rate Normalization −0.19 0.24

Fiducial Volume −0.04 0.04

Muon Rejection −0.04 0.02

Monte Carlo Statistics −0.04 0.04

Proton Reconstruction −0.09 0.09

Total 0.40

Table 7.7: Contribution to the systematic uncertainty on RQE in the second analysis

from each source. All conventions agree with Table 7.5.

)2 (GeV2Reconstructed Q0 0.2 0.4 0.6 0.8 1 1.2 1.4

# of

Eve

nts

0

5

10

15

20

25

30 SignalCCNuE0π w/ µ

0π no µ0π, µno

0π no µno Out of P0DData

Figure 7.10: Reconstructed neutrino distribution in Q2 of events passing all cuts.

Another distribution that is interesting to consider is the signal compared with

the background subtracted data as shown in Fig. 7.11. Previous analyses have

found discrepancies in this distribution for muon neutrinos [?]. This discrepancy

was attributed to possible mis-modeling in the Fermi Gas model. Visually a similar

discrepancy seems to exist, but within the current large errors no conclusions can

173

)2 (GeV2Reconstructed Q0 0.2 0.4 0.6 0.8 1 1.2 1.4

# of

Eve

nts

0

2

4

6

8

10

12

14

16

18

Signal

Data

Figure 7.11: Reconstructed distribution of CCQE-like events passing all cuts compared

to background subtracted data. The last bin is an overflow.

be drawn.