1. History of the proton spin puzzle: First hot debate during 1988-1995 9th Circum-Pan-Pacific Symposium on High-Energy Spin Physics Jinan, October 29, 2013 Hai-Yang Cheng Academia Sinica, Taipei

2. 22 EMC (European Muon Collaboration ’87) measured g 1 p (x) = ½∑e i 2  q i (x) with 0.01 =10.7 GeV 2 and its first moment  1 p   0 1 g 1 p (x)dx= 0.126  0.018 Combining this with the couplings g A 3 =u-d, g A 8 =u+d-2s measured in low-energy neutron & hyperon  decays   u = 0.77  0.06,  d = -0.49  0.06,  s = -0.15  0.06,  ≡  u+  d+  s = g A 0 = 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 (or proton helicity decomposition puzzle)

3. 3 Anomalous gluon interpretation Consider QCD corrections to order  s : Efremov, Teryaev; Altarelli, Ross; Leader, Anselmino; Carlitz, Collins, Muller (’88) Anomalous gluon contribution (  s /2  )  G arises from photon-gluon scattering. Since  G(Q 2 )  lnQ 2 and  s (Q 2 )  (lnQ 2 ) -1 ⇒  s (Q 2 )  G(Q 2 ) is conserved and doesn’t vanish in Q 2 →  limit  G(Q 2 ) is accumulated with increasing Q 2 from (a) from (b) Why is this QCD correction so special ?

4. 44 QCD corrections imply that If  G is positive and large enough, one can have  s  0 and  =  u+  d+  s   u+  d  0.60 ⇒ proton spin problem is resolved provided that  G  (2  /  s )(0.08)  1.9 ⇒ L q + G also increases with lnQ 2 with fine tuning This anomalous gluon interpretation became very popular after 1988 updated with COMPASS & HERMES data

5. 5 Historical remarks: 1.Moments of g 1,2 was first computed by Kodaira (’80) using OPE 2.In 1982 Chi-Sing Lam & Bing-An Li first discovered anomalous gluon contribution to  1 p and identified  G with 3.The photon-gluon box diagram was also computed by Ratcliffe (’83) using dimensional regularization 4.The original results in 1988 papers are not pQCD reliable According to INSPIRE as of today: Lam, Li (1982): 39 Ratcliffe (1983):121 Efremov,Teryaev (May 1988): ? Altarelli, Ross (June 1988): 682 Leader, Anselmino (July 1988): ? Carlitz, Collins, Mueller (Sept 1988): 595

6. 6 Operator Product Expansion moments of structure function=  1 0 x n-1 F(x)dx = ∑ C n (q) = short-distance  long-distance No twist-2, spin-1 gauge-invariant local gluonic operator for first moment OPE ⇒ Gluons do not contribute to  1 p ! One needs sea quark polarization to account for experiment (Jaffe, Manohar ’89) It is similar to the naïve parton model How to achieve  s  -0.08 ? 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 Q 2 dependent, against intuition

7. 7 A hot debate between anomalous gluon & sea quark interpretations before 1996 ! anomalous gluon sea quark Efremov, Teryaev Altarelli, Ross Carlitz, Collins, Muller Soffer, Preparata Stirling 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 … As a consequence of QCD, a measurement of  1 0 g 1 (x) does not measure . It measures only the superposition  -3  s /(2  )  G and this combination can be made small by a cancellation between quark and gluon contributions. Thus the EMC result ceases to imply that  is small. - Anselmino, Efremov, Leader (’95)

8. 88 First hot debate on proton spin puzzle (1988 ~ 1995): Are hard gluons contributing to  1 p ? Anomalous gluon or sea quark interpretation of smallness of  or g A 0 ?

9. 9 Factorization scheme dependence It was realized by Bodwin, Qiu (’90) and by Manohar (’90) that hard gluonic contribution to  1 p is a matter of convention used for defining  q Consider polarized photon-gluon cross section 1.Its hard part contributes to  C G and soft part to  q s. This decomposition depends on the choice of factorization scheme 2.It has an axial QCD anomaly that breaks down chiral symmetry fact. scheme dependent Int. J. Mod. Phys. A11, 5109 (1996)

10. Photon-gluon box diagram is u.v. finite, but it depends on IR cutoff.  C G is indep of choice of IR & collinear regulators, but depends on u.v. regulator of  q/G (x)   q G (x) The choice of u.v. cutoff for soft contributions specifies factorization convention Polarized triangle diagram has axial anomaly ⇒ a). u.v. cutoff respects gauge & chiral symmetries but not anomaly  q G is anomaly free b). u.v. cutoff respects gauge symmetry & axial anomaly but not chiral symmetry ⇒  q G  0 10

11. 11 CI anomaly GI Axial anomaly resides at k  2 →   q G convolutes with  G to become  q s HYC(’95) Muller, Teryaev (’97) chiral-invariant (CI) scheme (or “jet”, “parton-model”, “k T cut-off’, “Adler-Bardeen” scheme) Axial anomaly is at hard part, i.e.  C G, while hard gluons do not contribute to  q s due to chiral symmetry gauge-invariant (GI) scheme (or MS scheme) -- Axial anomaly is at soft part, i.e.  q G, which is non-vanishing due to chiral symmetry breaking and  1 0  C G (x)=0 (but  G  0 !) -- Sea polarization is partially induced by gluons via axial anomaly

12. 12  Anomalous gluon contribution to  g 1 p is matter of factorization convention used for defining  q  It is necessary to specify the factorization scheme for data analysis  Nowadays it is customary to adopt the MS scheme improved parton model OPE

13. 13 Original results obtained by Carlitz, Collins, Muller (CCM); Altarelli, Ross (AR); Ratcliffe in the CI scheme are not   G hard. They depend on infrared cutoff. One needs to substract   G soft in order to obtain   G hard

14. 14 In retrospect, the dispute among the anomalous gluon and sea-quark explanations…before 1996 is considerably unfortunate and annoying since the fact that g 1 p (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 My conclusion: Dust is settled down after 1995 !

15. 15 Developments after 1995:  G/G is very small and cannot explain the smallness of g A 0 via anomalous gluon effect, but  G  0.1 - 0.2 makes a significant contribution to the proton spin 1. Semi-inclusive DIS data of COMPASS & HERMES show no evidence of large negative  s 2. Three lattice calculations in 2012 : a). QCDSF  s = - 0.020  0.010  0.004 at Q = 2.7 GeV b). Engelhardt  s = - 0.031  0.017 at Q = 2 GeV c). Babich et al  s = G A s (0 ) = - 0.019  0.017 not renormalized yet It is still controversial about the size of sea polarization. Resolved by anomalous Ward identity ? Keh-Fei Liu

16. 16 Second hot debate on gauge-invariant decomposition of the proton spin (2008 ~ now) X. S. Chen Wakamatsu Hatta

17. 17 Conclusions Anomalous gluon contribution to  g 1 p is matter of factorization convention used for defining  q  & L q are factorization scheme dependent, but not J q =½  + L q DIS data ⇒  GI  0.33,  s GI  -0.08  G(x) &  q s (x) are weakly constrained