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Extraction of Neutrino Flux from Inclusive Neutrino-Nucleus Reaction. Osaka Univ. Tomoya Murata, Toru Sato. contents. 1. Introduction 2. Maximum Entropy Method(MEM) 3. Cross Section of Neutrino Nucleus Reaction 4. ’Data’ of muon energy distribution 5. Results 6. Summary. - PowerPoint PPT Presentation
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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 .