EMC Effect in Electron and Neutrino Scattering Ian Cloet¨ (Argonne National Lab) Collaborators Wolfgang Bentz (Tokai Uni.) and Tony Thomas (JLab) May 31, 2007 1 / 25 Theme ❖ Theme ❖ EMC Effect ● Are nucleon properties modified by the nuclear medium? ❖ Hadronic Tensor ❖ Parton Model ✦ Of fundamental importance. ❖ Calculation ❖ NJL model ✦ Remains an open question. ❖ Nucleon ... ❖ Quark Dis. ❖ Finite Density ● Areas where medium modifications seem important: ❖ Nucleon Dis. ❖ Expressions ✦ Quenching of gA in-medium ❖ Nucleon Dis. 12C ❖ Nucleon Dis. 28Si ✦ Nuclear magnetic moments ❖ Quark Dis. 12C 4 ❖ EMC effect ✦ Nuclear Form Factors (e.g. He) ❖ EMC ratios 28Si ❖ EMC effect ν (¯ν) ● ❖ EMC ratios 27Al Most importantly nuclear structure functions, this is the ❖ Is there medium modification EMC effect. ❖ Polarized EMC ❖ Conclusions 2 / 25 EMC Effect ❖ Theme ❖ EMC Effect ❖ Hadronic Tensor ❖ Parton Model ❖ Calculation ❖ NJL model ❖ Nucleon ... ❖ Quark Dis. ❖ Finite Density ❖ Nucleon Dis. ❖ Expressions ❖ Nucleon Dis. 12C ❖ Nucleon Dis. 28Si ❖ Quark Dis. 12C ❖ EMC effect ❖ EMC ratios 28Si ❖ EMC effect ν (¯ν) ❖ EMC ratios 27Al ❖ Is there medium modification ❖ Polarized EMC ❖ Conclusions ● J. J. Aubert et al. [European Muon Collaboration], Phys. Lett. B 123, 275 (1983). 3 / 25 Hadronic Tensor ❖ Theme ❖ EMC Effect ● Bjorken limit and Callen-Gross relations ❖ Hadronic Tensor (e.g. F2 =2xF1) ❖ Parton Model ❖ Calculation ✦ 1 ❖ NJL model For J = 2 target ❖ Nucleon ... ε qλP σ ❖ P ·q PµPν 2 µνλσ 2 Quark Dis. Wµν = gµν + F (x ,Q ) i F (x ,Q ) q2 P ·q 2 A ν 3 A ❖ Finite Density “ ” − ❖ Nucleon Dis. ❖ Expressions ❖ Nucleon Dis. 12C ✦ ❖ Nucleon Dis. 28Si For arbitrary J (2 J +2 structure functions) 12 ⌊ ⌋ ❖ Quark Dis. C ε qλP σ H P ·q pµpν JH 2 µνλσ JH 2 ❖ W = gµν + F (xA,Q ) i F (xA,Q ) EMC effect µν q2 P ·q 2 − ν 3 ❖ EMC ratios 28Si “ ” ❖ EMC effect ν (¯ν) 27 JH J H JH J H JH J H ❖ EMC ratios Al F2 = F2 − , F3 = F3 − , qs = q s− ❖ Is there medium − modification ❖ Polarized EMC ❖ Conclusions 4 / 25 Parton Model Structure Functions ❖ Theme ❖ EMC Effect ● Parton model expressions ❖ Hadronic Tensor ❖ Parton Model W + JH JH JH JH JH ❖ Calculation F1 =u ¯ + d + s +¯c ❖ NJL model + ❖ Nucleon ... W JH JH JH JH JH F3 = u¯ + d + s c¯ ❖ Quark Dis. − − ❖ Finite Density ❖ Nucleon Dis. J + + ❖ Expressions W 1 W JH 12 Fi (x) Fi (x). ❖ Nucleon Dis. C ≡ 2J +1 ❖ 28 HX= J Nucleon Dis. Si − ❖ Quark Dis. 12C ❖ EMC effect ● ❖ EMC ratios 28Si J +1 quark distributions for nucleus spinJ. ❖ ⌊ ⌋ EMC effect ν (¯ν) ● Twist-2 in QCD ❖ EMC ratios 27Al ❖ Is there medium modification W + ❖ Polarized EMC F2 (x) = Cq(x, αs) [¯u(x) + d(x) + s(x)+¯c(x)] ❖ Conclusions ⊗ 5 / 25 Calculation ❖ Theme ❖ EMC Effect ● Finite Nuclei quark distributions ❖ Hadronic Tensor ❖ Parton Model + + − ❖ Calculation JH P dξ− iP xA ξ /A qA (xA) = e ❖ NJL model A Z 2π ❖ Nucleon ... + ❖ Quark Dis. A, P, H ψ(0) γ ψ(ξ−) A, P, H . h | | i ❖ Finite Density ● ❖ Nucleon Dis. Using Convolution formalism ❖ Expressions 12 ❖ Nucleon Dis. C JH (JH) ❖ Nucleon Dis. 28Si qA (xA) = dyA dx δ(xA yA x) fκ,m (yA) qκ(x) . 12 Z Z − ❖ Quark Dis. C Xκ,m ❖ EMC effect ● ❖ EMC ratios 28Si Diagrammatically ❖ EMC effect ν (¯ν) 27 ❖ EMC ratios Al k + q ❖ Is there medium k k modification ❖ Polarized EMC p p ❖ Conclusions A 1 P − P (a) (b) (c) 6 / 25 Shell Model ❖ Theme ❖ EMC Effect ❖ Hadronic Tensor neutrons protons ❖ Parton Model ❖ Calculation ❖ NJL model 28 d5/2 (κ = 3) ❖ Nucleon ... Si − ❖ Quark Dis. ❖ Finite Density 16 p1/2 (κ = 1) ❖ Nucleon Dis. O ❖ Expressions 12 p (κ = 2) C 3/2 − ❖ Nucleon Dis. 12C ❖ Nucleon Dis. 28Si ❖ 12 Quark Dis. C 4He s1/2 (κ = 1) ❖ EMC effect − ❖ EMC ratios 28Si ❖ EMC effect ν (¯ν) ❖ EMC ratios 27Al ❖ Is there medium modification JH (JH) ❖ Polarized EMC qA (xA) = dyA dx δ(xA yA x) fκ,m (yA) qκ(x) . ❖ Z Z − Conclusions Xκ,m 7 / 25 Nambu–Jona-Lasinio Model ❖ Theme ❖ EMC Effect ● Low energy effective theory ❖ Hadronic Tensor ❖ Parton Model ❖ Calculation G ❖ NJL model ⇒ ❖ Nucleon ... ❖ Quark Dis. ❖ Finite Density ❖ Nucleon Dis. ● Investigate the role of quark degrees of freedom. ❖ Expressions ❖ 12 Nucleon Dis. C ● ❖ Nucleon Dis. 28Si Lagrangian has same symmetries as QCD: ❖ Quark Dis. 12C ❖ EMC effect ✦ Importantly chiral symmetry and CSB, ❖ EMC ratios 28Si Dynamically generated quark masses, ❖ EMC effect ν (¯ν) −→ ❖ EMC ratios 27Al Non-zero chiral condensate. ❖ Is there medium −→ modification ❖ Polarized EMC ● Lagrangian (Γ = Dirac, colour, isospin matrices) ❖ Conclusions 2 = ψ (i ∂ m) ψ + G ψΓψ . LNJL 6 − 8 / 25 Nucleon in the NJL model ❖ Theme ❖ EMC Effect ● Nucleon approximated as quark-diquark bound state. ❖ Hadronic Tensor ❖ Parton Model ● Use relativistic Faddeev approach: ❖ Calculation P k ❖ NJL model − k ❖ Nucleon ... ❖ Quark Dis. = ❖ Finite Density P P ❖ Nucleon Dis. P k − ❖ Expressions k ❖ Nucleon Dis. 12C ❖ Nucleon Dis. 28Si ● Diquark - bound state of two quarks: ❖ Quark Dis. 12C ❖ EMC effect ● Solve Bethe-Salpeter equation for diquark. ❖ EMC ratios 28Si ❖ EMC effect ν (¯ν) ❖ EMC ratios 27Al ❖ Is there medium = + modification ❖ Polarized EMC ❖ Conclusions ● We include scalar and axial-vector diquarks. 9 / 25 Nucleon quark distributions ❖ Theme ❖ EMC Effect ● Associated with a Feynman diagram calculation. ❖ Hadronic Tensor p-q ❖ Parton Model k k ❖ Calculation ❖ NJL model + ❖ Nucleon ... p p pk k p ❖ Quark Dis. q q ❖ Finite Density p-k q-k ❖ Nucleon Dis. ❖ Expressions ❖ 12 Nucleon Dis. C ● + k+ ❖ Nucleon Dis. 28Si q(x) X = γ δ(x p+ ) ❖ Quark Dis. 12C → − ❖ EMC effect ❖ EMC ratios 28Si ● Covariant and gives correct support. ❖ EMC effect ν (¯ν) ❖ EMC ratios 27Al ● Formalism satisfies baryon and momentum sum rules. ❖ Is there medium modification ❖ Polarized EMC 1 1 ❖ Conclusions dx q(x) = Nq, dxx [u(x) + d(x)]=1. Z0 Z0 10 / 25 uv(x) and dv(x) distributions ❖ Theme ❖ EMC Effect 1.6 ❖ Hadronic Tensor ❖ 2 2 Parton Model Q0 = 0.16 GeV ❖ Calculation 2 2 ) ) Q = 5.0 GeV x ❖ NJL model x 2 ( ( 1.2 MRST (5.0 GeV ) v ❖ Nucleon ... v ❖ Quark Dis. x u ❖ Finite Density x u ❖ Nucleon Dis. 0.8 ❖ Expressions ❖ Nucleon Dis. 12C ) and ) and ❖ 28 x Nucleon Dis. Si x ( ❖ 12 ( v Quark Dis. C v 0.4 ❖ EMC effect x d ❖ EMC ratios 28Si x d ❖ EMC effect ν (¯ν) ❖ EMC ratios 27Al 0 ❖ Is there medium modification 0 0.2 0.4 0.6 0.8 1 ❖ Polarized EMC xx ❖ Conclusions ● MRST, Phys. Lett. B 531, 216 (2002). 11 / 25 ∆uv(x) and ∆dv(x) distributions ❖ Theme ❖ EMC Effect ❖ Hadronic Tensor 2 2 ) ) 0.8 Q = 0.16 GeV ❖ Parton Model 0 x x 2 2 ( ❖ Calculation ( Q = 5.0 GeV v v u ❖ NJL model u 0.6 AAC ❖ Nucleon ... ∆ ∆ ❖ x Quark Dis. x 0.4 ❖ Finite Density ❖ Nucleon Dis. ❖ Expressions 0.2 ) and ❖ Nucleon Dis. 12C ) and x 28 x ( ❖ Nucleon Dis. Si ( v ❖ 12 v 0 d Quark Dis. C d ❖ EMC effect ∆ ∆ ❖ EMC ratios 28Si x x 0.2 ❖ EMC effect ν (¯ν) − ❖ EMC ratios 27Al ❖ Is there medium 0 0.2 0.4 0.6 0.8 1 modification xx ❖ Polarized EMC ❖ Conclusions ● M. Hirai, S. Kumano and N. Saito, Phys. Rev. D 69, 054021 (2004). 12 / 25 NJL Model at Finite Density ❖ Theme ● Re-calculate diagrams ❖ EMC Effect ❖ = ψ (i ∂ M ∗ V ) ψ + ′ Hadronic Tensor L 6 − − 6 L I ❖ Parton Model ❖ Calculation ● ❖ NJL model Equivalent to: ❖ Nucleon ... ❖ Quark Dis. ✦ Scalar field: via effective masses ❖ Finite Density ❖ Nucleon Dis. ✦ Vector field: via scale transformation ❖ Expressions ❖ Nucleon Dis. 12C ● ❖ Nucleon Dis. 28Si Nuclear Matter (εF = EF +3V0) ❖ Quark Dis. 12C ❖ EMC effect εF εF V0 ❖ EMC ratios 28Si qA (xA) = qA0 xA ❖ EMC effect ν (¯ν) EF EF − EF ❖ EMC ratios 27Al ❖ Is there medium ● Finite Nuclei (Mˆ Nκ = M N 3Vκ) modification − ❖ Polarized EMC ❖ Conclusions M N M Nκ Vκ qA,κ(xA) = qA0,κ xA Mˆ N MˆNκ − MˆNκ 13 / 25 Nucleon distribution functions ❖ Theme ❖ EMC Effect ● Definition ❖ Hadronic Tensor 3 ❖ Parton Model √2 M N d p ❖ Calculation fκm(yA) = 3 ❖ NJL model A Z (2π) ❖ Nucleon ... 3 + δ p + εκ MN yA Ψκm(~p ) γ Ψκm(~p ) , ❖ Quark Dis. − ❖ Finite Density ❖ Nucleon Dis. ❖ Expressions 12 ❖ Nucleon Dis. C ● Central Potential Dirac eigenfunctions ❖ Nucleon Dis. 28Si ❖ Quark Dis. 12C ❖ EMC effect ℓ Fκ(p) Ωκm(θ, φ) ❖ EMC ratios 28Si Ψκm(~p )=( i) , − Gκ(p) Ω κm(θ, φ) ❖ EMC effect ν (¯ν) − − ❖ EMC ratios 27Al ❖ Is there medium ✦ modification Dirac Equation ❖ Polarized EMC ❖ Conclusions i ~α ~ + β [M(r) Vs(r)] + Vv(r) ψκ(r) = εκ ψκ(r) h− · ∇ − i 14 / 25 Nucleon distributions: Results ❖ Theme ❖ EMC Effect ● Spin-independent nucleon distribution ❖ Hadronic Tensor ❖ Parton Model ❖ Calculation j−m j j k ❖ fκ,m(y )= ( 1) √2k+1 NJL model A k=0,2,...,2j − m m 0 ❖ Nucleon ... P “ − ” j+ 1 ℓkℓ ❖ ( 1) 2 (2j+1)(2ℓ+1)√2k+1 ℓkℓ Quark Dis. − 000 j s j ❖ Finite Density “ ”n o − MN ∞ 2 2 2 MN yA ελ ❖ Nucleon Dis. dp p Fκ(p) +Gκ(p) + (εk M N yA)Fκ(p)Gκ(p) Pk , 16π3 Λ p − „ p « ❖ Expressions R h i ❖ Nucleon Dis. 12C ❖ Nucleon Dis. 28Si 12 ❖ Quark Dis. C ✦ Λ = M N yA εκ ❖ EMC effect | − | ❖ EMC ratios 28Si ❖ EMC effect ν (¯ν) ● Infinite nuclear matter ❖ EMC ratios 27Al ❖ 3 2 Is there medium 3 εF pF 2 modification f(yA)= 4 p ε (1 yA) . “ F ” »“ F ” − − – ❖ Polarized EMC ❖ Conclusions 15 / 25 Nucleon distributions: 12C ❖ Theme ❖ EMC Effect ❖ Hadronic Tensor κ = 1, m = 1 ❖ Parton Model 4 2 12 − 1 ❖ κ = 2, m = Calculation C − 2 ❖ NJL model = 2 = 3 κ , m 2 ❖ − Nucleon ..