Upload
zubin
View
31
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Proton Spin Puzzle: 20 years later. Hai-Yang Cheng Academia Sinica Deep inelastic scattering Proton spin puzzle Experimental & Theoretical progresses. Lattice JC, October 19, 2007. Non-relativistic SU(6) constituent QM - PowerPoint PPT Presentation
Citation preview
Proton Spin Puzzle: 20 years later
Hai-Yang Cheng
Academia Sinica
Deep inelastic scattering
Proton spin puzzle
Experimental & Theoretical progresses
Lattice JC, October 19, 2007
2
Non-relativistic SU(6) constituent QM
⇒ proton spin comes from constitutent quark’s spin. U=4/3, D=-1/3, so that U+D=1. However, this model predicts gA=5/3, while gA=1.258 experimentally
Relativistic QM ⇒ quark spin + orbital angular momentum
= Q+ Lq ½(0.65+0.35)
How to explore the proton’s spin content ?
It can be studied in deep inelastic scattering (DIS)
3
Deep Inelastic Scattering
DIS process l+p→l+X was first studied by Friedman, Kendall, Taylor (’67-’69) at SLAC
Unpolarized structure functions: F1(x,Q2), F2(x,Q2)
F1(x) = ½ ∑ ei2[qi
+(x)+qi-(x)] = ½ ∑ ei
2qi(x)
x: fraction of proton’s momentum carried by the struck quark, 0<x<1
Structure functions ⇒
(i) 3 valence quarks
(ii) sea quarks
(iii) half of proton’s momentum carried by gluons
k’e(E,p)e’(E’,p’)
*
N
q+ :
q- :
4
Polarized DIS
Consider polarized DIS process: l+p→l+X and measure asymmetry
dd
ddA
q(x,Q2)=
g1p(x)= ½∑ei
2[qi+(x)-qi
-(x)]= ½∑ei2qi(x)
In general, q=qv+qs.
In absence of sea polarization 10 g1
p(x)dx=½∑eq2q=½(4/9 uv+1/9dv)
neutron decay ⇒ uv- dv= gA3 = 1.2695±0.0029
hyperon decay ⇒ uv + dv= gA8 = 0.585±0.025
uv = 0.93±0.02, dv = -0.34±0.02, 10 g1
p(x)dx 0.18
first derived by Ellis & Jaffe in 1974
5
SLAC (’76,’83) covers the range 0.1<x<0.7
0.70.1 g1
p(x)dx = 0.094±0.016
Extrapolation to the unmeasured x region ⇒ 10 g1
p(x)dx=0.17±0.05, consistent with Ellis-Jaffe sum rule
EMC (European Muon Collaboration, 87-89), 0.01<x<0.7 at <Q2>=10.7 GeV2
0.70.1 g1
p(x)dx = 0.090 ± 0.015
0.10.01 g1
p(x)dx = 0.030 ± 0.016
Hence,
10 g1
p(x)dx = 0.126 ± 0.018
Lower than EJ sum rule expectation importance of sea polarization⇒
6
Solving the three equations for q
u-d = 1.2695±0.0029, u+d-2s = 0.585±0.025
1
0 1 018.0126.09
1
9
1
9
4
2
1)( sdudxxg p
yields
u = 0.77±0.06, d = -0.49±0.06, s = -0.15±0.06
≡ u+d+s = 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
7
GqGq LGLJJ 2
1
2
1
The so-called “proton spin crisis” is not pertinent since the proton helicity content explored in the DIS experiment is, strictly speaking, defined in the infinite momentum frame in terms of QCD current quarks and gluons, whereas the spin structure of the proton in the proton rest frame is referred to the constituent quarks.
…..
It is not sensible to compare apple with orange. What trigged by the EMC experiment is the “proton helicity decomposition puzzle” rather than the “proton spin crisis”
HYC, hep-ph/0002157
q( momentum frame) qQM(rest frame)
8
Experimental Progress
1=10 g1(x)dx
x has been pushed down to O(10-3 - 10-4)
9
COMPASS, HERMES
=u+d+s=0.33±0.06
(0.14±0.18)
⇒u = 0.84±0.02 (0.77±0.06)
d = -0.43±0.02 (-0.49±0.06)
s = -0.09±0.02 (-0.15±0.06)
10
• Sea quark polarization
The result for s is very different from the inclusive DISplus SU(3) symmetry analysis!
HERMES result from Semi-inclusive DIS
Airapetian et al, PRL 92 (2004) 012005
11
COMPASS result from Semi-inclusive DISarXiv:0707.4077
uv+dv=0.41±0.07±0.05
u+d=0.0±0.04±0.03 ⇒ u & d are of opposite sign
⇒ asymmetric sea polarization
unpolarized sea: d > u (violation of Gottfried sum rule)
12
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 ?
13
QCD corrections imply that
09.02
43.02
84.02
Gss
Gdd
Guu
s
s
s
33.02
3 Gsdu s
If G is positive and large enough, one can have s 0 and u+d 0.60 proton spin problem is resolved provided that ⇒ G (2/s)(0.09) 1.7 L⇒ q+G also increases with lnQ2 with fine tuning
This anomalous gluon interpretation became very popular after 1988Historical remarks:
1. Moments of g1,2 was first computed by Kodaira (’80) using OPE
2. In 1982 Chi-Sing Lam & Bing-An Li obtained 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
GqGq LGLJJ 2
1
2
1
Lam, Li (1982): 36
Ratcliffe (1983):118
Efremov,Teryaev (May 1988): ?
Altarelli, Ross (June 1988): 618
Leader, Anselmino (July 1988): ?
Carlitz, Collins,Mueller (Sept 1988): 538
14
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)
How to achieve s -0.09 ? 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
15
A hot debate between anomalous gluon & sea quark interpretations before 1995 !
anomalous gluon sea quarkEfremov, Teryaev
Altarelli, Ross
Carlitz, Collins, Muller
Soffer, Perparata
Strirling
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
…
16
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
17
softhard),(,, 2/2
22
fGq
fqG x
QxCQxC
Photon-gluon box diagram is u.v. finite. CG is indep of choice of IR & collinear regulators, but depends on u.v. regulator of q/G(x)=qG(x)
Polarized triangle diagram has axial anomaly If u.v. cutoff respects ⇒gauge symmetry but breaks chiral symmetry ⇒ qG 0
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)
)1(2
1 2 xeq
18
Two extreme schemes of interest (HYC, ’95)
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
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
GIq
sCIq
p qeGqedxxg 21
0
21 2
1
22
1)(
Hard gluonic contribution to g1p is matter of factorization
convention used for defining q
It is necessary to specify the factorization scheme for data analysis
19
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:
20
How to probe gluon polarization ?
DIS via scaling violation in g1(x,Q2)
photon or jet or heavy quark production in polarized pp collider, lepton-
proton collider or lepton-proton fixed target
RHIC (at BNL): via direct high-pT prompt production,
jet production
HERMES (at DESY): via open charm production
COMPASS (at CERN): via open charm production
21
• Q-evolution in inclusive spin structure function g1(x,Q2)
NLO splitting functions Pij are available in ’95
van Neerven, Mertig, Zijlstra
⇒ A complete & consistent NLO analysis of g1 data is possible
Most analyses are done in MS scheme (GI)
uv(x), dv(x) are fairly constrained
Sea distribution is poorly constrained
G(x) is almost completely undetermined
)]()(
)()()([2
1)(1
xGxC
xqxCxqxg
G
qp
22
COMPASS:G(x)/G(x)= -0.57±0.41±0.17
HERMES: G(x)/G(x)=0.078±0.011±0.05 at <x>=0.204
Direct measurements do not discriminate between G>0 & G<0
Large G 2-3 ruled out by data
Direct measurement of G:
Photon-Gluon-Fusion process
23
RHIC:The First Polarised pp Collider
24
production in polarized pp collision at RHIC
• Jet production in polarized pp collision at RHIC
√s=200 GeV
arXiv:0710.2048
25
Calculating G & G(x) in models
Jaffe (’95) gave a pioneering estimate of G (in A+=0 gauge) in NR & bag models and obtained a negative G
Barone et al. (’98) pointed out additional one-body contribution that partially cancels two-body one positive ⇒ G
Ji et al. (’06) computed G(x) (gauge invariant, non-local) in QM and obtained G 0.34
26
Lattice QCD
Can lattice QCD shed some light on the protn spin content ?
sqq
spJspspJspspJspGIs
GIv
discon
,||,,||,,||, 555
Sea polarization from disconnected insertion
⇒ us= ds= s = -0.12±0.01
27
Quark orbital angular momentum
Orbital angular momentum can be inferred from lattice by considering T → Jq=0.30±0.07=½ +Lq (Mathur et al. 2000)
At Q2→, Ji, Tang & Hoodbhoy found (’96)
24.026.02
1
)47.0(2
1
316
16
2
1)()()(
)53.0(2
1
316
3
2
1)()(
2
1)(
222
222
Gq
fGG
f
fqq
JJ
nQLQGQJ
n
nQLQQJ
Analogous to the nucleon’s momentum partition: half of the proton’s momentum is carried by gluons
for nf=6
Experimentally, how to measure Jq ?
28
Jq is related to the GPDs by the Ji sum rule
0
1lim [ ( , , ) ( , , )]
2q q qtJ dxx H x t E x t
Ji, 1997
Study of hard exclusive processes leads to a new class of PDFs: four independent GPDs (at twist-2): (pol)
~ ,
~ ,(unpol) , EHEH
1
1
1
1
1
1 2
1
1 1
)(),,(~
),(),,(~
)(),,( ),(),,(
),()0,0,(~
),()0,0,(
tGtxEdxtGtxHdx
tFtxdxEtFtxdxH
xqxHxqxH
PA
DVCS in large s and small t region can probe GPDs
29
Ju=½ u+Lu
Jd=½ d+Ld
HERMES: hep-ex/0606061
JLab: nucl-ex/0709.0450
p-DVCS sensitive to Ju
n-DVCS sensitive to Jd
30
Lattice calculations of GPDs
arXiv:0705.4295 (LHPC,MILC): Hagler, Schroers,…arXiv:0710.1534 (QCDSF,UKQCD): Brommel, Gockeler, Schroers,…
Lu+d~0 & Jd~0 ) cancellation between Lu & Ld; ½¢d & Ld
From Ju=0.230, Jd= -0.004, Lu+d=0.025, )Lu=-0.190,Ld= 0.215
How about Ls ?
LHPC QCDSF
½u+d
Lu+d
Ju
Jd
Lu
Ld
arXiv:0709.1284 [hep-ph]
Though Jq & JG are separately gauge invariant, can one have gauge-invariant operators for Lq, G, LG?
It is generally believed that JG cannot be decomposed into gauge invariant gluon spin and orbital parts.
32
Conclusions
& Lq are factorization scheme dependent, but not Jq
DIS data ⇒ GI 0.33, sGI -0.09
G(x) & qs(x) are weakly constrained
SIDIS & RHIC data imply a small G ⇒ sGI=sCI-(s/2)G is induced
mostly from nonperturbative effects
At Q2→, Jq=0.26, JG=0.24 (a useful benchmark)
Lattice QCD ⇒ Lu~ -0.19, Ld ~ 0.22
GqGq LGLJJ 2
1
2
1
What do we learn in past 20 years about the proton helicity decomposition ?