Nuclear EMC effect Ian Cloet¨ (University of Washington) Collaborators Wolfgang Bentz Anthony Thomas (Tokai University) (Adelaide University) 3rd International Workshop on Nucleon Structure at Large Bjorken x JLab, October 2010 EMC Effect 1.2 56Fe 1.1 D 1 2 /F 0.9 Fe 2 F 0.8 EMC effect 0.7 Before EMC experiment Experiment (Gomez 1994) 0.6 0 0.2 0.4 0.6 0.8 1 x ● J. J. Aubert et al. [European Muon Collaboration], Phys. Lett. B 123, 275 (1983). ● Fundamentally challenged our understanding of nuclei ● Immediate parton model interpretation: ✦ valence quarks in nucleus carry less momentum than in nucleon ● What is the mechanism? After more than 25 years no consensus ● nuclear structure, pions, 6 quark bags, rescaling, medium modification 2 /24 EMC Effect 1.2 56Fe 1.1 D 1 2 /F 0.9 Fe 2 F 0.8 EMC effect 0.7 Before EMC experiment Experiment (Gomez 1994) 0.6 0 0.2 0.4 0.6 0.8 1 x ● Understanding EMC effect critical for QCD based description of nuclei ● Need new experiments accessing different aspects of the EMC effect ● Important near term measurements ✦ flavour decomposition & spin dependence of nuclear PDFs ● New experiments ✦ SIDIS, parity violating DIS, polarized DIS, νDIS, Drell-Yan 3 /24 Anti-quarks in Nuclei and Drell-Yan P ′ X X′ A′ µ− P ′, S′ q γ ¯ A q µ+ P, S X PX ● Pions play a fundamental role in traditional nuclear physics ✦ therefore expect pion (anti-quark) enhancement in nuclei ● Drell-Yan experiment set up to probe anti-quarks in target nucleus − ✦ qq¯ → µ+µ – E906: run ∼2011 FNAL, E772: Alde et al., PRL. 64, 2479 (1990). ✦ no pionic enhancement – very unexpected – energy loss? ● Important to understand anti-quarks in nuclei: Drell-Yan & PV DIS 4 /24 Nambu–Jona-Lasinio Model and PDFs ● NJL model interpreted as low energy chiral effective theory of QCD © G Θ(k2−Λ2) Z(k2) k2 ● Quark distributions given by Feynman diagram calculation p − q k k + p p p k k p q q p − k q − k 1.6 1 Q2 = 0.16 GeV2 0 0.9 2 2 2 2 Q = 5 GeV ) Q = 5.0 GeV x 2 0.8 ( 1.2 MRST (5.0 GeV ) v 0.7 ) x u x 0.6 ( 0 5 0.8 /u . ) x 0.4 ( ) and d x 0 3 ( . v 0.4 0.2 x d 0.1 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x x 5 /24 Constituent Quark PDFs ● Dress quarks with pions p − k β β α β α Z α + + q × p p p p p p − k p 0.5 0.5 uU uD 0.4 dU 0.4 dD u¯U u¯D 0.3 0.3 d¯U d¯D 0.2 0.2 0.1 0.1 Constituent up quark PDFs 0 0 Constituent down quark PDFs 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 x x 2 2 ● Gottfried Sum Rule: NMC 1994: SG = 0.258 ± 0.017 [Q = 4 GeV ] 1 dx 1 2 1 S = [F (x) − F (x)] = − dx d¯(x) − u¯(x) G x 2p 2n 3 3 Z0 Z0 ● 1 4 We find: SG = 3 − 9 (1 − Zq) = 0.252 [Zq = 0.817] 6 /24 Asymmetric Nuclear Matter ● Finite density Lagrangian: qq¯ interaction in σ, ω, ρ channels ∗ ′ L = ψq (i∂ − M − Vq) ψq + L I ● Fundamental physics: mean fields couple to the quarks in nucleons ● Finite density quark propagator −1 −1 ∗ S(k) = k/ − M − iε ➞ Sq(k) = k/ − M − V/q − iε ● Hadronization + mean–field =⇒ effective potential that provides Vu(d) = ω0 ± ρ0, ω0 = 6 Gω (ρp + ρn) , ρ0 = 2 Gρ (ρp − ρn) ✦ Gω ⇔ Z = N saturation & Gρ ⇔ symmetry energy 7 /24 Model Independent Results? ● The effect of vector-field is model independent under assumptions ✦ quarks feel nuclear medium ✦ struck quark does not feel vector-field (asymptotic freedom) ● Result [Thomas 1998, Bentz 2003, Miller 2005] + + + p p Vq q(x)= + + q0 + + x − + + p − V p − V p − V ! ● All medium modification models should obey this result ● Important observation 0 ✦ For N>Z ρ -field =⇒ Vd > Vu ✦ ρ0-field shifts momentum from u- to d-quarks ● As we will see this result has important testable consequences ✦ large flavour dependence of EMC effect for N >Z nuclei 8 /24 Isovector EMC effect 1.2 1.2 1.1 1.1 1 1 0.9 0.9 0.8 Z/N = 1.0 0.8 Z/N = 0 EMC ratios Z/N = 1/0.8 EMC ratios Z/N = 0.2 0.7 Z/N = 1/0.6 0.7 Z/N = 0.4 Z/N = 1/0.4 Z/N = 0.6 Z/N = 1/0.2 Z/N = 0.8 −3 −3 0.6 Z/N = ∞ ρ = ρp + ρn = 0.16 fm 0.6 Z/N = 1.0 ρ = ρp + ρn = 0.16 fm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x x F F 4 u (x)+ d (x) ● EMC ratio: R = 2A = 2A ≃ A A F2A,naive ZF2p + NF2n 4 uf (x)+ df (x) ● Density is fixed only changing Z/N ratio ● EMC effect essentially a consequence of binding at the quark level ● proton excess: u-quarks feel more repulsion than d-quarks (Vu > Vd) ● neutron excess: d-quarks feel more repulsion than u-quarks (Vd > Vu) 9 /24 Weak mixing angle and the NuTeV anomaly 0.250 Standard Model Completed Experiments 0.245 Future Experiments 0.240 SLAC E158 NuTeV MS W θ 2 APV(Cs) 0.235 sin Møller [JLab] Z-pole 0.230 Qweak [JLab] D0 PV-DIS [JLab] CDF 0.225 0.001 0.01 0.1 1 10 100 1000 10000 Q (GeV) 2 ● NuTeV: sin θW = 0.2277 ± 0.0013(stat) ± 0.0009(syst) ✦ G. P. Zeller et al. Phys. Rev. Lett. 88, 091802 (2002) 2 ● World average sin θW = 0.2227 ± 0.0004 : 3 σ =⇒ “NuTeV anomaly” ● Huge amount of experimental & theoretical interest [over 400 citations] ● No universally accepted complete explanation 10 /24 Paschos-Wolfenstein ratio ● Paschos-Wolfenstein ratio motivated the NuTeV study: νA νA¯ σNC − σNC 0 ± RP W = νA νA¯ , NC =⇒ Z , CC =⇒ W σCC − σCC ● For an isoscalar target uA ≃ dA and if sA ≪ uA + dA − − 1 2 7 2 xuA − xdA RP W = − sin θW + 1 − sin θW − − 2 3 xu + xd A A ● NuTeV “measured” RP W on an Fe target (Z/N ≃ 26/30) ● Correct for neutron excess ⇔ flavour dependent EMC effect ● Use our medium modified “Fe” quark distributions naive Fermi ρ0 ∆RP W = ∆RP W + ∆RP W + ∆RP W = − (0.0107 + 0.0004 + 0.0028) . ● Isoscalarity ρ0 correction can explain up to 65% of anomaly 11 /24 NuTeV anomaly cont’d ● Also correction from mu = md - Charge Symmetry Violation ✦ CSV+ρ0 =⇒ no NuTeV anomaly ✦ No evidence for physics beyond the Standard Model ● Instead “NuTeV anomaly” is evidence for medium modification ✦ Equally interesting ✦ EMC effect has over 850 citations [J. J. Aubert et al., Phys. Lett. B 123, 275 (1983).] ● Model dependence? ✦ sign of correction is fixed by nature of vector fields + + + p p Vq q(x)= p+−V + q0 p+−V + x − p+−V + , N>Z =⇒ Vd > Vu ✦ ρ0-field shifts momentum from u- to d-quarks ✦ size of correction is constrained by Nucl. Matt. symmetry energy ● ρ0 vector field reduces NuTeV anomaly – Model Independent!! 12 /24 Total NuTeV correction 0.250 Standard Model Completed Experiments 0.245 Future Experiments 0.240 SLAC E158 MS W θ 2 APV(Cs) 0.235 NuTeV sin Møller [JLab] Z-pole 0.230 Qweak [JLab] D0 PV-DIS [JLab] CDF 0.225 0.001 0.01 0.1 1 10 100 1000 10000 Q (GeV) ● Includes NuTeV functionals ● Small increase in systematic error ● NuTeV anomaly interpreted as evidence for medium modification ● Equally profound as evidence for physics beyond Standard Model 13 /24 Consistent with other observables? ● We claim isovector EMC effect explains ∼1.5σ of NuTeV result ✦ is this mechanism observed elsewhere? ● Yes!! Parity violating DIS: γZ0 interference dσ − dσ 1 − (1 − y)2 A = R L ∝ a (x) + a (x) PV dσ + dσ 2 1+(1 − y)2 3 R L γZ + + e F2 6u + 3d 2 a2(x) = −2gA γ = + + − 4 sin θW F2 4 u + d γZ − − e F3 2 2 u + d a3(x) = −2gV γ = 3 1 − 4 sin θW + + F2 4 u + d ● Parton model expressions γZ q q 1 2 F2 = 2 eq gV x (q +q ¯) , gV = ± 2 − 2eq sin θW γZ X q q 1 F3 = 2 eq gA (q − q¯) , gA = ± 2 X 14 /24 Parity Violating DIS: Iron & Lead 1.1 Z/N = 26/30 (Iron) 1.1 Z/N = 82/126 (Lead) 1 1 ) ) A A x x ( ( 2 2 a 0.9 a 0.9 a2 a2 naive naive a2 a2 0.8 2 2 9 2 0.8 2 2 9 2 Q = 5 GeV 5 − 4 sin θW Q = 5 GeV 5 − 4 sin θW 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 xA xA ● For a N ≃ Z target: + + 9 2 12 uA(x) − dA(x) a2(x)= − 4 sin θW − + + 5 25 uA(x)+ dA(x) ● “Naive” result has no medium corrections ● After naive isoscalarity corrections medium effects still very large ● Large x dependence of a2(x) ➞ evidence for medium modification 15 /24 PVDIS: Carbon (with anti-quarks) Preliminary 0.3 1.1 Z/N = 1 (Carbon) Z/N = 1 (Carbon) 0.2 1 ) ) A A x x 0 1 ( .