1. Neutrino-Nucleus scattering at high energies TUS K. Saito 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 1/17 DIS kinematics ― what can we see in DIS ? Neutrino scattering at high Q 2 Neutrino scattering at low Q 2 Summary

2. 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 2/17 0. Lepton reactions 2 1 DISRES Regge region BFKL evolution DGLAP evolution QE atmospheric T2K

3. 1. Kinematics of Deep Inelastic Scattering (DIS) Initial and final lepton 4-momentum: Virtual photon or boson 4-momentum squared: Initial nucleon (nucleus) 4-momentum: Final hadronic 4-momenyum squared: y variable (--> energy loss at T rest fr.): Bjorken variable: 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 3/17 High momentum flow High Q 2 : high resolution Partons in target W, Z, p pfpf

4. 2. Charged current differential cross section: lepton tensor current: hadronic tensor (including anti-symmetric part): 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 4/17 V - A Non-conservation of axial current Non-conservation of parity left-handed Cabibbo angle

5. 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 5/17  T: transverse  L: longitudinal

6. 3. Neutral-current differential cross section: 3 where 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 6/17 NC

7. 4. What can we see in the target in the Bjorken limit Bjorken limit The approximate Q^2-independence of the structure functions → the virtual photon sees point-like constituents in the target – quarks → using distributions of quarks and anti-quarks, (Callan-Gross relation) The small scaling violation is calculated by pQCD. DIS probes a current-current correlation in the target ground state. In the Bjorken limit, the probed correlation is light-like: ~ 2.0(fm) for x ~ 0.1 ~ 1.0(fm) for x ~ 0.2 ~ 0.4(fm) for x ~ 0.5 ~ 0.2(fm) for x ~ 1.0 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 7/17

8. 5. Simple consideration on the ν / ν reactions 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 8/17 The cross section may naively be given in terms of the incoherent sum of ν/ν-bar scattering off a quark: 1.neutrino-quark scattering (CC) Then, average over the quark probability distribution q(x’) in a target, 2. neutrino-anti-quark scattering (CC)

9. 3. Scattering-angle (or y-variable) dependence 4. Mixing-angle dependence 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 9/17  d’ term  s’ term h=-1/2 h=+1/2h=-1/2

10. 5. Results (Leading order) Average 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 10/17

11. 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 11/17 6. Parameterization of Nuclear PDF by HKN

12. 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 12/17 7. Neutrino reactions at low Q 2 2 1 DISRES ?

13. 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 13/17 Separate the axial current as (= pion current + heavy hadron current -- axial vector meson, ρπ continuum, etc.) But, the pion derivative does not contribute, because Thus, (interference main term between j π and A’)  πN (or A) scattering

14. 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 14/17 Adding the form factor to cut off the large-Q 2 contribution, we finally obtain The πN forward scattering amplitude (the total cross section) is given by the Regge parameterization:

15. 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 15/17 shadowing

16. 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 16/17 2. A la Bodek and Yang Their parameterization (for N) is very messy: i = valence – up, down sea – up, down, strange j = sea – up, down, starnge (for all Q 2 ) 2 2

17. At large Q 2, we can see the quark-gluon structure of a target – pQCD + higher order corrections. -- relatively easy to handle the structure functions (the quark-gluon distributions) even for a nucleus. At low Q 2, we need non-perturbative treatment: -- the Regge, the BFKL, BK and/or CGC approach, -- need a careful treatment on the axial current, -- nuclear (shadowing) effects. How do we connect the two pictures ? How do we connect to the resonance region ? 8. Summary 東海研究会 5 『レプトン原子核反応型模型の構築に向けて』 17/17

21. F 2 A /F 2 D Slope of the EMC ratio

22. SLAC

24. 3-1. Effect of the conventional nuclear physics ― Binding and Fermi motion How does the conventional nuclear physics affect F2(x) ? The nucleon is scattered incoherently in case of The light-cone momentum distribution of N in A: Spectral function Quasi-elastic reaction A(e,e’p)A’ → Koltun sum rule: E/A = (T-e)/2 (2body force only) 3. Theoretical approaches 3-1. Effect of the conventional nuclear physics ― Binding and Fermi motion 3-2. Shadowing effect at small x 3-3. Anti-shadowing ?

25. Convolution form: Assumptions in the convolution model: on-mass shell approximation → → if the binding is weak, OK? impulse approximation ― final state interactions and interference terms are ignored. If OK, we get Model-dependent calculations: ①Off-mass shell effect by Kulagin et al. ↓ ②Off-mass shell (↓) + final state interaction (MFA) by Saito et al. ↑ Ignored diagrams Note: Deuteron is also different from the average of proton and neutron ― small EMC effect.

26. Nonrelativistic calculation (by Li, Liu, Brown) (by Atti, Liuti)

27. Relativistic calculation (by Smith, Miller)

29. K. Saito, A.W.T., N.P.A574, 659 (1994). No fermi motion, no c.m. correction Quark picture, but no FSI Quark picture with FSI Naïve Bag model calculation – include not only FSI but also SRC

30. SLAC-E139 Fe & Ag Drell-Yan exp. FNAL-E772 W Chiral Quark Soliton model calculation R.S.Jason, G.A. Miller, P.R.L.91, 212301 (2003).

31. NJL model calculation I.C. Cloet, W. Bentz, A.W.T., Phys.Lett.B642, 210-217 (2006).

32. 3-2. Shadowing effect at small x Shadowing region → DIS occurs coherently: >> 1 for x > 0.1 << 1 for x < 0.1 for small x, the photon is supposed to be converted into vector mesons VMD → surface interaction

33. Shadowing effect (by Piller et al.) NMC+FNAL ( )

34. 3-3. Anti-shadowing ? Anti-shadowing region → An enhancement at small x region → pion field enhancement ??? Recent data of the giant Gamow-Teller states → the Landau-Migdal parameters

35. 4. Summary 1.The quark distribution in a nucleus is different from that in the free nucleon: ― about 20% reduction at x ~ 0.7-0.8 ― at small x, the structure function is reduced due to shadowing ― for large x, the EMC ratio is very enhanced because of Fermi motion and short-range correlation 2.The energy-momentum distribution of a nucleon in a nucleus is vital to explain the EMC effect, but its effect is insufficient ? ― the internal structure of a nucleon is modified in a nucleus ? 3. The sea quark is enhanced in a nucleus around x ~ 0.15 ? ― cf. the Drell-Yan result 4.At large x (>1), what happens ?  new JLab data !

36. x σ x = Q^2/2Mν, Q^2 fixed ν  large, x  small very low Q^2 A1 elastic

37. x σ very low Q^2 A1 elastic + excited states

38. x σ low Q^2 A1 QE peak displacement energy

39. x σ mid Q^2 A1 QE Δ N*

40. x σ mid Q^2 A1 Δ, N* duality QE peak of quark 1/3

41. x σ high Q^2 A1 valence quark 1/3

42. x σ very high Q^2 A1 sea + glue BK region 1/3

43. Comment on the QE peak in e-A scattering T. Suzuki, P.L.B101 (1981), 298 R. Rosenfelder, P.L.B79 (1978), 15

44.  QE peak in e-A scattering at low energy Differential cross section: The response functions (structure functions): S = W(L) or W(T) for longitudinal mode The characteristic function: (k-th energy weighted moment)

46. If we take Hamiltonian as, then we get (as an example, for longitudinal mode), which implies that the Wigner and Bartlett forces do not contribute to the displacement energy (for longitudinal mode) ! Summary: the displacement of QE peak is caused by some specific forces in nuclear force. the binding effect appears when FSI is ignored, while, if it is include, the binding is cancelled by FSI – Wigner force does not contribute. the energy shift is also caused by a non-local (energy dependent) one-body potential.

47. By Atti and West y scaling