1. Neutrino-induced meson productions off nucleon in the resonance region Satoshi Nakamura Osaka University Collaborators : H. Kamano (RCNP, Osaka Univ.), T. Sato (Osaka Univ.) T.-S.H. Lee (Argonne Nat’l Lab).

2. Contents ★ Introduction  interaction in resonance region  ★ Dynamical coupled-channels (DCC) model for     extended to    ★ Future plan matching with DIS cf. quark-hadron duality 

3. Wide kinematical region with different characteristic  Combination of different expertise is necessary Collaboration at J-PARC Branch of KEK Theory Center http://j-parc-th.kek.jp/html/English/e-index.html LBL -interaction (kinematics & characteristics)

4. Resonance region  2nd 3rd Many nucleon resonances in 2 nd and 3 rd resonance region (MeV) Not only 1  production but also … Multi-channel reaction  2  production is comparable to 1    productions (background of proton decay exp.)

5. Theoretical approach to  -interaction in resonance region PCAC (partially conserved axial current) at Q 2 =0, axial coupling  pion coupling Paschos et al. (2011); Kamano et al. (2012) Microscopic model resonant and non-resonant hadronic interactions Rein et al. (1981), (1987) ; Lalalulich et al. (2005), (2006) ; Hernandez et al. (2007), (2010) ; Lalakulich et al. (2010); Sato et al. (2003), (2005) ; …

6. Microscopic models for induced 1  production Rein et al. (1981), (1987) ; Lalalulich et al. (2005), (2006) Hernandez et al. (2007), (2010) ; Lalakulich et al. (2010) Sato, Lee (2003), (2005) resonant only + non-resonant (tree-level) + rescattering (  N unitarity)

7. ★ Dynamical coupled-channels (DCC) model for      Hadron dynamics & vector current fixed ★ Extension to     Axial form factors fixed to overcome the problems… Dealing with multi-channel reaction We develop Unitary coupled-channel model  Unitarity is missing in previous models  Important 2  production model is missing  Previous models for  and  production are not well tested by data Problems

8. DCC model for    Kamano, Nakamura, Lee, Sato, PRC 88, 035209 (2013)

9. Coupled-channel, 2&3-body unitarity is taken into acount

10. DCC analysis of meson production data Fully combined analysis of    (W ≤ 2.1 GeV) ~380 parameters (N* mass, N*  MB couplings, cutoffs) to fit ~ 20,000 data points Kamano, Nakamura, Lee, Sato, PRC 88 (2013)

11. Partial wave amplitudes of pi N scattering Kamano, Nakamura, Lee, Sato, 2013 Previous model (fitted to  N   N data only) [PRC76 065201 (2007)] Real partImaginary part

12. Kamano, Nakamura, Lee, Sato, 2012 Vector current (Q 2 =0) for 1  Production is well-tested by data

13. Eta production reactions Kamano, Nakamura, Lee, Sato, 2012

14. Kamano, Nakamura, Lee, Sato, 2013 Vector current (Q 2 =0) for  Production is well-tested by data

15. KY production reactions 1732 MeV 1845 MeV 1985 MeV 2031 MeV 1757 MeV 1879 MeV 1966 MeV 2059 MeV 1792 MeV 1879 MeV 1966 MeV 2059 MeV Kamano, Nakamura, Lee, Sato, 2012

16. Kamano, Nakamura, Lee, Sato, 2013 Vector current (Q 2 =0) for  Production is well-tested by data

19. Short Summary  scattering in resonance region is multi-channel reaction Unitary coupled-channels model is ideal DCC model for    is developed Model is extensively tested by    data  reliable vector current to be applied to -scattering

20. Extended DCC model for    1.PCAC-based calculation (Q 2 =0) Kamano, Nakamura, Lee, Sato, PRD 86, 097503 (2012) 2.Dynamical axial current (strategy) 3.Photon emission in NC process (some comments)

21. Objectives  Set a starting point for full dynamical model  Relative importance of different channels  Comparison with Rein-Sehgal model PCAC-based calculation for forward scattering of    Kamano et al., PRD 86, 097503 (2012) Cf. Paschos et al., arXiv:1212.4662

22. Formalism Cross section for   X ( X =  )    Q2Q2 CVC & PCAC LSZ & smoothness Finally    X  is from our DCC model

23. Results SL NN  N  NN   Prediction based on model well tested by data   dominates for W ≤ 1.5 GeV   becomes comparable to  for W ≥ 1.5 GeV  Smaller contribution from  and  Y O (10 -1 ) - O (10 -2 )  Agreement with SL (no PCAC) in  region

24. Comparison with Rein-Sehgal model Lower  peak of RS model  RS overestimate in higher energy regions (DCC model is tested by data) Similar findings by Leitner et al., PoS NUFACT08 (2008) 009 Graczyk et al., Phys.Rev. D77 (2008) 053001 Comparison in whole kinematical region will be done after axial current model is developed

25. Short summary 2 DCC model for forward    via PCAC  Prediction based on model well tested by data   comparable to  for W ≥ 1.5 GeV (first     First    Y based on data Comparison with Rein-Sehgal model :  RS has Lower  peak  RS overestimates cross section at higher energies

26. Full DCC model for    Kamano, Nakamura, Lee, Sato, in progress Vector current Q 2 =0  p    analysis has been done  n    n  analysis is ongoing   isospin separation necessary for calculating -interaction Q 2 ≠0 (electromagnetic form factors for VNN* couplings) obtainable from ( e,e’  data analysis ( will be done soon )

27. Previous analysis of 1  electroproduction data Juliz-Diaz et al., PRC 80, 025207 (2009) Fit to structure functions from CLAS for p (e,e’  p W < 1.6 GeV Q 2 < 1.5 (GeV/c) 2

28. Full DCC model for    Kamano, Nakamura, Lee, Sato, in progress Axial current Q 2 =0 non-resonant mechanisms resonant mechanisms Q 2 ≠0 (axial form factors of ANN* ) experimental information is necessary to fix this A A

29. How to fix axial form factors of ANN* Neutrino data on deuteron from ANL and BNL   d   - NN   N d d N W, Z Elementary amplitude Fermi motion of deuteron Hernandez et al., PRD 81 (2010) d d NN d d   Fermi motion of deuteron + rescattering effects Jiajun and Lee in progress

30. Hernandez et al., PRD 76 (2006); 81 (2010) How to fix axial form factors of ANN* Discrepancy of ANL and BNL data  new deuterium data are highly hoped Neutrino data = 1.00 ± 0.11 = 0.93 ± 0.07 (GeV)

31. How to fix axial form factors of ANN* Neutrino data (BNL) (Adler model)   production The discrepancy persists to higher energy PRD 34, 2554 (1986)

32. How to fix axial form factors of ANN* Neutrino data (BNL) Two-pion production Even the discrepancy, still the most useful information PRD 34, 2554 (1986)

33. Electron data : parity violation asymmetry How to fix axial form factors of ANN* G 0 @JLab, arXiv:1212.1637 −0.05 ± (0.35) stat ± (0.34) sys ± (0.06) th Comparison with theory Theory 

34. Quark-hadron duality : coming back to this later How to fix axial form factors of ANN*

35. Photon emission in NC  Region : Hill (2010), Zhang et al. (2012)  2 nd resonance : Wang et al. (2013) With our DCC model Relevant to T2K and MiniBooNE Photon emission in higher N* region relevant to future experiments ?? Background for e appearance in Cherenkov detector Low-energy e excess in MiniBooNE PRL 98, 231801 (2007) Motivation Recent works

36. Matching with DIS DIS region QE region RES region Atmospheric T2K DIS region QE region RES region Atmospheric T2K Purposes: Make sure smooth transition from RES to DIS (electron scattering) Fix axial form factors of ANN* (neutrino scattering)

37. Matching with DIS DIS region QE region RES region Atmospheric T2K DIS region QE region RES region Atmospheric T2K

38. Matching with DIS In terms of matrix elements of hadronic currents N(e, e’) N(, l’) For CC In terms of parton distribution functions (PDF) For N(e, e’) Matching F i DCC  F i PDF at W ≈ 2 GeV, Q 2 > 1 (GeV/c) 2 (overlapping region)

39. Matching with DIS Make sure smooth transition for electron scattering Some axial form factors of ANN* can be fixed for neutrino scattering Unitarity, coupled-channels are essential for matching only inclusive structure functions can be matched 2  contribution is large

40. Matching with DIS DIS region QE region RES region Atmospheric T2K DIS region QE region RES region Atmospheric T2K low-Q 2 region Model for low-Q 2 region Kulagin and Petti, PRD 76, 094023 (2007) PCAC + extrapolation to finite Q 2 from 0 Bodek and Yang, arXiv:1011.6592 PDF extrapolated to lower Q 2 from DIS region

41. Matching on the boundary Quark-hadron duality

42. Global duality in electron-nucleon scattering Ex. PDF from W ≈3 GeV, Q 2 ≈ 10 (GeV/c) 2

43. Quark-hadron duality Local duality in Neutrino-nucleon scattering in  region Nachtman variable : Matsui, Sato, Lee, PRC 72 (2005) Q 2 =0.4 (GeV/c) 2 1 2 4 CTEQ06 vs. SL model QH duality holds for isoscalar target

44. Quark-hadron duality Electron-nucleus scattering Broadening of resonance peaks  Fermi motion, many-body correlation, FSI Lalakulich et al, PRC 79 (2009)

45. Quark-hadron duality HOPE : Utilize QH duality practically PDF  Structure functions in resonance region Quantitative (theoretical) understanding of QH duality is prerequisite Neutrino scattering PDF  axial form factor of ANN* 1  2  model is necessary  DCC model can do Electron scattering Res SF  PDF (in kinematics where data are scarce)

46. Sometimes, QH duality could do a very bad job Q 2 =0.21 (GeV/c) 2 0.35 0.62 0.92 1.37 Comparison of SL model and Wandzura-Wilczek formula for electron scattering WW formula Matsui, Sato, Lee, PRC 72 (2005)

47. Quark-hadron duality HOPE : Utilize QH duality practically PDF  Structure functions in resonance region Neutrino scattering PDF  axial form factor of ANN* Quantitative (theoretical) understanding of QH duality is prerequisite 1  2  model is necessary  DCC model can do Can be (has been ?) studied in electron scattering critical comments are welcome Electron scattering Res SF  PDF (in kinematics where data are scarce)

48. Summary ★ Dynamical coupled-channels (DCC) model for     extended to    (ongoing) ★ Matching with DIS and low-Q 2 regions cf. quark-hadron duality

49. Questions/comments DCC model for    being developed (done for Q 2 =0) first serious 2  production model (1  and  are comparable in resonance region) Rein-Sehgal model needs to be improved (replaced) New deuterium experiment is highly hoped deuteron reaction model being developed NC photon emission in higher resonance region relevant ? Matching with DIS (low-Q 2 ) needs all coupled-channels   DCC model can do this Is making use of QH duality a promising direction to fix axial form factors ? Nuclear effects are another difficult problem

50. Neutrino-nucleus interaction

51. To be done with DCC model Our previous experience with Sato-Lee model PRC 54 2660 (1996)  channel only  only ✔ Incoherent 1  production ✔ Coherent 1  production Difficult remaining issues Final state interactions Medium effects (width broadening of resonances)

52. Sato-Lee (SL) model Sato and Lee, PRC 54 2660 (1996)  channel only  only ANL data

53. Inclusive -A scattering in  region Szczerbinska et al., PLB 649 132 (2007) Quasi-elastic (QE)  -excitation (1  )

57. (To be done with DCC model)

58. Another big issue Final state interaction transport model optical potential Medium effects on resonance properties (shift of mass, width) pion-nucleus scattering data

59. Coherent  production in -A scattering in  region Nakamura et al., PRC 81 035502 (2010) Motivation NC    can fake (     e ) event Puzzling experimental situation No evidence for CC K2K (2005), SciBooNE (2008) Signature for NC MiniBooNE Naive expectation from isospin matrix element : σ CC ∼ 2 σ NC

60. Theoretical approaches to coherent π production ∗ PCAC (Partially Conserved Axial Current)-based model Rein, Sehgal, NPB 223 (1983) Kartavtsev et al., PRD 74 (2006) Berger, Sehgal, PRD 79, (2009) Paschos, Schalla, PRD 80 (2009) ∗ Dynamical microscopic model Kelkar et al., PRC 55 (1997) Singh et al., PRL 96 (2006) Alvarez-Ruso et al., PRC 7576 (2007) Amaro et al., PRD 79 (2009) Hernandez et al., PRD 82 (2010) Leitner et al., PRC 79 (2009) Martini et al., PRC 80 (2009) Nakamura et al, PRC 81 (2010)

61. Dynamical model for coherent production ∗ Elementary amplitudes ( νN → μ - π + N, νN → νπ 0 N ) ∗ Medium effect on Δ (mass, width, non-locality) ∗ Final state interaction Ingredients SL model  -hole model } Nakamura et al, PRC 81 (2010)

63. (SL model)

71. BACKUP

73. F 2 from RS model

75. Spectrum of N* resonances Real parts of N* pole values L 2I 2J PDG 4* PDG 3* Ours Kamano, Nakamura, Lee, Sato,2012

76. SL model applied to  nucleus scattering 1  production Szczerbinska et al. (2007)

77. SL model applied to  nucleus scattering coherent  production   C       C    C    - +     C Nakamura et al. (2010)