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
p
EMC (European Muon Collaboration ’87) measured g1 (x) = ½∑ei2qi(x)
with 0.01<x<0.7, <Q2>=10.7 GeV2 and its first moment
1p 01 g1p(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)
2
Anomalous gluon interpretation
Consider QCD corrections to order s : Efremov, Teryaev; Altarelli, Ross;
Leader, Anselmino; Carlitz, Collins, Muller (’88)
from (a)
1p 
1  s 
s

2
1

e

q

G 

 q 
2
 
2


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
(1  x ) 2
g ( x) :
x
2
1
1 1  1(1  x )
  Pgq ( x )dx  
 0  G  0
0
0
x
1
g ( x) : ,
x


G(Q2) is accumulated with
increasing Q2
Why is this QCD correction so special ?
3
QCD corrections imply that
s
G  0.85
2

d  0.42  d  s G  0.42
2

s  0.08  s  s G  0.08
2
u  0.85
  0.34
 u 
updated with COMPASS
& HERMES data
3 s
  
G  0.34
2
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
1
1
 J q  J G    Lq  G  LG
2
2
This anomalous gluon interpretation became very popular after 1988
4
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 1p 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
5
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
1

0
1
eq2  p  | q   5q | p    3

2
14
1
1 
  u  d  s 
29
9
9 
g1p ( x )dx 

14
1
1

  uv   d v  [ 4  u s   d s   s s ] 
29
9
9

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,
6
against intuition
A hot debate between anomalous gluon & sea quark
interpretations before 1996 !
anomalous gluon
sea quark
Efremov, Teryaev
Jaffe, Manohar
Altarelli, Ross
Bodwin, Qiu
Carlitz, Collins, Muller
Ellis, Karlinear
Soffer, Preparata
Bass, Thomas
Stirling
…
Roberts
Ball, Forte
Gluck, Reya, Vogelsang
Lampe
Mankiewicz
Gehrmann
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)
Anselmino, Efremov, Leader
[Phys. Rep. 261, 1 (1995)]
7
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
g1p ( x) 

1
ei2 q ( x)  Cq ( x)  q( x)  CG ( x)  G ( x)

2
fact. scheme dependent
dy
x y
1
f ( x)  g ( x)  
x
f  g ( y )
 y

G
 hard
(x)
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
Int. J. Mod. Phys. A11, 5109 (1996)
9
1 2
eq (1  x )
2
 Q2 
 CG x, Q   Cq  x, 2   q / G ( x,  2f )  hard  soft
  
f 

2
 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
 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
GI
q ( x)  
G

0
d n 2 k 
[k2  m2  p 2 x(1  x)]2
 2

n 4 2
k

...

2
k
(
1

x
)

 
 

n

2




CI
anomaly
G
G
Axial anomaly resides at k2→ qGI
( x )  qCI
( x)  
s
(1  x )

qG convolutes with G to become qs
qsGI ( x )  qsCI ( x )  
s
(1  x )  G ( x )

HYC(’95)
Muller, Teryaev (’97)
11
improved parton model
1

0
g1p ( x )dx 
OPE
1
s
 1
2
2
e

q


G

e




q
CI
q qGI
2
2

 2
 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
g1p ( x, Q 2 ) 
1
s
2
2
2
G
2 
e

q
(
x
,
Q
)


f
(
x
)


q
(
x
,
Q
)



(
x
)


G
(
x
,
Q
)

q
q
2 q 
2


 ( x )  s
2


 Q2
1  x 

 1  2(1  x )
(2 x  1) ln 2  ln


x
fact




G
1
with
1  s 
  g ( x, Q )  1   q
2
 q
0
G
2
2


(
x
,
Q
,

fact )dx  0

0
1
p
1
2
12
Original results obtained by Carlitz, Collins, Muller (CCM); Altarelli,
Ross (AR); Ratcliffe in the CI scheme are not Ghard . They depend on
infrared cutoff.
 Q2

s
1

 CCM ( x, Q ) 
( 2 x  1) ln

ln

2
2
  p2

2
x


G
2

 Q2
s 
1  x 

 AR ( x ) 
 1  2(1  x )
( 2 x  1) ln 2  ln

2 
m
x



G

 R ( x )  s
2
G


 Q2
1 x 


(
2
x

1
)
ln

ln

1

2
(
1

x
)


 2

x
MS




One needs to substract Gsoft in order to obtain G hard
G
G
 G ( x, Q2 )   hard
( x, Q2 ,  2fact )   soft
( x, Q2 ,  2fact )
 Q2
s
1  x 
G

 hard ( x ) 
( 2 x  1) ln 2  ln
1
 

2
x
fact


1
with
G
2
2
  hard ( x, Q ,  fact )dx  
0
s
2
13
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 axialanomaly 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 !
14
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 = - 0.020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
15
Second hot debate on gauge-invariant
decomposition of the proton spin
(2008 ~ now)
X. S. Chen
Wakamatsu
Hatta
16
Conclusions
1
1
 J q  J G    Lq  G  LG
2
2
 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
17