23/04/181

How to Extrapolate a Neutrino Spectrum to a Far

Detector

Alfons Weber (Oxford/RAL)

NF International Scoping Study, RAL 27th April 2006

23/04/18

2

Overview

• Introduction– How to measure neutrino oscillation

parameters

• The Problem– Cross Section– Neutrino Flux– Reconstruction

• Different Solutions– Dead Reckoning– Near Detector fits– Near over Far ratios– Matrix

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3

Disclaimer

• What will be presented in this talk are

NOT MINOS RESULTS or METHODS!

• I present my private views on how different methods can be used to estimate a far detector energy spectrum given a near detector measurement.

• However, these methods have been investigated, discussed and used within the MINOS experiment.

• I present my best understanding of them and their differences.

• None of this is my work!

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4

Look for a deficit of νμ events at Far Detector

Unoscillated

Oscillated

νμ spectrum

Monte Carlo

Monte Carlo

ν ν 22

21 ssin inm L

PE

θΔ

μ μ

Spectrum ratio

MINOS Methodology

The Million $ Question: How to predict the Far Detector spectrum?

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Producing the Neutrino Beam

• 9μs spill of 120GeV protons every 2s• 0.2 MW average beam power• 20 1012 protons per pulse (ppp)

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The Neutrino Beam Spectrum

LE

pME

pHE

• How well do we know it this spectra?– neutrino flux depends on hadron production– neutrino cross section

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Problem 1:Hadron Production Uncertainties

Atherton400 GeV Be

Barton100 GeV C

Spy450 GeV Be

• Hadron production not well known!– 120 GeV proton beam – thick thick graphite target

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Problem 2:Cross Sections

• World knowledge on cross sections is limited– few measurements– theoretical

uncertainties

• Needs good beam prediction to make measurement

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LE-10 pME pHE

LE-10 pME pHE

Error envelopes shown on the plots reflect uncertainties due to cross-section modeling, beam modeling and calibration uncertainties

Reconstructed Energy (GeV)

Ratios of Data/MC

Dead Reckoning

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How to use this data

• Dead reckoning not good enough• We want to understand differences

• Two Steps1. Measure ND spectrum2. Extrapolate to Far Detector

• the ultimate goal

• Different methods can do this– NDFit– 2DGrid– N/F Ratio– Matrix

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Extrapolate to Far Detector

• Near and Far Detector energy spectra are not identical– Both detectors cover different solid angles– Near Detector sees extended line source

• Just kinematics

f

to FarDetector

Decay Pipe

(soft)

(stiff)

n

target

ND

2

2 2 2

1 11

FluxL γ θ

2 2

0.431

EE πν

γ θ

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NDFit Method

• Use un-tuned MC• Determine weights as a function of

– xf and pT of parent hadron, which generated the neutrino

– neutrino energy• Result

– modified Near Detector MC• Apply weight to Far Detector MC event

Far Detector energy spectrum• Contains

– improved hadron production model– Can treat cross section uncertainties the same way

• different beam setting help to untangle effects

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Re-weighting Function

• Parameterize hadrons distribution coming out of target

• with

• change cross section parameters– ma, mares, dis,...– uses generator

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Agreement between data and Fluka05 Beam MC is pretty good, but by tuning the MC by fitting to hadronic xF and pT, improved agreement can be obtained.

LE-10/185kA

pME/200kA

pHE/200kA

Weights applied as a function of hadronic xF and pT.

LE-10/Horns off

LE-10 eventsNot used in the fit

Result of Fit

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NDFit Method (II)

• Improved description of Near Detector energy spectrum

• Advantage – Very flexible, can be used to improve

• hadron production distributions (++)• cross sections (++)• horn currents distribution (++)• ...

• Disadvantage– Only works, if changes can be parameterised.

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2D Grid Method

• Bin data in reconstructed – Eν & y

• Fit weight as a function of true– Eν & y

• Corrects for un-modelled effects– cross section (+++)– Hadron production (++)– Reconstruction (+)

• Apply weight to Far Detector MC events

• Result– Far Detector Energy spectrum

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N/F Ratio

• Look at differences between data and MC in Near Detector as a function of reconstructed Energy

• Apply correction factor to each bin of re-constructed energy toFar Detector MC– c = ndata / nMC

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N/F Ratio (II)

• Predicts the right spectrum in the FD almost independently, whether the distortion was generated by– beam flux diff.– cross section diff– reconstruction diff.

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The Beam Matrix Method

• This method does not re-weight MC events• It uses the measure Near Detector distribution

and extrapolates it using a

BEAM Matrix

to the Far Detector.

• Can be used on original or wrong/bad MC

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Beam transport matrix

step A)

step B)

step C)

The Beam Matrix Method

• NC background subtraction• correct for selection efficiency and purity• correct for detector response

measured E (ND) true E (ND)

Maps true E from ND to FD using

• pion decay kinematics• beamline geometry

true E (FD) predicted visible E (FD)

• add detector response • efficiency• background• oscillations

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)()( binNCtrueCCtrue

CCtruebinPurity

)()( binCCall

CCtruebinEfficiency

1

2

Correction for purity

Step A, Beam Matrix Method

Reconstructed =>True and Correction for efficiency

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• Beam Matrix encapsulates the knowledge of pion 2-body decay kinematics & geometry.

• Beam Matrix provides a very good representation of how the Far Detector spectrum relates to the near one.

Beam Matrix Method : Near to Far extrapolation

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Predicted true FD spectrum

• higher than nominal FD MC in high energy tail

• expected, given that the ND visible energy spectrum is also higher than the nominal MC in this region

Predicted spectrum

Nominal MC

0.931020 POT

Predicted FD true spectrum from the Matrix

Method

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The Beam Matrix Method (II)

• Robust method to predict the FD spectrum

• Uses Near Detector data and hadron decay kinematics to predict FD spectrum

• Advantages– robust

• Disadvantages– implicitly assumes that all differences are due to

neutrino flux

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• 4 methods predict identical FD energy spectrum– NDfit– 2D Grid– F/N ratio– matrix

• Systematic error propagate differently

Predicted FD unoscillated spectra

Comparison of the Methods

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Summary

• NDFit method – Treats

• hadron prod. (+++)• cross section (+++)

• beam focus (++)

– Caveat• needs parameterisation

of effect (--)

• 2D Grid– Treats

• cross section (+++)• reconstruction (++)• beam/hadron

production (+)

• N/F Ration– Treats

• Reconstruction (+++)• cross section (++)• beam/hadron

production (+)

• Matrix– Treats

• beam/hadron production (+++)

• cross section (++) Reconstruction (+)

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Conclusions

• Near Detector is essential for oscillation analysis– hadron production / neutrino spectrum– cross section– reconstruction– only inclusive measurements can be done

• Conceptually different methods give same results– but all need a Near Detector

• Difficult to get a two detector experiment wrong