Challenges of the Standard Model and the Nucleon Spin Puzzle

Thomas Jefferson National Accelerator Facility (JLab)

Recent Results from JLab Spin Program

Summary and Outlook

Xiaochao ZhengUniv. of Virginia

October 17, 2009

Selected Results from the Nucleon Spin Program at Jefferson Lab

SU(2)L X

U(1)Y

SU(3)

C

Standard Model of Particle Physics

Success of the Standard Model in the strong interaction sector

QCD tested in the high energy (perturbative, = “weak”) region

Major Challenges within the Standard Model

Understand and test QCD in extreme conditions (RHIC, LHC)

Understand and test QCD in “strong” interaction region (non-perturbative)

Understand the nucleon structure, how quarks and gluons form the nucleon's mass, momentum, and spin

Standard Model of Particle Physics

energy (GeV) (~1/distance)

S

Success of the Standard Model in the strong interaction sector

QCD tested in the high energy (perturbative, = “weak”) region

Major Challenges within the Standard Model

Understand and test QCD in extreme conditions (RHIC, LHC)

Understand and test QCD in “strong” interaction region (non-perturbative)

Understand the nucleon structure, how quarks and gluons form the nucleon's mass, momentum, and spin

Standard Model of Particle Physics

Three Decades of Spin Structure Study• 1980s: EMC (CERN) + early SLAC quark contribution to proton spin is very small % ! ‘spin crisis’ (Ellis-Jaffe sum rule violated)• 1990s: SLAC, SMC (CERN), HERMES (DESY) % the rest: quark orbital angular momentum and gluons

Different decompositions: Jaffe, Ji, X. Chen et al. Bjorken Sum Rule verified to <10% level • 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … : ~ 30%;G probably small, quark orbital angular

momentum probably significant Test of various Sum Rules Transversity, Transverse-Momentum Dependent

Distributions Generalized Parton Distributions

=12± 9± 14

= 20~ 30

Facilities Accelerator Beam Time

FermiLab Tevatron 1.96 TeV low 1995 - ... ...

SLAC Stanford Linear Accelerator 50 GeV, 80% 1962 - ... ... 0.03%

J Lab “CW”

CERN Large e-/e+ Collider (LEP) 90-209 GeV low 1989-2000

DESY Deutsches Elektronen Synchrotron 27.5 GeV low

MAINZ Mainz Microtron MAMI 0.8/1.6 GeV 1979 - ... ... “CW”

MIT Bates MIT Bates Linear Accelerator 0.8 GeV 1975-2005

Energy,

polarizationLuminosity

(cm-2 s-1)

duty

factor

1036

Continuous Electron Beam

Accelerator Facility (CEBAF)

6 GeV, 85%

12 GeV, 85% 1038-39 1985 - ... ...

2015 - ... ...

1987 - ... ...

(DESY-II)

1038

1037

Medium & High Energy Physics Facilities for Lepton Scattering

e−.

e−.

e−. ,e.

,

e−. ,e.

,

e−. ,e.

High luminosity, and “continuous” polarized beam makes JLab an unique facility.

~ns: “continuous”>>ns: “pulsed”

Employment: ~650

User community: ~1200

Three Experimental HallsHall A:

pair of high resolution spectrometers (HRS), E' up to 4 GeV/c, = 7 msrluminosity up to 1039 cm-2 s-1

Hall C:High Momentum (HMS) and Short-Orbit Spectrometers (SOS)luminosity up to 1039 cm-2 s-1

Hall B:CEBAF Large Acceptance Spectrometer (CLAS) luminosity up to 1034 cm-2 s-1

Hall A polarized 3He target

longitudinal, transverse and verticalLuminosity=1036 (cm-

2s-1) (highest polarized luminosity in the world)High in-beam polarization > 65%Effective polarized neutron target

13 completed experiments 6 approved with 12 GeV (A/C)

15 uA

Hall B/C Polarized proton/deuteron

targets

• Polarized NH3/ND3 targets

• Dynamical Nuclear Polarization

• In-beam average polarization

70-90% for p

30-40% for d

• Luminosity up to

~ 1035 cm-2s-1(Hall C)

~ 1034 cm-2s-1(Hall B)

JLab Spin Experiments • Results:

– Spin in the valence (high-x) region– Quark-Hadron duality– Moments: Spin Sum Rules and Polarizabilities– Higher twists: g2/d2

• Just completed:– GDH on the proton at very low Q2;– Transversity (n)

• Planned at 6 GeV– g2

p at low Q2

• Future: 12 GeV– Inclusive: A1/d2, – Semi-Inclusive: Transversity, TMDs, Flavor-

decomposition

Review: Kuhn, Chen, Leader, arXiv:0812.3535, PPNP 63 (2009) 1

Longitudinal Spin (I)

Spin in Valence (high-x) Region

(where we can test pQCD and models such as RCQM)

Valence (high-x) A1p and A1

n results

Hall B CLAS, Phys.Lett. B641, 11 (2006)

Hall A E99-117, PRL 92, 012004 (2004) PRC 70, 065207 (2004)

pQCD with HHC

RCQMRCQM

RCQMRCQM

Data for q/q Before JLab With E99117

Data

pQCD with HHCpQCD with HHC

(HERMES data at large x not shown)

Inclusive Hall A and B and Semi-Inclusive HermesBBS(pQCDw/ HHC)

BBS+OAM

PRL99, 082001 (2007)

pQCD with Quark Orbital Angular Momentum

A1p at 11 GeV

Projections for JLab at 11 GeV

Quark Hadron Duality in Spin Structure Function

<resonances> = <DIS>?

Longitudinal Spin (II)

Duality in Spin-Structure: CLAS EG1b Results

Phys.Rev.C75:035203,2007

A13He (resonance vs DIS)

Duality in Spin-Structure: Hall A E01-012 Results

PRL 101, 182502 (2008)

1 resonance comparison with pdfs

integrated over resonances covered by the data, from the pion threshold to an xmin corresponding to W=1.905 GeV

Parton Distributions (CTEQ6 and DSSV)

DSSV, PRL101, 072001 (2008)

CTEQ6, JHEP 0207, 012 (2002)

Polarized PDFsUnpolarized PDFs

Moments of Spin Structure Functions

Sum Rules

Global Property

Spin Sum Rules for First Moments

Bjørken Sum Rule

gA: axial vector coupling constant from neutron -decay

CNS: Q2-dependent QCD corrections (for flavor non-singlet)

•A fundamental relation relating an integration of spin structure functions to axial-vector coupling constant

•Based on Operator Product Expansion within QCD or Current Algebra, plus isospin invariance.

• Valid at large Q2 (where higher-twist effects negligible)

•Data are consistent with the Bjørken Sum Rule at 5-10% level

1pQ2−1

n Q2=∫ [ g1px ,Q

2−g 1nx ,Q

2 ] d x=16

g AC NS

Gerasimov-Drell-Hearn Sum RuleCircularly polarized photon on longitudinally polarized

nucleon

• A fundamental relation between the nucleon spin structure and its anomalous magnetic moment

• Based on general physics principles • Lorentz invariance, gauge invariance low energy theorem• unitarity optical theorem• causality unsubtracted dispersion relation

applied to forward Compton amplitude

• First measurement on proton up to 800 MeV (Mainz) and up to 3 GeV (Bonn) agree with GDH with assumptions for contributions from un-measured regions. New measurements from LEGS provided complimentary results on the proton, more precise results on the deuteron.

∫ 0

∞ 1/ 2 − 3 / 2

d

=−2 2 EM

M 2 2

Generalized GDH Sum Rule

Many approaches: Anselmino, Ioffe, Burkert, Drechsel, …

Ji and Osborne (J. Phys. G27, 127, 2001):Forward Virtual-Virtual Compton Scattering Amplitudes: S1(Q2,), S2(Q2,)

Same assumptions: no-subtraction dispersion relation

optical theorem (low energy theorem)

S1Q2=4∫el

∞ G1Q2, d

Connecting GDH and Bjorken Sum Rules

• Q2-evolution of GDH Sum Rule provides a bridge linking strong QCD to pQCD• Bjorken and GDH sum rules are two limiting cases

High Q2, Operator Product Expansion : S1(p-n) ~ gA Bjorken

Q2~0, Low Energy Theorem: S1 ~ 2 GDH

• High Q2 (> ~1 GeV2): Operator Product Expansion• Intermediate Q2 region: Lattice QCD calculations• Low Q2 region (< ~0.1 GeV2): Chiral Perturbation

TheoryCalculations: HBPT: Ji, Kao, Osborne, Spitzenberg, Vanderhaeghen

RBPT: Bernard, Hemmert, Meissner

Reviews: Theory: Drechsel, Pasquini, Vanderhaeghen, Phys. Rep. 378,99 (2003)

Experiments: Chen, Deur, Meziani, Mod. Phy. Lett. A 20, 2745 (2005)

JLab E94-010 (Hall A)

Neutron spin structure moments and sum rules

• Q2 evolution of neutron spin structure moments (sum rules) with pol.3He

• transition from quark-gluon to hadron

• Test PT calculations

• Results published in several PRL/PLB’s

GDH integral on neutron

PRL 89 (2002) 242301 Q2

EG1b, PLB672, 12 (2009) EG1a, PRL 91, 222002 (2003)

1p

JLab CLAS Eg1a/Eg1b (Hall B)

Proton spin structure moments and sum rules

E94-010, from 3He, PRL 92, 022301(2004) E97-110, from 3He, preliminaryEG1a, EG1b: from d-p

very low Q2!

1n

Test fundamental understandingTest PT at very low Q2

GDH Sum and Spin Structure Function Moments at very low Q2

JLab CLAS EG4 (Hall B) Proton and deuteron spin structure moments

and sum rules at very Low Q2

Expected statistical accuracy from EG4

• Ran in 2006• Data being analyzed

1 of p-n – Bjorken Sum

EG1b, PRD 78, 032001 (2008)E94-010 + EG1a: PRL 93 (2004) 212001

agree well with PT

pQCD w/o HT corrections agree with data surprisingly well down to Q2=1 GeV2.

Effective Strong Coupling Constant

A new attempt at low Q2

Experimental Extraction of S from

Bjorken Sum

s (Q) is well defined in pQCD

at large Q2. Can be extracted from data (e.g. Bjorken Sum Rule).

Not well defined at low Q2, diverges at QCD

The strong coupling constant from pQCD

∫ g 1p−g 1

n dx=1p−n=

g A

6 1− s

3.58

s

2

Generalized Bjorken sum rule:

Definition of effective QCD couplingsPLB B95 70 (1980); PRD 29 2315 (1984); PRD 40 680(1989).

Prescription: Define effective couplings from a perturbative series truncated to the first term in

s.

Use to define an effective s

g1.

Process dependent. But can be related through “Commensurate scale relations”

S.J. Brodsky & H.J Lu, PRD 51 3652 (1995)S.J. Brodsky, G.T. Gabadadze, A.L. Kataev, H.J Lu, PLB 372 133 (1996)

Extend it to low Q2 down to 0: include all higher twists.

∫ g1p− g1

n dx= 1p−n=

g A

6 1− s

3.58

s

2 HigherTwists

1p−n=

g A

6 1 − s

g1

Effective Coupling Extracted from Bjorken Sum

s/

A. Deur, V. Burkert, J. P. Chen and W. Korsch PLB 650, 244 (2007) and PLB 665, 349 (2008)

first attempt of effective S extraction

at low Q2

no strong Q2 dependence of strong force at large distances

“Comparison” with theory ↔

Fisher et al.Bloch et al.Maris-TandyBhagwat et al. CornwallGodfrey-Isgur: Constituant Quark ModelFurui & Nakajima: Latticede Teramond et al:

AdS/CFT (preliminary)

Schwinger-Dyson

the conformality (no Q2 dependence) may imply that it's possible to use AdS/CFT correspondance to calculate strong interaction at low Q2.

Transverse Spin (I): Inclusive

g2 Structure Function and Moments

Burkhardt - Cottingham Sum Rule

g2: twist-3, q-g correlations

Experiments: transversely polarized targetSLAC E155x, (p/d)

JLab Hall A (n), Hall C (p/d)

g2 leading twist related to g1 by Wandzura-Wilczek relation

g2-g2WW: a clean way to access twist-3

contribution, quantify q-g correlations.

g 2 x , Q 2= g 2WW x , Q 2 g 2 x , Q 2

g 2WW x ,Q

2=−g1x ,Q2∫x

1g1 y ,Q

2dyy

Precision Measurement of g2n(x,Q2):

Search for Higher Twist Effects

• Measure higher twist, study quark-gluon correlations.

PRL 95, 142002 (2005)

BC Sum Rule BC Sum Rule

P

N

3HeBC = Meas+low_x+Elastic

0<X<1 :Total Integral

“low-x”: unmeasured low x part of the integral. Assume Leading Twist behaviour

Elastic: From well known form factors (<5%)

“Meas”: Measured x-range

Brown: SLAC E155xRed: Hall C RSS Black: Hall A E94-010Green: Hall A E97-110 (preliminary)Blue: Hall A E01-012 (preliminary)

very preliminary

2 Q 2 =∫0

2g 2 x , Q 2 dx=0

BC Sum Rule BC Sum Rule

P

N

3He BC satisfied w/in errors for 3He

BC satisfied w/in errors for Neutron (though just barely in vicinity of Q2=1)

BC satisfied w/in errors for JLab Proton, 2.8 violation seen in SLAC data

very preliminary

Spin Polarizabilities

Higher Moments of Spin Structure Functions at Low Q2

Higher Moments: Generalized Spin Polarizabilities

(how nucleons respond to virtual photons)• generalized forward spin polarizability 0

0Q2= 1

2 2 ∫ 0

∞ ,Q 2

TT ,Q2

3 d

0 Q2 0Q

2 0Q2= 16 M 2

Q 6 ∫0

x0

x2[ g1 x ,Q 2− 4 M 2 x2

Q 2 g 2 x ,Q 2] d x

0Q2≡ L T Q

2= 122 ∫ 0

∞ ,Q2

LT ,Q 2

Q 2 d

=16 M 2

Q6 ∫0

x0 [ g1 x ,Q 2g 2 x ,Q 2 ] d x

• generalized longitudinal-transverse spin polarizability LT

Neutron Spin Polarizabilities LT insensitive to resonance• Significant disagreement between data and both

PT calculations for LT

• Good agreement with MAID model predictions

0 LT

E94-010, PRL 93 (2004) 152301

Proton Spin Polarizability

• Only longitudinal data, model for transverse (g2)

• 0 sensitive to resonance

• Large discrepancies with PT!

0p 0

p Q6

PLB672, 12 (2009)

Summary of Comparison with PT

Results on GDH sum, 1p, 1

n, 1p-n in general agree

well with at least one of the PT calculations;

LT puzzle:

LT not sensitive to , one of the best quantities

to test PT,

data disagree with all calculations (HBPT, RBPT/) by several hundred %!

A challenge to PT theorists.

Very low Q2 data g1/g2 on n(3He) (E97-110), also g1 on p and D available soon (EG4)

Recently approved: g2 on proton E08-027

Color Polarizabilities and Higher Twists

Higher Moments of Spin Structure Functions at High Q2

d 2= X E2 X B/8

f 2= X E−2 X B /2

∫ g1p− g1

n dx= 1p−n=

g A

6 1− s

3.58

s

2 HigherTwists

1p−n=

g A

6 1− s

3.58

s

2 4

Q2 6

Q4

4

Q2=M 2

9 a24d 22 f 2

Color Polarizabilities and Higher Twists

leading twist(twist 2)

higher twists

leading twist, can be obtained from moments of g

1twist-3, can be obtained from moments of g2

twist-4

X. Zheng, October 17, 2009

BROWN : E155, PLB. 553 (2003) 18BLACK : E94010, PRL. 92 (2004) 022301RED : RSS. PRL 98(2007)132003.Magenta: E99-117, PRC 70(2004)065207

Existing World Data on d2:PROTON

NEUTRON

d 2 Q2 = 3∫0

1x 2 [ g 2 x ,Q 2 − g 2

WW x , Q 2 ] d x

d2(Q2)d2(Q2)

X. Zheng, October 17, 2009

MAID Model

stat only

NEUTRON

Some preliminary data

RED : RSS. (Hall C, NH3,ND3)arXiv:0812.0031

BLUE: E01-012. (Hall A, 3He) preliminaryGREEN: E97-110. (Hall A, 3He) courtesy of V. Sulkosky very preliminary

d2(Q2)d2(Q2)

other ongoing analysis: Hall C “SANE” - for the proton Hall A “d2n”

50

Proton: nucl-ex/0508022

Phys.Lett.B613:148-153,2005

f 2p −n=− 0.18± 0.05−0.05

0.04

Phys.Rev.Lett.93:212001,2004 6

p−n / M 4=0.12± 0.02± 0.01

fit Q2=0.66-10 GeV2,

f 2n=0.033± 0.043

6n / M 4=−0.019±0.017

En =0.033±0.029

Bn =−0.001±0.016

Bp=0.06±0.08−0.04

0.05

Ep =−0.08±0.02−0.08

0.07f 2p=−0.160±0.027−0.106

0.111

4p /M 2=−0.064±0.012−0.047

0.049

Neutron

Proton-Neutron

Color Polarizabilities and Higher Twists

fit Q2=0.6-10 GeV2,

For both proton and neutron, the value indicates the 4 term roughly cancel with 6 term, i.e. the total higher twist effect is small, down to Q2=1 GeV2.EG1b result in preparation, higher precision data are expected.

CHL-2CHL-2

Upgrade magnets Upgrade magnets and power suppliesand power supplies

Enhance equipment in Enhance equipment in existing hallsexisting halls

6 GeV CEBAF1112Add new hallAdd new hall

Solenoid spectrometer for SIDIS at 11 GeV

GEMs

Proposed for PVDIS at 11 GeV

Polarized 3He Target Performance

figure credit: C. Dutta

Several Target Groups: JLab, UVa, W&M, Temple, Kentucky, UNH, ...

Polarized 3He Target Performance

Summary• Spin structure study full of surprises and puzzles• A decade of experiments from JLab: exciting

results• valence spin structure, quark-hadron duality• spin sum rules, polarizabilities, and extraction of

effective S• test PT calculations, ‘LT puzzle’• precision measurements of g2/d2: higher twists• first quasi-elastic target SSA: 2-photon to probe GPDs• JLab plays a major role in recent experimental

efforts • shed light on our understanding of strong + QCD• Bright future• complete a chapter in spin structure study with 6

GeV• 12 GeV Upgrade will greatly enhance our capability• Goal: a full understanding of nucleon structure and

strong interaction