The EMC effect and the NuTeV Anomaly Ian Cloet¨ (University of Washington) Collaborators Wolfgang Bentz Anthony Thomas (Tokai University) (University of Adelaide) XIX International Workshop on Deep-Inelastic Scattering and Related Subjects Newport News, April 2011 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 ● Understanding EMC effect critical for QCD based description of nuclei 2 /19 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 2 2 Q0 = 0.16 GeV 2 2 ) Q = 0.16 GeV 2 2 0.8 0 x ) Q = 5.0 GeV 2 2 ( Q = 5.0 GeV x 2 v ( MRST (5.0 GeV ) 1.2 u v 0.6 AAC ∆ x u x 0.4 0.8 0.2 ) and ) and x x ( ( v 0.4 v 0 d x d ∆ x 0.2 − 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x x 3 /19 Asymmetric Nuclear Matter ● Finite density Lagrangian: qq¯ interaction in σ, ω, ρ channels ∗ ′ = ψ (i ∂ M V ) ψ + L q − − q q L I ● Fundamental physics: mean fields couple to the quarks in nucleons ● Finite density quark propagator − − ∗ S(k) 1 = k/ M iε ➞ S (k) 1 = k/ M V/ iε − − q − − q − ● Hadronization + mean–field = effective potential that provides ⇒ V = ω ρ , ω = 6 G (ρ + ρ ) , ρ = 2 G (ρ ρ ) u(d) 0 ± 0 0 ω p n 0 ρ p − n ✦ G Z = N saturation & G symmetry energy ω ⇔ ρ ⇔ 4 /19 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 [therefore ρ0 changing] ● 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) 5 /19 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) ● NuTeV: sin2 θ = 0.2277 0.0013(stat) 0.0009(syst) W ± ± ✦ G. P. Zeller et al. Phys. Rev. Lett. 88, 091802 (2002) ● World average sin2 θ = 0.2227 0.0004 : 3 σ = “NuTeV anomaly” W ± ⇒ ● Huge amount of experimental & theoretical interest [over 400 citations] ● No universally accepted complete explanation 6 /19 Paschos-Wolfenstein ratio ● Paschos-Wolfenstein ratio motivated the NuTeV study: νA νA¯ σNC σNC 0 ± RP W = − , NC = Z , CC = W σνA σνA¯ ⇒ ⇒ CC − CC ● For an isoscalar target u d and if s u + d A ≃ A A ≪ A A − − 1 2 7 2 xuA xdA RP W = sin θW + 1 sin θW − − − 2 − − 3 xu + xd A A ● NuTeV “measured” R on an Fe target (Z/N 26/30) P W ≃ ● 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 7 /19 NuTeV anomaly cont’d ● Also correction from m = m - Charge Symmetry Violation u d ✦ CSV+ρ + [x (s s¯)] = no NuTeV anomaly 0 − ⇒ ✦ 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)= + + q + + x + + , N>Z = V > V p −V 0 p −V − p −V ⇒ d u ✦ 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!! 8 /19 Total NuTeV correction 0.250 Standard Model Completed Experiments 0.245 Future Experiments 0.240 SLAC E158 MS W θ ν-DIS 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) ● Includes NuTeV functionals with: CSV+ρ + x (s s¯) 0 − ● Small increase in systematic error ● NuTeV anomaly interpreted as evidence for medium modification ● Equally profound as evidence for physics beyond Standard Model 9 /19 Observable elsewhere? ● We claim isovector EMC effect explains 1.5σ of NuTeV result ∼ ✦ is this mechanism observable elsewhere? ● Yes – parity violating DIS: γZ interference ✦ Z0 interaction violates parity ℓ′ k′,s′ ℓ θ k,s γ, Z0, W ± q X PX A P,S 10 /19 Observable elsewhere? ● We claim isovector EMC effect explains 1.5σ of NuTeV result ∼ ✦ is this mechanism observable elsewhere? ● Yes – parity violating DIS: γZ 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 γZ e F2 e F3 a2(x) = 2gA γ a3(x) = 2gV γ , − F2 − F2 ge ge = ignore a (x) V ≪ A ⇒ 3 ● Parton model expressions F γZ = 2 e gq x (q +q ¯) , gq = 1 2e sin2 θ 2 q V V ± 2 − q W F γZ = 2 X e gq (q q¯) , gq = 1 3 q A − A ± 2 X 11 /19 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 9 2 0 8 9 2 . Q2 = 5 GeV2 4 sin θ . Q2 = 5 GeV2 4 sin θ 5 − W 5 − W 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 12 /19 Flavour Dependence of EMC effect 1.2 1.2 Z/N = 82/126 (Lead) 1.1 Z/N = 26/30 (Iron) 1.1 1 1 0.9 0.9 0.8 γ 0.8 γ RFe RPb 0.7 dA/df 0.7 dA/df Q2 = 5.0 GeV2 Q2 = 5.0 GeV2 0.6 uA/uf 0.6 uA/uf Flavour dependent EMC ratios 0 0.2 0.4 0.6 0.8 1 Flavour dependent EMC ratios 0 0.2 0.4 0.6 0.8 1 x x ● γ γZ Flavour dependence determined by measuring F2A and F2A ● N >Z = d-quarks feel more repulsion than u-quarks: V > V ⇒ d u ✦ u quarks are more bound than d quarks ✦ ρ0 field has shifted momentum from u to d quarks + + + p p Vq q(x)= + + q + + x + + p −V 0 p −V − p −V ● If observed = very strong evidence for medium modification ⇒ 13 /19 Finite nuclei EMC effects ● EMC ratio F2A F2A R = naive = F2A ZF2p + NF2n ● Polarized EMC ratio H H H g1A g1A Rs = H,naive = H H P g1p + P g1n g1A p n ● Spin-dependent cross-section is suppressed by 1/A ✦ Must choose nuclei with A . 27 ✦ protons should carry most of the spin e.g. = 7Li, 11B, . ⇒ ● Ideal nucleus is probably 7Li ✦ J J From Quantum Monte–Carlo: Pp = 0.86 & Pn = 0.04 ● Ratios equal 1 in non-relativistic and no-medium modification limit 14 /19 EMC ratio 7Li, 11B and 27Al 1.2 1.2 7Li 11B 1.1 1.1 1 1 0.9 0.9 0.8 0.8 EMC Ratios EMC Ratios 0.7 Experiment: 9Be 0.7 Experiment: 12C Unpolarized EMC effect Q2 = 5 GeV2 Unpolarized EMC effect Q2 = 5 GeV2 0.6 Polarized EMC effect 0.6 Polarized EMC effect 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x x 1.2 27Al 1.1 1 0.9 0.8 EMC Ratios 0.7 Experiment: 27Al Unpolarized EMC effect Q2 = 5 GeV2 0.6 Polarized EMC effect 0 0.2 0.4 0.6 0.8 1 x 15 /19 Is there medium modification 1.2 27Al 1.1 1 0.9 0.8 EMCEMC Ratios Ratios 0.7 Experiment: 27Al Unpolarized EMC effect Q2 = 5 GeV2 0.6 Polarized EMC effect 0 0.2 0.4 0.6 0.8 1 xx 16 /19 Is there medium modification 1.2 27Al 1.1 1 0.9 0.8 EMCEMC Ratios Ratios 0.7 Experiment: 27Al Unpolarized EMC effect Q2 = 5 GeV2 0.6 Polarized EMC effect 0 0.2 0.4 0.6 0.8 1 xx ● Medium modification of nucleon has been switched off ● Relativistic effects remain ● Large splitting very difficult without medium modification 17 /19 Nuclear Spin Sum Proton spin states ∆u ∆d Σ gA p 0.97 -0.30 0.67 1.267 7Li 0.91 -0.29 0.62 1.19 11B 0.88 -0.28 0.60 1.16 15N 0.87 -0.28 0.59 1.15 27Al 0.87 -0.28 0.59 1.15 Nuclear Matter 0.79 -0.26 0.53 1.05 ● 1 1 Angular momentum of nucleon: J = 2 = 2 ∆Σ + Lq + Jg ✦ in medium M ∗ <M and therefore quarks are more relativistic ✦ lower components of quark wavefunctions are enhanced ✦ quark lower components usually have larger angular momentum ✦ ∆q(x) very sensitive to lower components ● Conclusion: quark spin ➞ orbital angular momentum in-medium 18 /19 Conclusion ● Illustrated the inclusion of quarks into a traditional description of nuclei ✦ complementary approach to traditional nuclear physics ● EMC effect and NuTeV anomaly are interpreted as evidence for medium modification of the bound nucleon wavefunction ✦ result can be tested using PV DIS ● Some important remaining challenges: ✦ polarized EMC effect [quark spin converted ➞ Lq in nuclei] ✦ flavour dependence of EMC effect ● Exciting new experiments: ✦ PV DIS, pion induced Drell-Yan, neutron knockout ● Significant omissions: quasi-elastic scattering ✦ in-medium form factors [Strauch], Coulomb sum rule [Meziani], etc ● Slowly building a QCD based understanding of nuclear structure 19 /19 Corrections to Rν and Rν¯ separately ● Recall NuTeV actually measured Rν and Rν¯, finding ✦ NuTeV = Rν = 0.3916(13) & Rν¯ = 0.4050(27) ⇒ ✦ Standard Model = Rν = 0.3950 & Rν¯ = 0.4066 ⇒ ● Corrections to Standard Model