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

22

EMC (European Muon Collaboration ’87) measured g1p(x) = ½∑ei

2qi(x)

with 0.01<x<0.7, <Q2>=10.7 GeV2 and its first moment

1p 0

1 g1p(x)dx= 0.1260.018

Combining this with the couplings gA3=u-d, gA

8=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)

3

Anomalous gluon interpretation

Consider QCD corrections to order s : Efremov, Teryaev; Altarelli, Ross; Leader, Anselmino; Carlitz, Collins, Muller (’88)

Gqe s

qsp

21

2

1 21

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

1

0

1

0

2

2

00)1(11

)(

)1(

:)( ,1

:)(

Gx

xdxxP

x

xxg

xxg

gq G(Q2) is accumulated with increasing Q2

from (a)

from (b)

Why is this QCD correction so special ?

44

QCD corrections imply that

08.02

08.0

42.02

42.0

85.02

85.0

Gss

Gdd

Guu

s

s

s

34.02

3 34.0 Gs

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 lnQ2 with fine tuning

This anomalous gluon interpretation became very popular after 1988

GqGq LGLJJ 2

1

2

1

updated with COMPASS & HERMES data

5

Historical remarks:

1. Moments of g1,2 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 <N|K|N>

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

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

]4[9

1

9

1

9

4

2

1

9

1

9

1

9

4

2

1

||2

1)(

1

0 352

1

sssvv

qp

sdudu

sdu

pqqpedxxg

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

7

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

anomalous gluon sea quarkEfremov, 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)

88

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 ?

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

)()()()()(2

1)( 2

1 xGxCxqxCxqexg Gqip

Consider polarized photon-gluon cross section

1. Its hard part contributes to CG and soft part to qs. This decomposition depends on the choice of factorization scheme

2. It has an axial QCD anomaly that breaks down chiral symmetry

fact. scheme dependent

)()()(1

ygy

xf

y

dyxgxf

x

Int. J. Mod. Phys. A11, 5109 (1996)

)(xGhard

softhard),(,, 2/2

22

fGq

fqG x

QxCQxC

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

10

)1(2

1 2 xeq

1111

0

222222

2

)1(2

42...

)]1([)( xk

n

nk

xxpmk

kdxq

nG

CI anomaly

GI

Axial anomaly resides at k2→ )1()()( xxqxq sGCI

GGI

qG convolutes with G to become qs

)()1()()( xGxxqxq sCIs

GIs

HYC(’95)

Muller, Teryaev (’97)

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 1

0 CG(x)=0 (but G 0 !) -- Sea polarization is partially induced by gluons via axial anomaly

12

GIq

sCIq

p qeGqedxxg 21

0

21 2

1

22

1)(

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

q

Gq

sq

p QxGxQxqxfQxqeQxg ),()(),()(2

),(2

1),( 22222

1

1

0

222

2

0),,( with)1(211

lnln)12(2

)( dxQxxx

xQxx fact

G

fact

sG

1

0

21 1

2

1),(

q

sp qQxg

improved parton model OPE

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.

1

0

222

2

2),,( with1

1lnln)12(

2)(

s

factGhard

fact

sGhard dxQx

x

xQxx

)1(211

lnln)12(2

)(

)1(211

lnln)12(2

)(

21

lnln)12(2

),(

2MS

2

2

2

22

22

xx

xQxx

xx

x

m

Qxx

xp

QxQx

sGR

sGAR

sGCCM

),,(),,(),( 22222fact

Gsoftfact

Ghard

G QxQxQx

One needs to substract Gsoft in order to obtain G hard

14

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

My conclusion:

Dust is settled down after 1995 !

15

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

16

Second hot debate on gauge-invariant decomposition of the proton spin (2008 ~ now)

X. S. ChenWakamatsuHatta

17

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

GqGq LGLJJ 2

1

2

1