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History of the proton spin puzzle: First hot debate during 1988-1995

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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∑ei2qi(x) with 0.01<x<0.7, <Q2>=10.7 GeV2 and its first moment

1p01g1p(x)dx= 0.1260.018

Combining this with the couplings gA3=u-d, gA8=u+d-2s measured in low-energy neutron & hyperon decays

u = 0.770.06, d = -0.490.06, s = -0.150.06,

≡ u+d+s = gA0 = 0.140.18

- 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)

2

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+su+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

4

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)
- J5 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

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 10g1(x) does not measure . It measures only the superposition -3s/(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

(1988 ~ 1995):

- Are hard gluons contributing to 1p ?
- Anomalous gluon or sea quark
interpretation of smallness of or gA0 ?

8

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)

- 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 10CG(x)=0 (but G 0 !)

-- Sea polarization is partially induced by gluons via axial anomaly

GI

anomaly

CI

Axial anomaly resides at k2→

qG convolutes with G to become qs

HYC(’95)

Muller, Teryaev (’97)

11

improved parton model OPE

- 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:

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

Dust is settled down after 1995 !

Developments after 1995:

- 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 = - 0.0200.0100.004 at Q= 2.7 GeV

b). Engelhardt s = - 0.0310.017 at Q= 2 GeV

c). Babich et al s = GAs(0) = - 0.0190.017 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

Wakamatsu

Hatta

Conclusions

- 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