Extraction of Neutrino Flux from Inclusive Neutrino-Nucleus Reaction

1. Extraction of Neutrino Flux from Inclusive Neutrino-Nucleus Reaction Osaka Univ. Tomoya Murata, Toru Sato

2. 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

3. １．Introduction Neutrino Oscillation The neutrino flavor changes during propagating Flavoreigen states are expressed by linear combination of masseigen states Flavor eigen state Mass eigen state PDG 2013 Mass hierarchy problem CP symmetry breaking in lepton sector

4. Determination of Neutrino Mixing Parameter Ex.) Oscillation probability in two flavor model We must know the absolute value and the energy dependence of Neutrino Flux p n Conventional method to determine the flux Quasi Elastic reaction reconstruct the neutrino energy by energy momentum conservation law

5. Flux averaged cross section We can observe only the flux averaged cross section. Neutrino-nucleus charged current reaction cross section T2K PRD87,012001(2013) Neutrino Flux

6. Various reaction mechanisms Reaction mechanisms at QE region QE with FSI violates the above simple relation If pion or nucleon cannot be observed, they are misidentified as QE abs. MEC FSI We need to reconstruct the neutrino flux without using‘ideal’QE.

7. The Objective Without assuming QE, using only information of inclusive cross section, canwereconstruct the neutrino flux? Inclusive cross section of muon production observable Flux averaged distribution of muon energy and scattering angle Neutrino Flux Reconstruct the Neutrino Flux by using Maximum Entropy Method

8. 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 fluxso that minimize this quantity the prior information of the flux. (default model) ,

9. ３．Cross Section of Neutrino Nucleus Reaction =3GeV =2GeV =4GeV =5GeV =1GeV Quasi-Elastic Pion production B.Szczerbinska , T.Sato , K.Kubodera , T.-S.H.Lee PLB649 132 T.Sato , D.Uno , T.-S.H.Lee PRC67 065201 dynamical model

10. ４．’Data’ofmuon energy distribution (flux detected at Near Detector of T2K) (Oscillation probability of two flavor approximation) error ＝７％ Gaussian distribution Resolution of muon energy 100MeV

11. ５．Result reconstruct the neutrino flux from‘data’ by MEM MEM

12. Reconstructed Neutrino Flux (=10°) ‘data’of muon distribution Reconstructed Neutrino Flux MEM Flux was reconstructed successfully.

13. Dependence of Default Model (=10°) Original Flux Reconstructed Flux by MEM Default Model Default Model | | The prior information of the flux Original Flux Constant Without oscillation Dependence of default model is not much. We use the model of without oscillation.

14. Change the error sizes (=10°) ‘data’of muon distribution MEM Reconstructed Neutrino Flux

15. ６．Summary • We 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

16. Future Works • Construction of the accurate model of neutrino nucleus reaction • Studyappearance reaction.() • Examine the method for the deep inelastic scattering region. Thank You .