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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

Proton Spin Puzzle: 20 years later

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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

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Page 1: Proton Spin Puzzle: 20 years later

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

Page 2: Proton Spin Puzzle: 20 years later

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)

Page 3: Proton Spin Puzzle: 20 years later

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- :

Page 4: Proton Spin Puzzle: 20 years later

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

Page 5: Proton Spin Puzzle: 20 years later

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⇒

Page 6: Proton Spin Puzzle: 20 years later

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

Page 7: Proton Spin Puzzle: 20 years later

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)

Page 8: Proton Spin Puzzle: 20 years later

8

Experimental Progress

1=10 g1(x)dx

x has been pushed down to O(10-3 - 10-4)

Page 9: Proton Spin Puzzle: 20 years later

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)

Page 10: Proton Spin Puzzle: 20 years later

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

Page 11: Proton Spin Puzzle: 20 years later

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)

Page 12: Proton Spin Puzzle: 20 years later

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 ?

Page 13: Proton Spin Puzzle: 20 years later

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

Page 14: Proton Spin Puzzle: 20 years later

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

Page 15: Proton Spin Puzzle: 20 years later

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

Page 16: Proton Spin Puzzle: 20 years later

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

Page 17: Proton Spin Puzzle: 20 years later

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

Page 18: Proton Spin Puzzle: 20 years later

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

Page 19: Proton Spin Puzzle: 20 years later

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:

Page 20: Proton Spin Puzzle: 20 years later

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

Page 21: Proton Spin Puzzle: 20 years later

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

Page 22: Proton Spin Puzzle: 20 years later

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

Page 23: Proton Spin Puzzle: 20 years later

23

RHIC:The First Polarised pp Collider

Page 24: Proton Spin Puzzle: 20 years later

24

production in polarized pp collision at RHIC

• Jet production in polarized pp collision at RHIC

√s=200 GeV

arXiv:0710.2048

Page 25: Proton Spin Puzzle: 20 years later

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

Page 26: Proton Spin Puzzle: 20 years later

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

Page 27: Proton Spin Puzzle: 20 years later

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 ?

Page 28: Proton Spin Puzzle: 20 years later

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

qq

DVCS in large s and small t region can probe GPDs

Page 29: Proton Spin Puzzle: 20 years later

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

Page 30: Proton Spin Puzzle: 20 years later

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

Page 31: Proton Spin Puzzle: 20 years later

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.

Page 32: Proton Spin Puzzle: 20 years later

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 ?