Extraction of Neutrino Flux from

Inclusive Neutrino-Nucleus Reaction

Osaka Univ.Tomoya Murata, Toru Sato

contents

１． Introduction２． Maximum Entropy Method(MEM)３． Cross Section of Neutrino Nucleus Reaction４．’ Data’ of muon energy distribution５． Results６． Summary

１． Introduction

Flavoreigen state

Masseigen state

PDG 2013

𝑚3>𝑚1 ,𝑚2>𝑚3? ?

CP symmetry breaking in lepton sector Mass hierarchy problem

(𝜈𝑒𝜈𝜇

𝜈𝜏)=( 𝑐12𝑐13 𝑠12𝑐13 𝑠13𝑒−𝑖 𝛿

−𝑠12𝑐23−𝑐12𝑠23 𝑠13𝑒− 𝑖𝛿 𝑐12𝑐23−𝑠12 𝑠23𝑠13𝑒

𝑖𝛿 𝑠23𝑐13𝑠12 𝑠23−𝑐12𝑐23𝑠13𝑒

𝑖𝛿 −𝑐12𝑠23−𝑠12𝑐23 𝑠13𝑒𝑖𝛿 𝑐23𝑐13

)(𝜈1𝜈2𝜈3)Flavor eigen states are expressed by linear combination of mass eigen states

𝜈𝜇 𝜈𝜏

The neutrino flavor changes during propagating

Neutrino Oscillation

Determination of Neutrino Mixing Parameter

Quasi Elastic reaction

𝜈𝜇𝜇−

𝜈𝜇𝜇−

pn

reconstruct the neutrino energy by energy momentum conservation law

Ex.) Oscillation probability in two flavor model

We must know the absolute value and the energy dependence of Neutrino Flux

Conventional method to determine the flux

Flux averaged cross section

Neutrino Flux

Neutrino-nucleus charged current reaction cross section

We can observe only the flux averaged cross section.

T2KPRD87,012001(2013)

𝑑2𝜎

𝑑Ω

𝜇𝑑𝐸

𝜇

𝐸𝜈=600𝑀𝑒𝑉𝐸𝜈=780𝑀𝑒𝑉𝐸𝜈=940𝑀𝑒𝑉𝐸𝜈=1140𝑀𝑒𝑉

Various reaction mechanisms

Reaction mechanisms at QE region

𝐸𝜈 (𝐸𝜇 ,𝜃𝜇)=𝐸𝜇−𝑚𝜇

2 / (2𝑀 )1−(𝐸𝜇−𝑃𝜇cos𝜃𝜇) /𝑀

QE with FSI violates the above simple relation

FSI MEC abs.

If pion or nucleon cannot be observed, they are misidentified as QE

We need to reconstruct the neutrino fluxwithout using‘ideal’QE .

𝜇𝑝

𝜋 𝑁

The Objective

Reconstruct the Neutrino Flux by using Maximum Entropy Method

observableFlux averaged distribution of muon energy and scattering

angle

Inclusive cross section of muon production Neutrino

Flux

Without assuming QE, using only information of inclusive cross section, can we reconstruct the neutrino flux?

２． Maximum Entropy Method (MEM)Maximize the probability → Neutrino Flux

・ : experimental data 、 prior information of flux , the probability of having .

・ experimantel data : ( , ) ・・・ energy and scattering angle distribution of muon

・ prior information of flux : () ・・・ guess of neutrino flux

find the flux so that minimize this quantity

the prior information of the flux.(default model)

𝑃 [Φ|𝐺 , 𝐼 ]∝ exp[−( 12 𝜒2−𝛼𝑆)] ,

３． Cross Section of Neutrino Nucleus Reaction

=1GeV

=2GeV =3GeV=4GeV

=5GeV

Pion production

Quasi-Elastic

dynamical model

𝜈𝜇𝜇−

B.Szczerbinska , T.Sato , K.Kubodera , T.-S.H.Lee PLB649 132T.Sato , D.Uno , T.-

S.H.LeePRC67 065201

𝜈𝜇

𝜇−𝜋

𝜈𝜇+ 𝐶❑12 →𝜇−+𝑋

𝑑𝜎𝑑Ω𝜇𝑑𝐸𝜇

(𝜃¿¿𝜇=10∘)¿

𝑑2𝜎𝑑Ω𝜇𝑑 𝐸𝜇

４．’ Data’of muon energy distribution

error＝７％

Gaussian distribution

Resolution of muon energy100MeV

(flux detected at Near Detector of T2K)

(Oscillation probability of two flavor approximation)

MEM

５． Result

reconstruct the neutrino flux from‘data’ by MEM

MEM

Reconstructed Neutrino Flux (=10°)‘data’ofmuon

distributionReconstructed Neutrino Flux

Flux was reconstructed successfully.

Dependence of Default Model (=10°)Original FluxReconstructed Flux by MEMDefault Model

Original Flux Without oscillation

Constant

Dependence of default model is not much.We use the model of without oscillation.

Default Model| |

The prior information of the flux

Change the error sizes (=10°)

MEM

¿Φ>¿ 42.3±2.0 ¿Φ>¿ 43.5±2.9

‘data’ofmuon

distribution

ReconstructedNeutrino Flux

６． SummaryWe proposed a method of reconstruction the neutrino

flux from muon distribution in inclusive neutrino nucleus charged current reaction.

We regarded the reconstruction problem as the Inverse problem and use maximum entropy method.

reconstruct neutrino flux without assuming CCQE.

The neutrino flux was successfully reconstructed.

MEM

Future Works

• Construction of the accurate model of neutrino nucleus reaction

• Study appearance reaction.()

• Examine the method for the deep inelastic scattering region.

Thank You .