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Neutrino-Nucleus scattering at high energies TUS K. Saito

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 ? N eutrino scattering at high Q 2 Neutrino scattering at low Q 2 Summary. 0. Lepton reactions. atmospheric. (GeV 2 ). GeV 2. QE.

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Neutrino-Nucleus scattering at high energies TUS K. Saito

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  1. Neutrino-Nucleus scattering at high energiesTUS 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 scatteringat high Q2 • Neutrino scatteringat low Q2 • Summary

  2. 0. Lepton reactions atmospheric (GeV2) GeV2 QE DGLAP evolution T2K RES DIS BFKL evolution 1 Regge region (GeV) 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

  3. 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: High momentum flow 1. Kinematics of Deep Inelastic Scattering (DIS) W, Z, pf p High Q2: high resolution Partons in target 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

  4. 2. Charged current differential cross section: • lepton tensor current: • hadronic tensor (including anti-symmetric part): V - A left-handed Cabibbo angle Non-conservation of parity Non-conservation of axial current 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

  5. The structure functions: • 3 • , because • : VV + AA contributions, : VA contributions. •  difference between weak and EM interactions • Virtual boson helicity cross sections: • Def: , where • , where , •  average over T-polarizations •  the right-left asymmetry • Note;  T: transverse  L: longitudinal 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

  6. 3. Neutral-current differential cross section: 3 where NC 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

  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 The cross section may naively be given in terms of the incoherent sum of ν/ν-bar scattering off a quark: neutrino-quark scattering (CC) Then, average over the quark probability distribution q(x’) in a target, 2. neutrino-anti-quarkscattering (CC) 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

  9. 3. Scattering-angle (or y-variable) dependence 4. Mixing-angle dependence h=-1/2 h=-1/2 h=+1/2  d’ term  s’ term 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

  10. 5. Results (Leading order) Average isospin singlet (u d) 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. 6. Parameterization of Nuclear PDF by HKN 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

  12. GeV2 • 7. Neutrino reactions at low Q2 (GeV2) RES DIS 1 ? (GeV) 2 • 1. Kulagin prescription •  only for low momentum transfer • the transverse cross section  finite as Q2  0 (photo-absorption); FT  0 •  shadowing, VMD model, etc. • the longitudinal cross section contains the VV and AA parts. • the vector-current part FLVC  0, because of the CVC; . • only the axial-current part remains, because of the PCAC; 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

  13. 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, (interferencemain term between jπand A’)  πN (or A) scattering 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

  14. Adding the form factor to cut off the large-Q2 contribution, we finally obtain The πN forward scattering amplitude (the total cross section) is given by the Regge parameterization: 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

  15. shadowing 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

  16. 2. A la Bodekand Yang Their parameterization (for N) is very messy: i = valence – up, down sea – up, down, strange j = sea – up, down, starnge (for all Q2) 2 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』 16/17

  17. 8. Summary • At large Q2, we can see the quark-gluonstructure of a target – pQCD + higher order corrections. -- relatively easy to handle the structure functions (the quark-gluon distributions) even for a nucleus. • At low Q2, we need non-perturbative treatment: -- the Regge, the BFKL,BK and/or CGC approach, -- need a careful treatment on the axialcurrent, -- nuclear(shadowing)effects. • How do we connect the two pictures? • How do we connect to the resonance region? 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

  18. F2A/F2D Slope of the EMC ratio

  19. SLAC

  20. 3-1. Effect of the conventional nuclear physics ― Binding and Fermi motion 3-2. Shadowing effect at small x 3-3. Anti-shadowing ? 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

  21. 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: • Off-mass shell effect by Kulagin et al. ↓ • Off-massshell (↓) + 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.

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

  23. Relativistic calculation(by Smith, Miller)

  24. What is missing ? Final state interaction: q 2 pQCD (OPE) kdi-quark (light-cone exp.) pMF A-1 A

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

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

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

  28. 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

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

  30. 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

  31. 4. Summary 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 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 ? The sea quark is enhanced in a nucleus around x ~ 0.15 ? ― cf. the Drell-Yan result At large x (>1), what happens ?  new JLab data !

  32. x = Q^2/2Mν, Q^2 fixed ν large, x  small very low Q^2 σ elastic x 1 A

  33. very low Q^2 σ elastic + excited states x 1 A

  34. low Q^2 σ QE peak displacement energy x 1 A

  35. mid Q^2 σ Δ N* QE x 1 A

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

  37. high Q^2 σ valence quark x 1/3 1 A

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

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

  40. 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)

  41. The characteristic function is described in terms of the cumulants; The displacement energy at the peak of QE cross section can be given by the cumulants; (0). σ ω The 1st moment is then given by

  42. 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.

  43. y scaling By Atti and West

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