Nuclear structure functions TUS K. Saito

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1 Nuclear structure functions TUS K. Saito
DIS kinematics　―　what can we see in DIS ? Experiments　―　what is the nuclear EMC effect ? Theoretical approaches　―　can we understand it ? Summary 東海研究会『レプトン原子核反応型模型の構築に向けて』 1/26

2 1. Kinematics of Deep Inelastic Scattering (DIS)
Initial and final lepton 4-momentum: Virtual photon 4-momentum squared: Initial nucleon (nucleus) 4-momentum: Final hadronic 4-momenyum squared: Inelasticity (energy transfer in Lab): Bjorken variable: High momentum flow High Q2: high resolution Partons in target 東海研究会『レプトン原子核反応型模型の構築に向けて』 2/26

3 東海研究会『レプトン原子核反応型模型の構築に向けて』 3/26
The differential cross section (unpolarized): lepton tensor (symmetric part): hadronic tensor (symmetric part): Structure functions F1 and F2: Bjorken limit: Bjorken scaling x: Bjorken variable 東海研究会『レプトン原子核反応型模型の構築に向けて』 3/26

4 東海研究会『レプトン原子核反応型模型の構築に向けて』 4/26
What can we see in DIS ? 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『レプトン原子核反応型模型の構築に向けて』 4/26

5 東海研究会『レプトン原子核反応型模型の構築に向けて』 5/26
Nucleus target in DIS High momentum flow P-QCD : N str. func. F2 Convolution form Low momentum flow Non-perturbative : spect. func. 東海研究会『レプトン原子核反応型模型の構築に向けて』 5/26

6 東海研究会『レプトン原子核反応型模型の構築に向けて』 6/26
2. Experiments 東海研究会『レプトン原子核反応型模型の構築に向けて』 6/26

7 東海研究会『レプトン原子核反応型模型の構築に向けて』 7/26
F2A/F2D Slope of the EMC ratio 東海研究会『レプトン原子核反応型模型の構築に向けて』 7/26

8 東海研究会『レプトン原子核反応型模型の構築に向けて』 8/26
SLAC 東海研究会『レプトン原子核反応型模型の構築に向けて』 8/26

9 東海研究会『レプトン原子核反応型模型の構築に向けて』 9/26

10 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 ? 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) 東海研究会『レプトン原子核反応型模型の構築に向けて』 10/26

11 東海研究会『レプトン原子核反応型模型の構築に向けて』 11/26
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-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. 東海研究会『レプトン原子核反応型模型の構築に向けて』 11/26

12 東海研究会『レプトン原子核反応型模型の構築に向けて』 12/26
Nonrelativistic calculation (by Li, Liu, Brown) (by Atti, Liuti) 東海研究会『レプトン原子核反応型模型の構築に向けて』 12/26

13 東海研究会『レプトン原子核反応型模型の構築に向けて』 13/26
Relativistic calculation (by Smith, Miller) 東海研究会『レプトン原子核反応型模型の構築に向けて』 13/26

14 東海研究会『レプトン原子核反応型模型の構築に向けて』 14/26
What is missing ? Final state interaction: q pQCD (OPE) k di-quark (light-cone exp.) p MF ≅ A-1 A 東海研究会『レプトン原子核反応型模型の構築に向けて』 14/26

15 東海研究会『レプトン原子核反応型模型の構築に向けて』 15/26
Naïve Bag model calculation – include not only FSI but also SRC Quark picture with FSI Quark picture, but no FSI No fermi motion, no c.m. correction K. Saito, A.W.T., N.P.A574, 659 (1994). 東海研究会『レプトン原子核反応型模型の構築に向けて』 15/26

16 東海研究会『レプトン原子核反応型模型の構築に向けて』 16/26
Chiral Quark Soliton model calculation R.S.Jason, G.A. Miller, P.R.L.91, (2003). SLAC-E139 Fe & Ag Drell-Yan exp. FNAL-E772 W 東海研究会『レプトン原子核反応型模型の構築に向けて』 16/26

17 東海研究会『レプトン原子核反応型模型の構築に向けて』 17/26
NJL model calculation I.C. Cloet, W. Bentz, A.W.T., Phys.Lett.B642, (2006). 東海研究会『レプトン原子核反応型模型の構築に向けて』 17/26

18 東海研究会『レプトン原子核反応型模型の構築に向けて』 18/26
3-2. Shadowing effect at small x Shadowing region → DIS occurs coherently: >> 1 for x > 0.1 << 1 for x < for small x, the photon is supposed to be converted into vector mesons VMD　→ surface interaction 東海研究会『レプトン原子核反応型模型の構築に向けて』 18/26

19 東海研究会『レプトン原子核反応型模型の構築に向けて』 19/26
Shadowing effect (by Piller et al.) NMC+FNAL ( ) 東海研究会『レプトン原子核反応型模型の構築に向けて』 19/26

20 東海研究会『レプトン原子核反応型模型の構築に向けて』 20/26
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 東海研究会『レプトン原子核反応型模型の構築に向けて』 20/26

21 東海研究会『レプトン原子核反応型模型の構築に向けて』 21/26
4. Summary The quark distribution in a nucleus is different from that in the free nucleon: ― about 20% reduction at x ~ ― 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 ! 東海研究会『レプトン原子核反応型模型の構築に向けて』 21/26

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

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

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

25 mid Q^2 σ Δ N* QE x 1 A

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

27 high Q^2 σ valence quark x 1/3 1 A

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

29 東海研究会『レプトン原子核反応型模型の構築に向けて』 22/26
Comment on the QE peak in e-A scattering T. Suzuki, P.L.B101 (1981), 298 R. Rosenfelder, P.L.B79 (1978), 15 東海研究会『レプトン原子核反応型模型の構築に向けて』 22/26

30 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) 東海研究会『レプトン原子核反応型模型の構築に向けて』 23/26

31 東海研究会『レプトン原子核反応型模型の構築に向けて』 24/26
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; 𝝐= 𝝀 𝟏 − 𝝀 𝟏 (0). 　　　　　　　　　　σ ω The 1st moment is then given by 東海研究会『レプトン原子核反応型模型の構築に向けて』 24/26

32 東海研究会『レプトン原子核反応型模型の構築に向けて』 25/26
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. 東海研究会『レプトン原子核反応型模型の構築に向けて』 25/26

33 東海研究会『レプトン原子核反応型模型の構築に向けて』 27/26
By Atti and West 東海研究会『レプトン原子核反応型模型の構築に向けて』 27/26