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
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
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
⇒ 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)
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
According to INSPIRE as of today:
Lam, Li (1982): 39
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)
A hot debate between anomalous gluon & sea quark interpretations before 1996 !
anomalous gluon sea quark
Carlitz, Collins, Muller
Gluck, Reya, Vogelsang
Anselmino, Efremov, Leader [Phys. Rep. 261, 1 (1995)]
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):
interpretation of smallness of or gA0 ?
Factorization scheme dependence
fact. scheme dependent
Consider polarized photon-gluon cross section
Int. J. Mod. Phys. A11, 5109 (1996)
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
Axial anomaly is at hard part, i.e. CG, while hard gluons do not contribute to qs due to chiral symmetry
-- 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
Axial anomaly resides at k2→
qG convolutes with G to become qs
Muller, Teryaev (’97)
improved parton model OPE
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
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:
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 ?
Second hot debate on gauge-invariant decomposition of the proton spin
(2008 ~ now)
X. S. Chen
convention used for defining q
DIS data ⇒ GI 0.33, sGI -0.08
G(x) & qs(x) are weakly constrained