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
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
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