The structure of a bound nucleon

Transcription

1 The structure of a bound nucleon Ian Cloët (University of Washington) Collaborators Wolfgang Bentz Anthony Thomas (Tokai University) (Adelaide University) Tony s 60 Fest 5 9 Feburary 200

2 Theme Gain insights into nuclear structure from a QCD viewpoint Highlight opportunities provided by nuclear systems to study QCD Present complementary approach to traditional nuclear physics formulated as a covariant quark theory grounded in good description of mesons and baryons at finite density self-consistent mean-field approach Fundamental difference bound nucleons differ from free nucleons medium modification effects typically 0 20% Possible answers to many long standing questions: we address the EMC effect [European Muon Collaboration] the NuTeV anomaly [Neutrinos at the Tevatron] 2 /30

3 Weak mixing angle and the NuTeV anomaly Standard Model Completed Experiments Future Experiments sin 2 θ W MS APV(Cs) SLAC E58 NuTeV Møller [JLab] Qweak [JLab] PV-DIS [JLab] Z-pole D0 CDF Q (GeV) NuTeV: sin 2 θ W = ± 0.003(stat) ± (syst) G. P. Zeller et al. Phys. Rev. Lett. 88, (2002) World average sin 2 θ W = ± : 3 σ = NuTeV anomaly Huge amount of experimental & theoretical interest [over 400 citations] No universally accepted complete explanation 3 /30

4 EMC Effect.2 56 Fe F 2 Fe /F 2 D x Pre 983: before the EMC experiment Nucleon quark distributions unchanged in medium Long distance nuclear effects not expected to influence short distance quark physics Fermi motion of nucleons dominate at large x 4 /30

5 EMC Effect.2 56 Fe F 2 Fe /F 2 D EMC effect Before EMC experiment Experiment (Gomez 994) J. J. Aubert et al. [European Muon Collaboration], Phys. Lett. B 23, 275 (983). Immediate parton model interpretation: x valence quarks in nucleus carry less momentum than in nucleon Nuclear effects do influence quark physics What is the mechanism? After 25 years no consensus EMC medium modification NuTeV anomaly? 5 /30

6 EMC Effect.2 56 Fe F 2 Fe /F 2 D EMC effect Before EMC experiment Experiment (Gomez 994) J. J. Aubert et al. [European Muon Collaboration], Phys. Lett. B 23, 275 (983). Immediate parton model interpretation: x valence quarks in nucleus carry less momentum than in nucleon Nuclear effects do influence quark physics What is the mechanism? After 25 years no consensus EMC medium modification NuTeV anomaly? 6 /30

7 Medium Modification What does this mean? 50 years of traditional nuclear physics tells us that the nucleus is composited of nucleon-like objects However if a nucleon property is not protected by a symmetry its value may change in medium e.g. mass, magnetic moments, radii quark distributions, form factors, GPDs, etc There must be medium modification: nucleon propagator is changed in medium off-shell effects: in-medium nucleon has 2 form factors consequently for example F p (Q 2 = 0) Need to understand these effects as first step toward QCD based understanding of nuclei 7 /30

8 Finite Nuclei quark distributions Definition of finite nuclei quark distributions q A (x A ) = P + dξ A 2π e ip + xa ξ A A,P ψ q (0) γ + ψ q (ξ ) A,P Approximate using a modified convolution formalism q A (x A ) = dy A dx δ(x A y A x)f α,κ,m (y A ) q α,κ (x) α,κ,m neutrons protons 28 Si d 5/2 (κ = 3) 6 O 2 C p /2 (κ = ) p 3/2 (κ = 2) 4 He s /2 (κ = ) 8 /30

9 Nambu Jona-Lasinio Model Interpreted as low energy chiral effective theory of QCD G Θ(k2 Λ2) Z(k 2 ) Can be motivated by infrared enhancement of gluon propagator e.g. DSEs and Lattice QCD G(k 2 )/k 2 (GeV 2 ) ω = 0.4 ω = 0.5 α s (k 2 )/k 2 A. Holl, et al, Phys. Rev. C 7, (2005) Investigate the role of quark degrees of freedom. NJL has same symmetries as QCD Lagrangian: L NJL = ψ ( i/ m ) ψ + G ( ψ Γ ψ ) k 2 (GeV 2 ) 9 /30

10 Nucleon in the NJL model Nucleon approximated as quark-diquark bound state. Use relativistic Faddeev approach: P k k Nucleon quark distributions = P P P k dξ q(x) = p + 2π ei x p+ ξ p,s ψ q (0)γ + ψ q (ξ ) p,s c, q(x) = γ + γ 5 k Associated with a Feynman diagram calculation k k p q p p p k [q(x), q(x), T q(x)] X = δ + p ( x k+ q k ) q k [γ +,γ + γ p + 5,γ + γ ] γ 5 k q p 0 /30

11 Results: proton quark distributions x dv(x) and x uv(x) Q 2 0 = GeV 2 Q 2 = 5.0 GeV 2 MRST (5.0 GeV 2 ) x x dv(x) and x uv(x) Q 2 0 = GeV 2 Q 2 = 5.0 GeV 2 AAC x Empirical spin-independent distributions: Martin, Roberts, Stirling and Thorne, Phys. Lett. B 53, 26 (2002). Empirical helicity: M. Hirai, S. Kumano and N. Saito, Phys. Rev. D 69, (2004). Dotted line = model result, Solid line = evolved model result Dashed line = empirical result Approach is covariant, satisfies all sum rules & positivity constraints /30

12 Recall: Shell Model Picture neutrons protons 28 Si d 5/2 (κ = 3) 6 O 2 C p /2 (κ = ) p 3/2 (κ = 2) 4 He q A (x A ) = α,κ,m dy A s /2 (κ = ) dx δ(x A y A x)f α,κ,m (y A ) q α,κ (x) We now discuss κ or density dependence For nuclear matter f α,κ,m (y A ) & hence α,κ,m greatly simplify 2 /30

13 Asymmetric Nuclear Matter: Lagrangian Finite Density Lagrangian: σ, ω, ρ mean fields L = ψ (i M V )ψ + L I σ: isoscalar-scalar attractive ω: isoscalar-vector repulsive ρ: isovector-vector attractive/repulsive Fundamental physics: mean fields couple to the quarks in nucleons Finite density quark propagator S(k) = /k M iε S q (k) = /k M /V q iε 3 /30

14 Effective Potential Hadronization Effective potential E = E V ω2 0 4 G ω ρ2 0 4 G ρ + E p + E n E V : vacuum energy E p(n) : energy of nucleons moving in σ, ω, ρ fields Effective potential provides ω 0 = 6G ω (ρ p + ρ n ), ρ 0 = 2G ρ (ρ p ρ n ), E M = 0 G ω Z = N saturation & G ρ symmetry energy Vector potentials: V u(d) = ω 0 ± ρ 0 V p(n) = 3ω 0 ± ρ 0 Recall: quark propagator: S q (k) = [ /k M /V q ] 4 /30

15 Results: Nuclear Matter xa ua(xa) / A free scalar + Fermi + vector Z/N = xa ua(xa) / A free scalar + Fermi + vector Z/N = xa da(xa) / A x A free scalar + Fermi + vector Z/N = xa da(xa) / A x A free scalar + Fermi + vector Z/N = x A ρ p + ρ n = fixed Differences arise from: naive: different number protons and neutrons x A medium: p & n Fermi motion and V u(d) differ u p (x) d n (x),... 5 /30

16 Isovector EMC Effect EMC ratios Z/N =.0 Z/N = / Z/N = / Z/N = /0.4 Z/N = /0.2 Z/N = ρ = ρ p + ρ n = fm 3 EMC ratios Z/N = 0 Z/N = 0.2 Z/N = 0.4 Z/N = Z/N = Z/N =.0 ρ = ρ p + ρ n = fm x x EMC ratio: R γ = F 2A F naive 2A 4 u A(x)+d A (x) 4 u 0 (x)+d 0 (x), u(x)=z A u p(x)+ N A u n(x)... Effect comes largely from the changing ρ 0 field Proton rich: u(x) > d(x) and V u > V d Neutron rich: u(x) < d(x) and V u < V d Density is fixed, only Z/N changes = non-trivial isospin dependence 6 /30

17 Paschos-Wolfenstein ratio Paschos-Wolfenstein ratio motivated the NuTeV study: R PW = σν NC A σ ν NC A σcc ν A σ ν CC A, NC = Z 0, CC = W ± Expressing R PW in terms of quark distributions: R PW = sin2 θ W x u A sin2 θ W x d A +x s A x d A +x s A 3 x u A For an isoscalar target u A d A and if s A u A + d A R PW = 2 sin2 θ W + R PW NuTeV measured R PW on an Fe target (Z/N 26/30) Correct for neutron excess isoscalarity corrections 7 /30

18 Isovector EMC correction to NuTeV General form of isoscalarity corrections ( ) R PW = 2 sin2 θ W + ( 73 ) x u sin2 A θ x d A W x u A + x d A NuTeV assumed nucleons in Fe are like free nucleons Ignored some medium effects: Fermi motion & ρ 0 -field Use our medium modified Fe quark distributions R PW = RPW naive + RFermi PW + Rρ0 PW = ( ). Recall NuTeV requires R PW = R SM PW ±... (= 2 sin2 θ W ) R NuTeV PW = ±... Isoscalarity ρ 0 correction can explain up to 65% of anomaly 8 /30

19 NuTeV anomaly cont d Also correction from m u m d - Charge Symmetry Violation CSV+ρ 0 = 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 23, 275 (983).] Model dependence? sign of correction is fixed by nature of vector fields q(x) = p+ p + V + q 0 ( p + ) V q + p + V + p + V +, N > Z = V u < V d ρ 0 -field shifts momentum from u- to d-quarks size of correction is constrained by Nucl. Matt. symmetry energy ρ 0 vector field reduces NuTeV anomaly Model Independent!! 9 /30

20 Total NuTeV correction Standard Model Completed Experiments Future Experiments sin 2 θ W MS APV(Cs) SLAC E58 NuTeV Møller [JLab] Qweak [JLab] PV-DIS [JLab] Z-pole D0 CDF Q (GeV) Small increase in systematic error NuTeV anomaly interpreted as evidence for medium modification Equally profound as evidence for physics beyond Standard Model 20 /30

21 Consistent with other observables? We claim Isovector EMC effect explains.5σ of NuTeV result but can this mechanism be observed elsewhere? Yes!! Parity violating DIS Z 0 interaction violates parity A PV = dσ R dσ L dσ R +dσ L [a 2 (x) +...]; Parton model expressions a 2 (x) = g e A F γz 2 F γ 2 F γz 2 = 2x e q g q V (q + q), gq V = ± 2 2e q sin 2 θ W Measuring a 2 = F γz 2 or sin 2 θ W For N Z target a 2 (x) ( sin2 θ W ) 2 25 u + A (x) d+ A (x) u + A (x)+d+ A (x) Measurement of a 2 (x) at each x = a NuTeV experiment!! 2 /30

22 Parity Violating DIS: a 2 ratios.. Z/N = 26/30 (Iron) Z/N = 82/26 (Lead) a2(xa) 0.9 a2(xa) 0.9 a 2 a naive sin2 θ W a 2 a naive sin2 θ W x A x A a 2 (x) sin2 θ W 2 25 u + A (x) d+ A (x) u + A (x)+d+ A (x) Isoscalarity corrections are independent of sin 2 θ W An advantage over Paschos-Wolfenstein ratio After naive isoscalarity corrections medium effects still very large Large x dependence of a 2 (x), even after naive correction Cannot be from sin 2 θ W Evidence for medium modification 22 /30

23 Recall Shell Model Picture neutrons protons 28 Si d 5/2 (κ = 3) 6 O 2 C p /2 (κ = ) p 3/2 (κ = 2) 4 He s /2 (κ = ) q A (x A ) = α,κ,m dy A dx δ(x A y A x) f α,κ,m (y A ) q κ (x) Finite nucleus calculation 23 /30

24 Nucleon distributions: 28 Si 4 28 Si κ =, m = 2 κ = 2, m = 2 fκm(ya) 3 2 κ = 2, m = 3 2 κ =, m = 2 κ = 3, m = 2 κ = 3, m = 3 2 κ = 3, m = y A 24 /30

25 EMC effects EMC ratio R = F 2A F naive 2A = F 2A Z F 2p + N F 2n Least model dependent way to definite EMC effect Polarized EMC ratio Rs JH = gjh A ga,naive JH = P JH p g JH A g p + P JH n g n Spin-dependent cross-section is suppressed by /A Must choose nuclei with A 27 protons should carry most of the spin e.g. = 7 Li, B,... Ideal nucleus is probably 7 Li From Quantum Monte Carlo: P JJ p = 6 & P JJ n = 0.04 Ratios equal in non-relativistic and no-medium modification limit. 25 /30

26 EMC ratio 7 Li, B, 5 N and 27 Al.2. 7 Li.2. B EMC Ratios 0.9 EMC Ratios Experiment: 9 Be Unpolarized EMC effect Polarized EMC effect Q 2 = 5 GeV Experiment: 2 C Unpolarized EMC effect Polarized EMC effect Q 2 = 5 GeV x x.2. 5 N Al EMC Ratios Experiment: 2 C Unpolarized EMC effect Polarized EMC effect Q 2 = 5 GeV 2 EMC Ratios Experiment: 27 Al Unpolarized EMC effect Polarized EMC effect Q 2 = 5 GeV x x 26 /30

27 Is there medium modification Al EMC Ratios Experiment: 27 Al Unpolarized EMC effect Polarized EMC effect Q 2 = 5 GeV x 27 /30

28 Is there medium modification Al EMC Ratios Experiment: 27 Al Unpolarized EMC effect Polarized EMC effect Q 2 = 5 GeV x Medium modification of nucleon has been switched off 28 /30

29 Nuclear Spin Sum u d Σ g A p Li B N Al Nuclear Matter Angular momentum of nucleon: J = 2 = 2 Σ + L q + J g In-medium lower components of quark wavefunctions are enhanced since M < M and therefore quarks are more relativistic lower components have L = q(x) very sensitive to lower components because of γ 5 Conclusion: quark spin orbital angular momentum in-medium 29 /30

30 Conclusion Effective quark theories can be used to incorporate quarks into a traditional description of nuclei fundamentally different approach to nuclear physics The major outstanding discrepancy with Standard Model predictions for Z 0 was NuTeV anomaly resolved by CSV and isovector EMC effect corrections EMC effect and NuTeV anomaly are interpreted as evidence for medium modification of the bound nucleon wavefunction This result can be tested using PV DIS measurements predict large medium modification in PV DIS predict flavour dependence of EMC effect can be large In nuclei quark spin converted to orbital angular momentum Polarized EMC effect Important implications for nuclear physics 30 /30

31 Model Parameters Free Parameters: Λ IR, Λ UV, M 0, G π, G s, G a, G ω and G ρ Constraints: f π = 93 MeV, m π = 40 MeV & M N = 940 MeV 0 dx ( u v(x) d v (x)) = g A =.267 (ρ,e B /A) = ( fm 3, 5.7 MeV) a 4 = 32 MeV Λ IR = 240 MeV We obtain [MeV]: Λ UV = 644 M 0 = 400, M s = 690, M a = 990,... Can now study a very large array of observables: e.g. meson and baryon: quark distributions, form factors, GPDs, finite temp. and density, neutron stars 3 /30

32 Regularization Proper-time regularization X n = (n )! 0 dτ τ n e τ X (n )! /(ΛIR ) 2 /(Λ UV ) 2 dτ τ n e τ X Λ IR eliminates unphysical thresholds for the nucleon to decay into quarks: simulates confinement D. Ebert, T. Feldmann and H. Reinhardt, Phys. Lett. B 388, 54 (996). E.g.: Quark wave function renormalization Z(k 2 ) = e Λ UV (k 2 M 2) e Λ IR(k 2 M 2 ) Z(k 2 = M 2 ) = 0 = no free quarks Needed for: nuclear matter saturation, baryon, etc W. Bentz, A.W. Thomas, Nucl. Phys. A 696, 38 (200) 32 /30

33 Gap Equation & Mass Generation Quark Propagator: = + + π, ρ, ω,... /p m + iε Mass is generated via interaction with vacuum /p M + iε +... Dynamical Quark Mass (MeV) m q = 0 MeV m q = 5 MeV m q = 50 MeV G/G crit M(p) [GeV] Rapid acquisition of mass is effect of gluon cloud p [GeV] m = 0 (Chiral limit) m = 30 MeV m = 70 MeV Dynamically generated quark masses ψψ 0 DχSB Proper-time regularization: Λ IR and Λ UV No free quarks = Confinement [Z(k 2 = M 2 ) = 0] 33 /30

34 Off-Shell Effects For an off-shell nucleon, photon nucleon vertex given by Γ µ N (p,p) = [ ] Λ α (p ) γ µ f αβ + iσµν q ν 2M fαβ 2 + q µ f αβ 3 Λ α (p) α,β=+, In-medium nucleon is off-shell, extremely difficult to quantify effects However must understand to fully describe in-medium nucleon Simpler system: off-shell pion form factors relax on-shell constraint p 2 = p 2 = m 2 π Very difficult to calculate in many approaches, e.g. Lattice QCD q p p = (p + p) µ F π, (p 2, p 2, Q 2 ) + (p p) µ F π,2 (p 2, p 2, Q 2 ) For p 2 = p 2 = m 2 π we have F π, F π and F π,2 = 0 34 /30

35 Pion Off-Shell Form Factors Fπ,(p 2, p 2, Q 2 ) t = m 2 π t = 0.2 t = 0.4 Empirical p 2 = m 2 π p 2 = t Fπ,2(p 2, p 2, Q 2 ) t = m 2 π t = 0.2 t = 0.4 p 2 = m 2 π p 2 = t Q 2 (GeV 2 ) Q 2 (GeV 2 ) Potentially important for experimental extraction of F π q π + dσ/dt (µb/gev 2 ) 6 Q 2 =.60 σ L σ T 2 Q 2 = p p n t (GeV 2 ) t (GeV 2 ) May also be important for extracting G E /G M ratio from 4 He(e,e p) 3 H 35 /30

36 F γ 2 and F γz 2 EMC ratios Carbon.2. Z/N = (Carbon) EMC ratios R γ R γz Q 2 = 5.0 GeV 2 I. Sick and D. Day, Phys. Lett. B 274, 6 (992). Recall EMC ratio: x R i = F i 2A F i,naive 2A = F i 2A Z F i 2p + N F i 2n i γ, γz,... R γ 4 u A(x) + d A (x) 4 u 0 (x) + d 0 (x), RγZ.6 u A(x) + d A (x).6 u 0 (x) + d 0 (x) 36 /30

37 F γ 2 and F γz 2 EMC ratios Iron & Lead.2.2. Z/N = 26/30 (Iron). Z/N = 82/26 (Lead) EMC ratios R γ R γz Q 2 = 5.0 GeV 2 EMC ratios R γ R γz Q 2 = 5.0 GeV 2 I. Sick and D. Day, Phys. Lett. B 274, 6 (992). I. Sick and D. Day, Phys. Lett. B 274, 6 (992) x x R γ 4 u A(x)+d A (x) 4 u 0 (x)+d 0 (x) & R γz.6 u A(x)+d A (x).6 u 0 (x)+d 0 (x) Neutron rich Z/N < : u A (x) < d A (x) medium modification of u A increases & d A decreases u A dominates R γ however R γz almost isoscalar ratio ρ 0 -field = R γz > R γ Model Independent 37 /30

38 Flavour Dependence of EMC effect Flavour dependent EMC ratios R Fe R u Fe R d Fe Z/N = 26/30 (Iron) Q 2 = 5.0 GeV x Flavour dependent EMC ratios R Pb R u Pb R d Pb Z/N = 82/26 (Lead) Q 2 = 5.0 GeV x Flavour dependence is defined above by R A = F 2A q F2A naive = F q 2A q F q,naive R q A = F q 2A 2A F2A q, naive Flavour dependence determined by measuring e.g. F γ A q A q 0 If observed = strong evidence for medium modification and F γz A 38 /30