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Proton Spin Puzzle: 20 years later

Proton Spin Puzzle: 20 years later. Hai-Yang Cheng Academia Sinica Deep inelastic scattering Proton spin puzzle Experimental & Theoretical progresses. Lattice JC, October 19, 2007. Non-relativistic SU(6) constituent QM

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Proton Spin Puzzle: 20 years later

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  1. Proton Spin Puzzle: 20 years later • Hai-Yang Cheng • Academia Sinica • Deep inelastic scattering • Proton spin puzzle • Experimental & Theoretical progresses Lattice JC, October 19, 2007

  2. Non-relativistic SU(6) constituent QM ⇒ proton spin comes from constitutent quark’s spin. U=4/3, D=-1/3, so that U+D=1. However, this model predicts gA=5/3, while gA=1.258 experimentally Relativistic QM ⇒ quark spin + orbital angular momentum = Q+ Lq ½(0.65+0.35) How to explore the proton’s spin content ? It can be studied in deep inelastic scattering (DIS)

  3. Deep Inelastic Scattering e’(E’,p’) k’ e(E,p)  DIS process l+p→l+X was first studied by Friedman, Kendall, Taylor (’67-’69) at SLAC * N q+ : Unpolarized structure functions: F1(x,Q2), F2(x,Q2) F1(x) = ½ ∑ ei2[qi+(x)+qi-(x)] = ½ ∑ ei2qi(x) x: fraction of proton’s momentum carried by the struck quark, 0<x<1 q- : • Structure functions ⇒ • 3 valence quarks • sea quarks • half of proton’s momentum carried by gluons

  4. Polarized DIS Consider polarized DIS process: l+p→l+X and measure asymmetry g1p(x)= ½∑ei2[qi+(x)-qi-(x)]= ½∑ei2qi(x) Dq(x,Q2)= In general, q=qv+qs. In absence of sea polarization 10 g1p(x)dx=½∑eq2q=½(4/9 uv+1/9dv) neutron  decay ⇒ uv- dv= gA3 = 1.2695±0.0029 hyperon  decay ⇒ uv + dv= gA8 = 0.585±0.025 uv = 0.93±0.02, dv = -0.34±0.02, 10 g1p(x)dx  0.18 first derived by Ellis & Jaffe in 1974

  5. SLAC (’76,’83) covers the range 0.1<x<0.7 0.70.1 g1p(x)dx = 0.094±0.016 Extrapolation to the unmeasured x region⇒ 10 g1p(x)dx=0.17±0.05, consistent with Ellis-Jaffe sum rule EMC (European Muon Collaboration, 87-89), 0.01<x<0.7 at <Q2>=10.7 GeV2 0.70.1 g1p(x)dx = 0.090 ± 0.015 0.10.01 g1p(x)dx = 0.030 ± 0.016 Hence, 10 g1p(x)dx = 0.126 ± 0.018 Lower than EJ sum rule expectation ⇒ importance of sea polarization

  6. Solving the three equations for q u-d = 1.2695±0.0029, u+d-2s = 0.585±0.025 • yields • u = 0.77±0.06, d = -0.49±0.06, s = -0.15±0.06 • ≡ u+d+s = 0.14±0.18 • Two surprises: • strange sea polarization is sizable & negative • very little of the proton spin is carried by quarks ⇒ Proton Spin Crisis

  7. The so-called “proton spin crisis” is not pertinent since the proton helicity content explored in the DIS experiment is, strictly speaking, defined in the infinite momentum frame in terms of QCD current quarks and gluons, whereas the spin structure of the proton in the proton rest frame is referred to the constituent quarks. ….. It is not sensible to compare apple with orange. What trigged by the EMC experiment is the “proton helicity decomposition puzzle” rather than the “proton spin crisis” HYC, hep-ph/0002157 q( momentum frame) qQM(rest frame)

  8. Experimental Progress 1=10 g1(x)dx • x has been pushed down to O(10-3 - 10-4)

  9. COMPASS, HERMES =u+d+s=0.33±0.06 (0.14±0.18) ⇒ u = 0.84±0.02 (0.77±0.06) d = -0.43±0.02 (-0.49±0.06) s = -0.09±0.02 (-0.15±0.06)

  10. HERMES result from Semi-inclusive DIS Airapetian et al, PRL 92 (2004) 012005 • Sea quark polarization The result for s is very different from the inclusive DIS plus SU(3) symmetry analysis!

  11. COMPASS result from Semi-inclusive DIS arXiv:0707.4077 uv+dv=0.41±0.07±0.05 u+d=0.0±0.04±0.03 ⇒ u & d are of opposite sign ⇒ asymmetric sea polarization unpolarized sea: d > u (violation of Gottfried sum rule)

  12. Anomalous gluon interpretation Consider QCD corrections to order s : Efremov, Teryaev; Altarelli, Ross; Leader, Anselmino; Carlitz, Collins, Muller (88’) from (a) from (b) Anomalous gluon contribution (s/2)G arises from photon-gluon scattering. Since G(Q2)  lnQ2 and s(Q2)  (lnQ2)-1⇒ s(Q2)G(Q2) is conserved and doesn’t vanish in Q2→ limit G(Q2) is accumulated with increasing Q2 Why is this QCD correction so special ?

  13. QCD corrections imply that If G is positive and large enough, one can have s  0 and u+d  0.60 ⇒ proton spin problem is resolved provided that G  (2/s)(0.09)  1.7 ⇒ Lq+G also increases with lnQ2 with fine tuning This anomalous gluon interpretation became very popular after 1988 Lam, Li (1982): 36 Ratcliffe (1983):118 Efremov,Teryaev (May 1988): ? Altarelli, Ross (June 1988): 618 Leader, Anselmino (July 1988): ? Carlitz, Collins,Mueller (Sept 1988): 538 • Historical remarks: • Moments of g1,2 was first computed by Kodaira (’80) using OPE • In 1982 Chi-Sing Lam & Bing-An Li obtained anomalous gluon contribution to 1p and identified G with <N|K|N> • The photon-gluon box diagram was also computed by Ratcliffe (’83) using dimensional regularization • The original results in 1988 papers are not pQCD reliable

  14. Operator Product Expansion moments of structure function= 10 xn-1F(x)dx = ∑ Cn(q)<p,s|On|p,s> = short-distance  long-distance No twist-2, spin-1 gauge-invariant local gluonic operator for first moment • OPE ⇒ Gluons do not contribute to 1p ! One needs sea quark polarization to account for experiment (Jaffe, Manohar ’89) • How to achieve s  -0.09 ? Sea polarization (for massless quarks) cannot be induced perturbatively from hard gluons (helicity conservation ⇒ s=0 for massless quarks) • J5 has anomalous dimension at 2-loop (Kodaira ’79) ⇒ q is Q2 dependent, against intuition

  15. A hot debate between anomalous gluon & sea quark interpretations before 1995 ! anomalous gluon sea quark Efremov, Teryaev Altarelli, Ross Carlitz, Collins, Muller Soffer, Perparata Strirling Roberts Ball, Forte Gluck, Reya, Vogelsang Lampe Mankiewicz Gehrmann …. Anselmino, Efremov, Leader [Phys. Rep, 261, 1 (1995)] Jaffe, Manohar Bodwin, Qiu Ellis, Karlinear Bass, Thomas …

  16. Factorization scheme dependence • It was realized by Bodwin, Qiu (’90) and by Manohar (’90) that hard gluonic contribution to 1p is a matter of convention used for defining q fact. scheme dependent • Consider polarized photon-gluon cross section • Its hard part contributes to CG and soft part to qs. This decomposition depends on the choice of factorization scheme • It has an axial QCD anomaly that breaks down chiral symmetry Int. J. Mod. Phys. A11, 5109 (1996)

  17. Photon-gluon box diagram is u.v. finite. CG is indep of choice of IR & collinear regulators, but depends on u.v. regulator of q/G(x)=qG(x) • Polarized triangle diagram has axial anomaly ⇒ If u.v. cutoff respects gauge symmetry but breaks chiral symmetry ⇒ qG 0 GI anomaly CI Axial anomaly resides at k2→ qG convolutes with G to become qs HYC(’95) Muller, Teryaev (’97)

  18. Two extreme schemes of interest (HYC, ’95) • gauge-invariant (GI) scheme (or MS scheme) • -- Axial anomaly is at soft part, i.e. qG, which is non-vanishing due to chiral symmetry breaking and 10CG(x)=0 (but G  0 !) • -- Sea polarization is partially induced by gluons via axial anomaly • chiral-invariant (CI) scheme (or “jet”, “parton-model”, “kT cut-off’, “Adler-Bardeen” scheme) Axial anomaly is at hard part, i.e. CG, while hard gluons do not contribute to qs due to chiral symmetry • Hard gluonic contribution to  g1p is matter of factorization convention used for defining q • It is necessary to specify the factorization scheme for data analysis

  19. My conclusion: In retrospect, the dispute among the anomalous gluon and sea-quark explanations…before 1996 is considerably unfortunate and annoying since the fact that g1p(x) is independent of the definition of the quark spin density and hence the choice of the factorization scheme due to the axial-anomaly ambiguity is presumably well known to all the practitioners in the field, especially to those QCD experts working in the area. hep-ph/0002157

  20. How to probe gluon polarization ? • DIS via scaling violation in g1(x,Q2) • photon or jet or heavy quark production in polarized pp collider, lepton- proton collider or lepton-proton fixed target RHIC (at BNL): via direct high-pT prompt ,  production, jet production HERMES (at DESY): via open charm production COMPASS (at CERN): via open charm production

  21. Q-evolution in inclusive spin structure function g1(x,Q2) • NLO splitting functions Pij are available in ’95 • van Neerven, Mertig, Zijlstra • ⇒ A complete & consistent NLO analysis of g1 data is possible • Most analyses are done in MS scheme (GI) • uv(x), dv(x) are fairly constrained • Sea distribution is poorly constrained • G(x) is almost completely undetermined

  22. Direct measurement of G: Photon-Gluon-Fusion process • COMPASS:G(x)/G(x)= -0.57±0.41±0.17 HERMES: G(x)/G(x)=0.078±0.011±0.05 at <x>=0.204 • Direct measurements do not discriminate between G>0 & G<0 • Large G 2-3 ruled out by data

  23. RHIC:The First Polarised pp Collider

  24. Jet production in polarized pp collision at RHIC •  production in polarized pp collision at RHIC √s=200 GeV arXiv:0710.2048

  25. Calculating G & G(x) in models • Jaffe (’95) gave a pioneering estimate of G (in A+=0 gauge) in NR & bag models and obtained a negative G • Barone et al. (’98) pointed out additional one-body contribution that partially cancels two-body one ⇒ positive G • Ji et al. (’06) computed G(x) (gauge invariant, non-local) in QM and obtained G  0.34

  26. Lattice QCD Can lattice QCD shed some light on the protn spin content ? Sea polarization from disconnected insertion ⇒ us= ds= s = -0.12±0.01

  27. Quark orbital angular momentum Orbital angular momentum can be inferred from lattice by considering T→ Jq=0.30±0.07=½ +Lq (Mathur et al. 2000) At Q2→, Ji, Tang & Hoodbhoy found (’96) for nf=6 Analogous to the nucleon’s momentum partition: half of the proton’s momentum is carried by gluons Experimentally, how to measure Jq ?

  28. Jq is related to the GPDs by the Ji sum rule Ji, 1997 Study of hard exclusive processes leads to a new class of PDFs: four independent GPDs (at twist-2): DVCS in large s and small t region can probe GPDs

  29. HERMES: hep-ex/0606061 JLab: nucl-ex/0709.0450 Ju=½u+Lu Jd=½ d+Ld p-DVCS sensitive to Ju n-DVCS sensitive to Jd

  30. Lattice calculations of GPDs arXiv:0705.4295 (LHPC,MILC): Hagler, Schroers,… arXiv:0710.1534 (QCDSF,UKQCD): Brommel, Gockeler, Schroers,… QCDSF LHPC Lu+d~0 & Jd~0 ) cancellation between Lu & Ld; ½¢d & Ld ½u+d Lu+d From Ju=0.230, Jd= -0.004, Lu+d=0.025, ) Lu=-0.190, Ld= 0.215 Ju Ld Jd How about Ls ? Lu

  31. Though Jq & JG are separately gauge invariant, can one have gauge-invariant operators for Lq, G, LG? It is generally believed that JG cannot be decomposed into gauge invariant gluon spin and orbital parts. arXiv:0709.1284 [hep-ph]

  32. Conclusions What do we learn in past 20 years about the proton helicity decomposition ? • & Lq are factorization scheme dependent, but not Jq DIS data ⇒ GI 0.33, sGI -0.09 G(x) & qs(x) are weakly constrained • SIDIS & RHIC data imply a small G ⇒ sGI=sCI-(s/2)G is induced mostly from nonperturbative effects • At Q2→, Jq=0.26, JG=0.24 (a useful benchmark) Lattice QCD ⇒ Lu~ -0.19, Ld ~ 0.22

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