September 10, 2002

M. Fechner 1

Energy reconstruction in quasielastic events unfolding physics and detector effects

M. Fechner, Ecole Normale Supérieure

In collaboration with M. Campanelli

Supervised by A. Blondel

September 10, 2002

M. Fechner 2

Introduction • Study of low energy Super Beam + water Cherenkov detector •Quasi elastic events are dominant (< 1 GeV) and easier to reconstruct than DIS •But they require taking into account detector efficiency and nuclear physics effects (Fermi motion, Pauli blocking)• Most previous studies rely on counting the number of oscillated events

General unfolding method based on the Monte Carlo re weighting technique in order to recover spectral information

September 10, 2002

M. Fechner 3

Neutrino energy reconstruction

CC quasi elastic interactions: only the lepton can be observed (proton

below Cherenkov threshold) For a target nucleon at rest, neutrino

energy can be exactly reconstructed from lepton information only

pn

llln

lnpln

PEm

mmmEm

E cos

2

222

But in the presence of nuclear effects this does not work anymore

September 10, 2002

M. Fechner 4

Fast Monte Carlo simulation

Two body kinematics Center of mass lepton angle

distribution given by in Gaisser et al. (1986) Fermi momentum kF=225 MeV/c (nucleon momentum isotropic in

sphere of radius kF)

n p

kF

September 10, 2002

M. Fechner 5

Fast Monte Carlo simulation

Pauli blocking: outgoing proton momentum p > kF

Nuclear potential well: Standard SPL+UNO event rates

considered (baseline 130 km i.e. CERN->Fréjus). Detector resolution (from SuperK):

MeV 50 EE

• Angular resolution: ~3° (for e and )• Momentum resolution: (E)/E~3% (Ee)/Ee~ %5.0

E(GeV)%5.2

Energy reconstruction

Using the above formula for e and at low energy (< 1.5 GeV)

Ege

n

E rec

onst

ruct

e

d

e Perfectdetection

Detector resolutiononly

Nuclear effects only

All effects included

6

Results of the MC simulation

20% average resolution, 5% negative bias

Erec-Egen Resolution

e e

7

September 10, 2002

M. Fechner 8

Need for an unfolding method

disappearance

Using true energy

Using reconstructed energy

Oscillation dip invisible

Large water Cherenkov illuminated by SPL->Fréjus superbeam200 kTyear exposure

September 10, 2002

M. Fechner 9

Fitting for oscillation parameters in presence of distorting effects

• Classical problem in HEP Solution: Monte Carlo reweighting (used previously e.g. at LEP for W mass fits)• Principle: Production of a large MC correspondence table between the real quantity (E

gen ) and the measured one (Erec )

and approximate each data event with the MC events sufficientlyclose to it• Since only one MC sample is produced, using a given set ofoscillation parameters, events are given a weight according tothe ratio of oscillation probabilities

),(),(),(

0 ENENE

),(.)(),(.)(),(

),(.)(),(.)(),(

EPEEEPEEEN

EPEEEPEEEN

eeeee

ee

September 10, 2002

M. Fechner 10

The box method 2 sets of data: ‘experimental’ sample (uses SPL spectra) MC sample For each data event: box around

measured value. All MC events inside the box are good approximations of the data and used in the likelihood

Box reweighting at workReconstructed distribution

MC events in the box

reconstructed

generated

Data event

Image of the box

weights

MC correspondence table

September 10, 2002

M. Fechner 12

Likelihood functionLikelihood function with 2 factors, one from the spectral shape (i.e. box method) and the other describing the Poisson probabilityfor the number of events

)())(log(

);(1)(log);(1log)(log

expectedexpected

10expected

1 1

NNN

iN

NiV

L

DATA

N

i MC

N

j

N

ij

MCDATA j

Where is the weight and is the oscillation param. set

Counting Spectral shape (box method)

September 10, 2002

M. Fechner 13

Comments on the results We have used binned data (20 MeV

wide bins): sum over bins rather than events

MC sample ~500 times larger than ‘exp.’ sample

The method is general and not limited to event reconstruction in water Cherenkov detectors

September 10, 2002

M. Fechner 14

Fits to m232

Error ~1%

Good linearity and precisionover the whole relevant range

m12= 0 eV2

sin2223=1, sin2 213=0.05

September 10, 2002

M. Fechner 15

Fitting the atmospheric parameters

2D plots in the plane•‘Counting’ likelihood: large open contours due to correlations•‘Spectral’ likelihood: uses the reweighting method to extract the maximal amount of information from the spectrum

22323

2 ,2sin m

Plots

m23=2.5 10-3

m12=5.44 10-5

tan2 12=0.4

sin2223=0.95

sin2 213=0.02

=0

Using theparameters

Counting Spectral reconstruction

Error on m2 ~ 0.7 10-4 eV2

Error on sin22 ~ 2%

Counting+box

September 10, 2002

M. Fechner 17

Precision on 13

does not modify the energy spectrum (in 1rst approximation) information mostly contained in the number of events, so the reweighting does not improve the measurement of sin2213

sin2213sin2213

m2 23

m2 23

m23=2.5 10-3

m12=5.44 10-5

tan2 12=0.4

sin2223=0.95

sin2 213=0.02

=0

Counting only Counting + box

September 10, 2002

M. Fechner 18

Application to CP-violation• Same oscillation parameters in MC and ‘experience’• With neutrinos only and 200 kTyear, sin2213=0.02,

Need for antineutrinos !

m23=2.5 10-3

m12=5.44 10-5

tan2 12=0.4

sin2223=0.95

Counting onlyCounting+box

September 10, 2002

M. Fechner 20

CP-violation: using antineutrinos

•Neutrinos ‘exp.’ sample : 200 kTyear statistics sin22=0.02, •Antineutrino ‘exp.’sample : 1000 kTyear stats sin22=0.02, •MC sample: 600 times larger than ‘exp.’ with: sin22=0.04,

Likelihood computed with and

m23=2.5 10-3eV2

m12=5.44 10-5eV2

tan2 12=0.4

sin2223=0.95

ee

September 10, 2002

M. Fechner 21

antineutrinos neutrinos

If the box method is not used:

With the reweighting method:

Error on is ~3 times worse

Counting only

~120°

~35°

Counting+Box

Counting+Box

September 10, 2002

M. Fechner 22

Conclusion Spectral information is essential in a Super Beam

experiment Distortion due to detector and nuclear effects is large Necessity of using adequate unfolding technique to

recover spectral information MC reweighting method is very general and can

unfold any effect provided they are described correctly in the MC

Very good precision on main oscillation parameters. Significant improvements in the CP violation sector.