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

4. Determination of Neutrino Mixing Parameter Quasi Elastic reaction p n 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

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

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

7. The Objective Reconstruct the Neutrino Flux by using Maximum Entropy Method observable Flux 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?

8. ２． Maximum Entropy Method (MEM) the prior information of the flux. (default model)

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

10. ４． ’Data’of muon energy distribution Resolution of muon energy 100MeV

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

12. MEM ‘data’of muon distribution Reconstructed Neutrino Flux Flux was reconstructed successfully.

13. Original Flux Reconstructed Flux by MEM Default 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

14. MEM ‘data’of muon distribution 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 Thank You.