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 2 /19 n of nuclei medium modification 1 , 275 (1983). 123 8 . 0 6 . 0 x 4 . 0 2 . [European Muon Collaboration], Phys. Lett. B 0 EMC effect Before EMC experiment Experiment (Gomez 1994) et al. Fe 56 valence quarks in nucleus carry less momentum than in nucleo 0 2 1 9 8 7 6 1
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1 1 0 0 0 0
Understanding EMC effect critical for QCD based description Fundamentally challenged our understanding of nuclei J. J. Aubert Immediate parton model interpretation: ✦ What is the mechanism?nuclear After structure, more pions, than 6 25 quark years bags, no rescaling, consensus
2 2
F /F
Fe D ● ● EMC Effect ● ● ● ● 3 /19 1 8 . 0 of QCD 6 . 0 p x 4 ) . 2 2 0 2 Λ − 2 k k 0 GeV 16 GeV q k . . − − Θ( 2 = 5 = 0 p q . 2 2 0 0 G k AAC Q Q q q 0 p 2 0 8 6 4 2 . . . . . 0 0 0 0 0
−
v v ) ( ∆ and ) ( ∆ x u x x d x © + 1 p ) 2 2 2 ) 16 GeV 0 GeV 2 . . 8 2 . k 0 k ( = 0 = 5 k Z 2 0 2 − Q Q MRST (5.0 GeV p 6 k k . 0 x p 4 . 0 2 . 0 0 6 2 8 4 0 NJL model interpreted as low energy chiral effective theory Quark distributions given by Feynman diagram calculation
. . . .
1 1 0 0
v v ) ( and ) ( x u x x d x
Nambu–Jona-Lasinio Model and PDFs ● ● 4 /19 ) n ρ − p ρ ( iε ρ − G q / V channels = 2 − 0 ∗ I M ′ σ, ω, ρ L − , ρ / k + ) q n = symmetry energy ψ ρ 1 ) q − ⇔ + ) V ρ p k effective potential that provides ( ρ G q − ( ∗ S ω ⇒ interaction in = G M ¯ qq − ➞ = 6 ∂ mean fields couple to the quarks in nucleons i 0 ( iε : q − ψ saturation & = M , ω N 0 L − ρ = / k ± Z = 0 1 ω ⇔ − ) = ω k ) ( G d ( S u V Fundamental physics Hadronization + mean–field Finite density Lagrangian: Finite density quark propagator ✦
Asymmetric Nuclear Matter ● ● ● ● 5 /19 ) ) d u 1 3 − > V > V 16 fm u d 8 . evel . 0 V V ) ) ( ( = 0 x x n ( ρ ( f A + p 6 d d ρ . 0 = ρ changing] x )+ )+ -quarks -quarks 0 x x d u ρ ( ( 4 . 0 f A u 0 8 6 4 2 u . . . . . 4 = 1 = 0 = 0 = 0 = 0 = 0 4 2 . Z/N Z/N Z/N Z/N Z/N Z/N 0 ≃ n 2 [therefore 0
2 1 9 8 7 6 1 ......
NF 1 1 0 0 0 0 M ratios EMC A ratio 2 + F p 2 1 Z/N 3 − ZF 16 fm 8 . = . 0 = 0 n ρ A + naive 2 p 6 ρ . 0 A, F = 2 -quarks feel more repulsion than -quarks feel more repulsion than ρ d u F x : = 4 . : 0 2 4 6 8 . . . . 0 0 0 0 R 0 / / / / . ∞ = = 1 = 1 = 1 = 1 = 1 2 . Z/N Z/N Z/N Z/N Z/N Z/N 0 0
2 1 9 8 7 6 1 ......
1 1 0 0 0 0 EMC ratio: EMC effect essentially a consequence of binding at the quark l Density is fixed only changing proton excess neutron excess M ratios EMC ● Isovector EMC effect ● ● ● ● 6 /19 10000 ) “NuTeV anomaly” CDF [over 400 citations] D0 syst ⇒ 1000 = -pole Z σ 100 0009( . : 3 0 10 ± NuTeV ) 0004 . 1 0 stat (GeV) , 091802 (2002) ± Q 88 1 . 0 27 0013( . PV-DIS [JLab] 0 22 . 01 . ± 0 complete explanation SLAC E158 = 0 Qweak [JLab] 77 Standard Model Completed Experiments Future Experiments Møller [JLab] 001 W . 22 0 θ . 2 APV(Cs) Phys. Rev. Lett. = 0 sin W 250 245 240 235 230 225 et al.
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θ 0 0 0 0 0 0
W
sin
θ 2 MS 2 sin G. P. Zeller No universally accepted NuTeV: ✦ World average Huge amount of experimental & theoretical interest ● Weak mixing angle and the NuTeV anomaly ● ● ● 7 /19 − A − A ) ± 30 xd xd W / A + − ⇒ d 26 . − A − A = ) + ≃ 0 xu xu A ρ P W u R 0028 . Z/N 0 ≪ , CC W 0 + + ∆ θ A s Z 2 ⇒ sin Fermi P W 0004 = . 7 3 R 0 and if − flavour dependent EMC effect A 1 d + ∆ ⇔ ≃ + 0107 + on an Fe target ( . A naive P W , NC u (0 R W P W ¯ ¯ νA νA CC NC − θ R σ σ 2 = ∆ = − − sin correction can explain up to 65% of anomaly P W − νA CC νA NC 0 R σ σ 2 1 ρ ∆ = = P W R P W R Correct for neutron excess Isoscalarity Paschos-Wolfenstein ratio motivated the NuTeV study: For an isoscalar target NuTeV “measured” Use our medium modified “Fe” quark distributions ● ● ● ● ● Paschos-Wolfenstein ratio ● 8 /19 u > V d V , 275 (1983).] 123 ⇒ = , Phys. Lett. B et al. , N>Z vector fields -quarks [J. J. Aubert d Nucl. Matt. symmetry energy + V + q − - to V + u p − no NuTeV anomaly - Charge Symmetry Violation x d + m ⇒ V is evidence for medium modification + = − p = + )] u p ¯ s is fixed by nature of is constrained by m − 0 q s ( + x V [ + − p + + p 0 ρ “NuTeV anomaly” )= x -field shifts momentum from ( 0 q CSV+ No evidence for physics beyond the Standard Model Equally interesting EMC effect has over 850 citations ρ sign of correction size of correction vector field reduces NuTeV anomaly – Model Independent!! 0 ρ Also correction from ✦ ✦ Instead ✦ ✦ Model dependence? ✦ ✦ ✦
NuTeV anomaly cont’d ● ● ● ● 9 /19 l on 10000 ) ¯ s CDF D0 − 1000 s ( -pole x Z + 100 0 ρ 10 -DIS ν CSV+ 1 (GeV) Q 1 . 0 PV-DIS [JLab] 01 . 0 SLAC E158 Qweak [JLab] Standard Model Completed Experiments Future Experiments Møller [JLab] 001 . 0 APV(Cs) 250 245 240 235 230 225
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0 0 0 0 0 0
W
sin θ
MS 2 Includes NuTeV functionals with: Small increase in systematic error NuTeV anomaly interpreted as evidence for medium modificati Equally profound as evidence for physics beyond Standard Mode
Total NuTeV correction ● ● ● ● 10 /19 X X P of NuTeV result σ ′ ℓ ± ′ 1.5 ,s ′ ∼ , W 0 k θ γ, Z q P,S interference γZ A k,s ℓ interaction violates parity 0 is this mechanism observable elsewhere? Z We claim isovector EMC effect explains ✦ Yes – parity violating DIS: ✦
Observable elsewhere? ● ● 11 /19 W θ ) 2 x ( sin 3 q a , e 2 2 of NuTeV result 2 ) ) γ 2 γZ 3 y y σ − F F − − 2 1 2 1 e 1.5 V ± ± g (1 ) ∼ 2 x = = − ( − 3 1 1+(1 q V q A a = + ) ) x ( interference x 3 ( , g 2 a ) , g a ignore γZ q ) ¯ q + ¯ ∝ − q ⇒ ( L L q = γ ( 2 x γZ 2 dσ dσ F F q q V A − + g g e A e A q q g g R R e e 2 dσ dσ ≪ − X X e V = = g ) x = 2 = 2 PV ( 2 A a γZ γZ 2 3 is this mechanism observable elsewhere? F F We claim isovector EMC effect explains ✦ Yes – parity violating DIS: Parton model expressions
Observable elsewhere? ● ● ● 12 /19 1 W θ 2 8 . 0 4 sin − 2 naive 2 9 5 a a 6 . 0 126 (Lead) ery large / A x = 82 4 . ) ) 0 x x ( ( Z/N 2 + A + A d d 2 . 0 − = 5 GeV )+ ) 2 x x Q ( ( + A + A 0 u u 1 1 9 8
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1 0 0
A ) ( x a 2 12 25 evidence for medium modification 1 − ➞ W θ ) 2 W x 8 θ . ( 0 2 4 sin 2 a − 2 naive 2 5 9 a a 4 sin 6 . 0 30 (Iron) − / A 5 9 x = 26 4 . 0 target: )= Z/N x Z ( 2 2 ≃ a dependence of 2 . 0 x N = 5 GeV 2 Q 0 1 1 9 8
Large For a After naive isoscalarity corrections medium effects still v “Naive” result has no medium corrections . . .
1 0 0
A ) ( x a 2 ● ● Parity Violating DIS: Iron & Lead ● ● 13 /19 1 2 u 8 . 0 > V = 5.0 GeV d A 2 γZ 2 V Q F 6 . 0 126 (Lead) / x and = 82 4 . A 0 γ -quarks: 2 f f u Z/N F /u /d γ Pb A A quarks + d R u 2 d . V + 0 q − V to + p u − 0 1 2 1 9 8 7 6 quarks
x ......
1 1 0 0 0 0 lvu eedn M ratios EMC dependent Flavour d + V + 1 − p + 2 p 0 8 . 0 q = 5.0 GeV + 2 V Q + − p 6 . 30 (Iron) + 0 / p x = 26 very strong evidence for medium modification -quarks feel more repulsion than )= d 4 . x 0 ⇒ ( Z/N f f = q /u /d ⇒ γ Fe A A d R u = 2 . 0 field has shifted momentum from quarks are more bound than 0 u ρ 0
2 1 9 8 7 6 1 ✦ N >Z Flavour dependence determined by measuring ✦ If observed ......
1 1 0 0 0 0 lvu eedn M ratios EMC dependent Flavour ● Flavour Dependence of EMC effect ● ● 14 /19 . . . on limit 04 . B, 11 = 0 Li, J n 7 P /A 1 ⇒ = & n 1 g n 2 86 H n . P A NF H 1 + A = 0 g 2 p + J p 1 F p g P 2 27 H p . P ZF A = = Li 7 A A 2 A naive H 1 naive 2 F A g H, 1 F g = = R H s R Must choose nuclei with protons should carry most of the spin e.g. From Quantum Monte–Carlo: EMC ratio Polarized EMC ratio Spin-dependent cross-section is suppressed by ✦ ✦ Ideal nucleus is probably ✦ Ratios equal 1 in non-relativistic and no-medium modificati
Finite nuclei EMC effects ● ● ● ● ● 15 /19 1 2 8 . = 5 GeV 0 2 Q 6 . 0 x 1 4 C . 0 12 2 8 2 . . = 5 GeV 0 0 Experiment: Unpolarized EMC effect Polarized EMC effect 2 Q B 11 6 0 . 0
2 1 9 8 7 6 1 ......
1 1 0 0 0 0 M Ratios EMC x Al 4 . 27 0 1 2 Al 27 2 8 . . = 5 GeV 0 0 Experiment: Unpolarized EMC effect Polarized EMC effect 2 Q Al 27 6 . B and 0 0 1 2 1 9 8 7 6 ......
11
1 1 0 0 0 0 x M Ratios EMC 4 Be . 9 Li, 0 7 2 . 0 Experiment: Unpolarized EMC effect Polarized EMC effect Li 7 0
2 1 9 8 7 6 1 ......
1 1 0 0 0 0 M Ratios EMC
EMC ratio 16 /19 1 2 8 . = 5 GeV 0 2 Q 6 . 0 xx Al 4 . 27 0 2 . 0 Experiment: Unpolarized EMC effect Polarized EMC effect Al 27 0
2 1 9 8 7 6 1 ......
1 1 0 0 0 0
M Ratios Ratios EMC EMC
Is there medium modification 17 /19 1 2 8 . = 5 GeV 0 2 Q 6 . 0 xx Al 4 . 27 0 2 . 0 Experiment: Unpolarized EMC effect Polarized EMC effect Al 27 0
2 1 9 8 7 6 1 ......
1 1 0 0 0 0
M Ratios Ratios EMC EMC Large splitting very difficult without medium modification Medium modification of nucleon has beenRelativistic switched off effects remain
Is there medium modification ● ● ● 18 /19 m A g g J in-medium + q L Σ ∆Σ + 1 2 d = ∆ 2 1 = J u ∆ 0.970.91 -0.300.88 -0.290.87 0.67 -0.280.87 0.62 -0.28 1.267 0.79 0.60 -0.28 1.19 0.59 -0.26 1.16 0.59 1.15 0.53 1.15 1.05 orbital angular momentum and therefore quarks are more relativistic ➞ Nuclear Spin Sum ● ● 19 /19 ], etc re in nuclei] ription of nuclei q L ➞ [quark spin converted complementary approach to traditional nuclear physics result can be tested using PV DIS polarized EMC effect flavour dependence of EMC effect PV DIS, pion induced Drell-Yan, neutron knockout in-medium form factors [Strauch], Coulomb sum rule [Meziani ✦ EMC effect and NuTeV anomaly aremedium interpreted modification of as the evidence for bound nucleon✦ wavefunction Slowly building a QCD based understanding of nuclear structu Illustrated the inclusion of quarks into✦ a traditional desc Some important remaining challenges: ✦ Exciting new experiments: ✦ Significant omissions: quasi-elastic scattering ✦ Conclusion ● ● ● ● ● ● 20 /19 rd Model , , 4050(27) 4066 . . A A ¯ s s 0016(8) . = 0 = 0 A A 4034(28) . ¯ ν ¯ x x ν R R − A = +0 = 0 − A d + 6 + 6 & d & ¯ ¯ ν ν A A A , finding A ¯ ¯ R x ¯ d d ν x δR A A R − − x x − A − A + u & & u and + 3 A 3916(13) A 3950 . ν A . ¯ x u A x R ¯ u A = 0 = 0 x A ν x 2 Rd ν separately + 2 Ru g R R g ¯ ν A 0017(8) . + 3 d + 0 R + 3 3933(15) A A . − ⇒ ⇒ d x 2 Lu 2 Ld = = g A g = = 0 3 and x ν + 3 ν 2 + 2 ν A R − δR u A R u A x A 3 x = = ¯ ν ν NuTeV Standard Model δR δR Both results, after corrections, basically agree with Standa Recall NuTeV actually measured ✦ ✦ Corrections to Standard Model expressions are: We find: This implies: Corrections to ● ● ● ● ● 21 /19 3) ) − x = ( A, P κ | ( 2) ) α,κ = 1) − q − 2 κ / ξ = ( 5 ) ( d κ 1) q A ( 2 − / y ψ 1 ( 2 p = / + 3 κ p γ ( 2 α,κ,m / (0) f 1 s q ) ψ x | protons A y A, P − A /A x ( − ξ A x dx δ + iP Z e modified convolution formalism A − π neutrons dy 2 dξ He 4 Z Z C using a + 12 O A X α,κ,m P 16 Si )= 28 )= A A x x ( ( A A q q Approximate Definition of finite nuclei quark distributions Finite nuclei quark distributions ● ● 22 /19 rs ) p d ( ts value β Λ i leus is αβ 3 f µ q + αβ 2 f ν q µν iσ 1 M 2 + αβ 1 f ) µ 2 γ h for example: M ) ′ p = ( 2 α p Λ − , =+ α,β X = mass, magnetic moment, size quark distributions, form factors, GPDs, etc nucleon propagator is changed in medium off-shell effects ( Lorentz covariance implies bound nucleon has 12 EM form facto µ J composed of nucleon-like objects may change in medium – understanding of nuclei Need to understand these effects as first step toward QCD base 50 years of traditional nuclear physics tells us that the nuc However if a nucleon property is not protected by a symmetry✦ i ✦ There must be medium modification: ✦ ✦ ✦ Medium Modification ● ● ● ● 23 /19 d ts value leus is ) p ( u ) 2 Q ( 2 F ν q µν iσ 1 M 2 ) )+ 2 2 Q M ( 1 = F 2 µ p γ ) ′ p ( u = ¯ µ J mass, magnetic moment, size quark distributions, form factors, GPDs, etc nucleon propagator is changed in medium off-shell effects ( Becomes 2 form factors for an on-shell nucleon composed of nucleon-like objects may change in medium – for example: understanding of nuclei Need to understand these effects as first step toward QCD base 50 years of traditional nuclear physics tells us that the nuc However if a nucleon property is not protected by a symmetry✦ i ✦ There must be medium modification: ✦ ✦ ✦ Medium Modification ● ● ● ● 24 /19 ) s tions nuclei ! + V N >Z + q − V + p -quarks − d x u + - to u V > V + d − p V + p ⇒ 0 = q + V + -field − p 0 + p )= [Thomas 1998, Bentz 2003, Miller 2005] x ( N>Z ρ q -field shifts momentum from 0 quarks feel nuclear medium struck quark does not feel vector-field (asymptotic freedom For ρ large flavour dependence of EMC effect for ✦ Result As we will see this result has important testable consequence The effect of vector-field is model independent✦ under assump ✦ All medium modification models should obey thisImportant result observation ✦ ✦ Model Independent Results? ● ● ● ● ● F γ F γZ 2 and 2 EMC ratios – “Iron” & “Lead” 1.2 1.2 1.1 Z/N = 26/30 (Iron) 1.1 Z/N = 82/126 (Lead) 1 1 0.9 0.9 0.8 0.8 EMC ratios EMC ratios γ γ 0.7 R 0.7 R RγZ Q2 = 5.0 GeV2 RγZ Q2 = 5.0 GeV2 0.6 I. Sick and D. Day, Phys. Lett. B 274, 16 (1992). 0.6 I. Sick and D. Day, Phys. Lett. B 274, 16 (1992). 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x x i ● Ri = F2A , Rγ 4 uA(x)+dA(x) & RγZ 1.16 uA(x)+dA(x) F i 4 u0(x)+d0(x) 1.16 u0(x)+d0(x) 2A,naive ∼ ∼ γ γZ ● uA dominates R whereas R is almost isoscalar ratio ● N >Z: d-quarks feel more repulsion than u-quarks: Vd > Vu + + + p p Vq q(x)= + + q + + x + + p −V 0 p −V − p −V ● ρ -field = RγZ >Rγ – Model Independent 0 ⇒ 25 /19 26 /19 H ) A 2 − 2 ] F , Q A ) = 2 x ) ( A H 1 2 A H 1 F x, Q g ( xF 1 σ g p ] ⇒ λ = 2 σ = q q p 2 λ F q p q ( µνλσ structure functions p iε parity µνλσ γ iε )+ ; 2 + 1 ) )+ J 2 , Q A 2 [ x A ( x quark distributions Callen-Gross ( H A x, Q ( A q & H 2 2 J + 1 F F 6 )+ J 2 A [ ν ν q q H x are nuclei p p ( µ µ 1 6 p p H A p p q J > + + A J Bjorken limit − x q q 2 2 : 2 q q q e p p J : in q µν µν target g g 1 2 X = = = )= J H µν µν A x W W ( only targets with study QCD and nucleon structure at finite density For For arbitrary A H 2 F Hadronic Tensor Parton model expressions Why nuclear targets? ✦ ✦ ✦ ✦ DIS on Nuclear Targets ● ● ● 27 /19 H ) A 2 − 2 F , Q A ) = 2 x ) ( A H 1 2 A H 1 F x, Q g xF ( 1 σ g p ] ⇒ λ = 2 σ = q q p 2 λ F q p q µνλσ p iε parity µνλσ structure functions] iε )+ ; 2 + 1 ) )+ J 2 , Q A 2 [ x A ( x quark distributions ( H A x, Q ) ( A q H 2 2 x J + 1 ( F F A 6 )+ J H 2 2 A [ ν ν F q q H x p p ( J µ µ 6 p p H A p p − q = J + + J H A − x q q 2 2 X : 2 q q q e p p J q + 1 µν µν target 1 g g J 1 2 X 2 = = = )= )= J H x µν µν A ( x W W A ( For For arbitrary 2 A H 2 F F Parton model expressions Hadronic Tensor: in Bjorken limit &✦ Callen-Gross ( ✦ DIS on Nuclear Targets ● ● J 28 /19 2 ,..., 2 , 2 / rmalism A 2 1 1 2 = 0 q F y distributions K − ≃ 3 2 2 q , / A ) 3 2 x = F ( H (2) q q ⇒ = 0 H 3 2 − 2 1 q J J K = H + J 3 2 q + 1 = K 2 (0) √ q H − J −→ 1) 2 3 − ( = H and for example if: J X 8 & ≡ ) A x ( ) If K ( q This is a model independent result within the convolution fo Assume all spin is carried by the✦ valence nucleons Introduce multipole quark distributions Example: Higher multipoles encapsulate difference between helicit ● Convolution Formalism: implications ● ● ● ● 29 /19 4 2 . . 1 1 2 . 1 0 (1) A . 1 u ∆ (1) A A 0 d . x 1 ∆ 8 . A 0 x 8 . 0 A 6 A x . 0 x 6 . 0 4 . 4 0 . 0 2 . 2 . 0 0 Al Al 27 27 0 0 0 0 2 0 8 6 4 2 2 0001 0002 0003 0002 0001 ...... . . . . . 1 1 0 0 0 0 0 0 0 0 0 0 A − A A A − − ) ( ∆ x q x A A ) ( A x u x (1) (4) 2 2 . . 1 1 0 0 . . 1 1 8 . 8 . 0 0 6 A . 6 A 0 . x 0 x multipole PDFs would be very surprising 4 . 4 0 1 . 0 large off-shell effects &/or non-nucleon components, etc 2 . 0 2 . K > 0 Al ⇒ Al = 27 27 0 0 0 004 003 002 001 001 002 4 0 6 2 8 4 0 ...... Large ✦ ...... 0 0 0 0 0 0 2 2 1 1 0 0 A A A A − − A A ) ( A x u x ) ( A x u x (0) (2) Some multipole quark distributions result ● F γ F γZ 2 and 2 EMC ratios – “Carbon” 1.2 1.1 Z/N = 1 (Carbon) 1 0.9 0.8 EMC ratios γ 0.7 R RγZ Q2 = 5.0 GeV2 0.6 I. Sick and D. Day, Phys. Lett. B 274, 16 (1992). 0 0.2 0.4 0.6 0.8 1 x ● Recall EMC ratio: F i F i Ri = 2A = 2A i γ, γZ, ... i,naive ZF i + NF i ∈ F2A 2p 2n 4 u (x)+ d (x) 1.16 u (x)+ d (x) Rγ A A , RγZ A A ∼ 4 u0(x)+ d0(x) ∼ 1.16 u0(x)+ d0(x) 30 /19 F γ F γZ 2 and 2 EMC ratios – “Iron” & “Lead” 1.2 1.2 1.1 Z/N = 26/30 (Iron) 1.1 Z/N = 82/126 (Lead) 1 1 0.9 0.9 0.8 0.8 EMC ratios EMC ratios γ γ 0.7 R 0.7 R RγZ Q2 = 5.0 GeV2 RγZ Q2 = 5.0 GeV2 0.6 I. Sick and D. Day, Phys. Lett. B 274, 16 (1992). 0.6 I. Sick and D. Day, Phys. Lett. B 274, 16 (1992). 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x x ● Rγ 4 uA(x)+dA(x) & RγZ 1.16 uA(x)+dA(x) ∼ 4 u0(x)+d0(x) ∼ 1.16 u0(x)+d0(x) γ γZ ● uA dominates R where R almost isoscalar ratio ● N >Z: d-quarks feel more repulsion than u-quarks: Vd > Vu + + + p p Vq q(x)= + + q + + x + + p −V 0 p −V − p −V ● ρ -field = RγZ >Rγ – Model Independent 0 ⇒ 31 /19 32 /19 = 0 E ) x ( (5) q ∆ 2 x D , 343 (1989). = n EMC effect in light nuclei ● ● ● 34 /19 ucleus PV DIS , 2479 (1990). 64 , PRL. et al. E772: Alde , − + µ µ E906: running FNAL – ′ γ X X − µ ′ X + X P P µ ¯ q q → ¯ therefore expect pion (anti-quark) enhancement in nuclei sees no pion enhancement compared to free nucleon qq ′ , S Pions play a fundamental role in✦ traditional nuclear physics Drell-Yan experiment set up to probe anti-quarks✦ in target n ✦ Important to understand anti-quarks in nuclei: Drell-Yan & ′ P, S P ′ A A Anti-quarks in Nuclei and Drell-Yan ● ● ● 35 /19 MeV ρ G = 940 and . . . N 267 ω ) . M , G , = 1 MeV a A 7 G g . = 990 , a s 15 M MeV & G − : quark distributions, form factors, GPDs, )) = , , 3 x , ( π − v G d fm = 140 , ∆ 0 = 690 π 16 . − s M m ) : , M x ( MeV v , UV )=(0 u MeV, MeV Λ : [MeV]: /A (∆ , = 644 B = 240 meson and baryon = 400 IR = 93 dx = 32 0 Λ IR UV 1 4 π 0 ρ, E finite temp. and density, neutron stars f R ( a Λ Λ M e.g. We obtain Free Parameters Constraints ✦ ✦ ✦ ✦ ✦ ✦ ✦ Can now study a very✦ large array of observables: ● ● ● Model Parameters ● 36 /19 τX − e 1 − n , etc dτ τ 2 2 ) ) ) baryon 2 IR UV M ∆ (Λ − for the nucleon to decay into , / (Λ 2 1 / k , 154 (1996). 1 ( Z 388 τX IR − Λ e − 1)! no free quarks 1 e 1 − − , 138 (2001) − n n ) ( 696 2 ⇒ M dτ τ − 2 ∞ k 0 ( −→ Z UV )=0 = Λ unphysical thresholds 2 1)! − e 1 nuclear matter saturation − M simulates confinement n = ( )= 2 2 → k k = : ( ( n eliminates Z Z 1 D. Ebert, T. Feldmann and H. Reinhardt, Phys. Lett. B W. Bentz, A.W. Thomas, Nucl. Phys. A X IR ➞ Λ Proper-time regularization quarks ✦ E.g.: Quark wave function renormalization ✦ Needed for: ✦ Regularization ● ● ● ● 37 /19 SB χ D . . . m = 0 (Chiral limit) m = 30 MeV m = 70 MeV + 2 3 ⇐⇒ iε p [GeV] π, ρ, ω,... + ) = 0] = 0 2 1 Rapid acquisition of mass is effect of gluon cloud 1 M M − ψψ = / p 2 k 0 ( 0 0.1 0.3 0.2 0.4 ➞ [GeV] M(p) Z [ ⇐⇒ + UV iε Λ + 1 0 . m 2 and 8 . − 1 IR / p Λ 6 . 1 : 4 + . Confinement 1 1 − 2 . ⇒ 1 = crit 0 . 1 : G/G 8 . 0 6 . 0 = 50 MeV = 5 MeV = 0 MeV = q q q 1 m m m 4 . − 0 2 . 0 0 No free quarks 0 50 400 350 300 250 200 150 100 yaia ur as(MeV) Mass Quark Dynamical Quark Propagator Mass is generated via interaction with vacuum Dynamically generated quark masses Proper-time regularization ➞ Gap Equation & Mass Generation ● ● ● ● 38 /19 ) 2 n , Q ) 2 p QCD ( ,p α 2 ′ p Λ ( 2 tify effects π, αβ 3 F f µ ) µ p q = 0 − + ′ 2 p π, αβ 2 F f ν )+( q 2 2 π M µν and m , Q 2 2 iσ π = ,p F 2 2 + ′ p p ( → αβ 1 1 = 1 f π, 2 ′ π, F µ p F µ γ ) p ) ′ + p ′ ( p α Λ =( we have − , 2 π =+ m X ′ p α,β = q 2 p )= = ,p ′ 2 p ′ p p However must understand to fully describe in-medium nucleo relax on-shell constraint Very difficult to calculate in many approaches, e.g. Lattice ( µ N Γ Simpler system: off-shell pion form factors ✦ For For an off-shell nucleon, photon–nucleon vertex given by In-medium nucleon is off-shell, extremely difficult to✦ quan ✦ Off-Shell Effects ● ● ● ● 39 /19 2 . 2 . 1 1 ,... 6 6 . . ) 0 x . free scalar + Fermi + vector 0 = 0 . free scalar + Fermi + vector 1 = 0 1 ( n d Z/N Z/N 8 . 8 . 0 0 = ) x 6 A . 6 A . ( 0 x 0 x p u 4 . 4 . 0 0 ➞ 2 . 2 . 0 0 differ ) d 0 0 ( 0 2 0 8 6 4 2 ...... 0 2 0 8 6 4 2 u ...... 1 1 0 0 0 0 1 1 0 0 0 0 A A A ) ( A x u x A A A ) ( A x d x V 2 . 2 . 1 1 = 1 0 . = 1 free scalar + Fermi + vector 0 . free scalar + Fermi + vector 1 1 Z/N Z/N 8 . 8 . 0 Fermi motion and 0 n Differences arise from: 6 A . 6 A . & – 0 x 0 x p : 4 . 4 . 0 0 fixed : different number protons and neutrons = 2 . 2 . 0 0 n ρ naive medium + 0 0 2 0 8 6 4 2 0 ...... 0 2 0 8 6 4 2 p ...... 1 1 0 0 0 0 1 1 0 0 0 0 A A A ) ( A x u x ρ ✦ ✦ A A A ) ( A x d x Results: Nuclear Matter ● 40 /19 5 2 π H 3 m 4 2 ) . . 2 2 π − t m = 0 = = 0 4 = = =2.45 t t t 2 2 2 ′ -t (GeV Q − − − p p 3 ) He(e,e’p) 2 4 (GeV π 2 F Q 2 from 0.1 0.2 0.3 0.4 2 1 0 of ) 2 L T σ σ ratio =1.60 1 2 Q -t (GeV M /G 0 E 3 2 1 0 . . . G 0 0 0 π, ′ ) ( Q , p , p F 2 2 2 2 6 4 2 0 5 0.05 0.1 0.15 0.2 0.25 ) b/GeV ( /dt d µ σ 2 2 π m 4 2 . . 2 π − t m = = 0 = 0 4 extracting = = t t t 2 2 ′ − Empirical − − p p + π 0 3 ) 2 6 n (GeV 2 2 p Q 2 q important for experimental extraction 1 p 0 0 0 8 6 4 2 . . . . . 1 0 0 0 0 Potentially May also be important for π, ′ ) ( Q , p , p F 1 2 2 2 Pion Off-Shell Form Factors ● ●