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

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History of the proton spin puzzle:

First hot debate during 1988-1995

Hai-Yang Cheng

Academia Sinica, Taipei

9th Circum-Pan-Pacific Symposium on High-Energy Spin Physics

Jinan, October 29, 2013

EMC (European Muon Collaboration ’87) measured g1p(x) = ½∑ei2qi(x) with 0.01<x<0.7, <Q2>=10.7 GeV2 and its first moment

1p01g1p(x)dx= 0.1260.018

Combining this with the couplings gA3=u-d, gA8=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 = gA0 = 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)


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 ?

QCD corrections imply that

updated with COMPASS & HERMES data

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 ⇒ Lq+G also increases with lnQ2 with fine tuning

This anomalous gluon interpretation became very popular after 1988


Historical remarks:

  • Moments of g1,2 was first computed by Kodaira (’80) using OPE

  • In 1982 Chi-Sing Lam & Bing-An Li first discovered 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

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

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)

  • 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 Q2 dependent, against intuition

A hot debate between anomalous gluon & sea quark interpretations before 1996 !

anomalous gluon sea quark

Efremov, Teryaev

Altarelli, Ross

Carlitz, Collins, Muller

Soffer, Preparata



Ball, Forte

Gluck, Reya, Vogelsang





Anselmino, Efremov, Leader [Phys. Rep. 261, 1 (1995)]

Jaffe, Manohar

Bodwin, Qiu

Ellis, Karlinear

Bass, Thomas

As a consequence of QCD, a measurement of 10g1(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)

First hot debate on proton spin puzzle interpretations before 1996 !

(1988 ~ 1995):

  • Are hard gluons contributing to 1p ?

  • Anomalous gluon or sea quark

    interpretation of smallness of  or gA0 ?


Factorization scheme dependence interpretations before 1996 !

  • 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)

  • Photon-gluon box diagram is u.v. finite, but it depends on IR cutoff. CG is indep of choice of IR & collinear regulators, but depends on u.v. regulator of q/G(x) qG(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

     qG is anomaly free

    b). u.v. cutoff respects gauge symmetry & axial anomaly but not

    chiral symmetry ⇒ qG 0

  • 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

  • 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




Axial anomaly resides at k2→

qG convolutes with G to become qs


Muller, Teryaev (’97)


improved parton model OPE “parton-model”, “k

  • Anomalous gluon contribution to  g1p 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

Original results obtained by Carlitz, Collins, Muller (CCM); Altarelli, Ross (AR); Ratcliffe in the CI scheme are not Ghard . They depend on infrared cutoff.

One needs to substract Gsoft in order to obtain Ghard

My conclusion: Altarelli, Ross (AR); Ratcliffe in the CI scheme are not

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.


Dust is settled down after 1995 !

Developments after 1995: Altarelli, Ross (AR); Ratcliffe in the CI scheme are not

  • G/G is very small and cannot explain the smallness of gA0 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 = GAs(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

Second hot debate on gauge-invariant decomposition of the proton spin

(2008 ~ now)

X. S. Chen



Conclusions proton spin

  • Anomalous gluon contribution to  g1p is matter of factorization

    convention used for defining q

  • & Lq are factorization scheme dependent, but not Jq=½ +Lq

    DIS data ⇒ GI 0.33, sGI -0.08

    G(x) & qs(x) are weakly constrained