Spin Study at JLab: from Longitudinal to Transverse

J. P. Chen, Jefferson LabBerkeley Summer Spin Program, 2009, LBNL, California

Introduction

Longitudinal and transverse spin

Selected results from JLab

Recently completed and planned measurements

12 GeV plan

Strong Interaction and QCD• Strong interaction, running coupling ~1 -- QCD: accepted theory for strong interaction -- asymptotic freedom (2004 Nobel) perturbation calculation works at high energy -- interaction significant at intermediate energy quark-gluon correlations -- interaction strong at low energy (nucleon size)

confinement

theoretical tools: pQCD, OPE, Lattice QCD, ChPT, …

• A major challenge in fundamental physics: Understand QCD in strong interaction region Study and understand nucleon structure

E

s

Nucleon Structure and Sum Rules

• Global properties and structure

Mass: 99% of the visible mass in universe

~1 GeV, but u/d quark mass only a few MeV each!

Momentum: quarks carry ~ 50%

Spin: ½, quarks contribution ~30% Spin Sum Rule

Magnetic moment: large part anomalous, >150% GDH Sum Rule

Axial charge Bjorken Sum Rule

Angular momentum Ji’s Sum Rule

Polarizabilities (Spin, Color)

Tensor charge

Three Decades of Spin Structure Study• 1980s: EMC (CERN) + early SLAC quark contribution to proton spin is very small = (12+-9+-14)% ! ‘spin crisis’ (Ellis-Jaffe sum rule violated)

• 1990s: SLAC, SMC (CERN), HERMES (DESY) = 20-30% the rest: gluon and quark orbital angular momentum

A+=0 (light-cone) gauge (½) + Lq+ G + Lg=1/2 (Jaffe)

gauge invariant (½) + Lq + JG =1/2 (Ji) A new decomposition (X. Chen, et. al) Bjorken Sum Rule verified to <10% level

• 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … : ~ 30%;G probably small, orbital angular momentum probably significant Transversity, Transverse-Momentum Dependent Distributions Generalized Parton Distributions

Unpolarized and Polarized Structure functions

Parton Distributions (CTEQ6 and DSSV)

DSSV, PRL101, 072001 (2008)

CTEQ6, JHEP 0207, 012 (2002)

Polarized PDFsUnpolarized PDFs

Jefferson Lab Experimental Halls

HallA: two HRS’ Hall B:CLAS Hall C: HMS+SOS

6 GeV polarized CW electron beam Pol=85%, 180A

Will be upgraded to 12 GeV by ~2014

Jefferson Lab Hall A Experimental Setup Jefferson Lab Hall A Experimental Setup for inclusive polarized n (for inclusive polarized n (33He) He)

ExperimentsExperiments

Hall A polarized 3He target

longitudinal, transverse and vertical

Luminosity=1036 (1/s) (highest in the world)

High in-beam polarization > 65%

Effective polarized neutron target

12 completed experiments 1 are currently running 6 approved with 12 GeV (A/C)

15 uA

Hall B/C Polarized proton/deuteron target

• Polarized NH3/ND3 targets

• Dynamical Nuclear Polarization

• In-beam average polarization

70-90% for p

30-40% for d• Luminosity up to ~ 1035 (Hall C)

~ 1034 (Hall B)

JLab Spin Experiments

• Results:• Moments: Spin Sum Rules and Polarizabilities• Higher twists: g2/d2

• Quark-Hadron duality• Spin in the valence (high-x) region

• Just completed: • d2

p (SANE) and d2n

• Transversity (n)

• Planned• g2

p at low Q2

• Future: 12 GeV• Inclusive: A1/d2,

• Semi-Inclusive: Transversity, TMDs, Flavor-decomposition

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

Longitudinal Spin (I)

Spin in Valence (high-x) Region

Valence (high-x) A1p and A1

n results

Hall B CLAS, Phys.Lett. B641 (2006) 11 Hall A E99-117, PRL 92, 012004 (2004) PRC 70, 065207 (2004)

Inclusive Hall A and B and Semi-Inclusive Hermes

BBS

BBS+OAM

F. Yuan, H. Avakian, S. Brodsky, and A. Deur, arXiv:0705.1553

pQCD with Quark Orbital Angular Momentum

A1p at 11 GeV

Projections for JLab at 11 GeV

u and d at JLab 11 GeV

Flavor decomposition with SIDISFlavor decomposition with SIDIS

Polarized Sea

JLab @11 GeV

Longitudinal Spin (II)

Quark Hadron Duality in Spin Strcuture Function

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

• g1/g2 and A1/A2 (3He/n) in resonance region,

1 < Q2 < 4 GeV2

• Study quark-hadron duality in spin structure.

<Resonances> = <DIS> ?

• PRL 101, 1825 02 (2008)

A13He (resonance vs DIS)

Duality in Spin-Structure: Partial Moment Results

1 resonance comparison with pdfs

Spin Sum Rules: Zeroth Moments

Moments of Spin Structure Functions

Sum Rules

Global Property

Bjørken Sum Rule

1p (Q2) 1

n (Q2) {g1p (x,Q2) g1

n (x,Q2)}dx1

6gACNS

gA: axial vector coupling constant from neutron -decayCNS: 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

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

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

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• casuality 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, MAMI(2), …

1 2 ( ) 3 2 () d

2 2EM

M 2 2

in

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)

• Generalized GDH Sum Rule

el v

dvvQGQS

),(4)(

212

1

Connecting GDH with 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 at Low Q2

• 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

First Moment of g1p and g1

n :1p and 1

n

EG1b, arXiv:0802.2232 EG1a, PRL 91, 222002 (2003)

1p

Test fundamental understanding ChPT at low Q2, Twist expansion at high Q2, Future Lattice QCD

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

1n

1 of p-n

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

Effective Strong Coupling

A new attempt at low Q2 Experimental Extraction 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

...)58.3

1(6

)( 2)(111

ssAnpnp g

dxgg

Generalized Bjorken sum rule:

Definition of effective QCD couplings

G. Grunberg, PLB 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.

tsHigherTwisg

dxgg ssAnpnp ...)

58.31(

6)( 2)(

111

)1(6

1)(

1 g

sAnp g

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.

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)

“Comparison” with theory

Furui & Nakajima

↔

Fisher et al.Bloch et al.Maris-TandyBhagwat et al. Cornwall

Godfrey-Isgur: Constituant Quark ModelFurui & Nakajima: Lattice

Schwinger

-Dyson

Transverse Spin (I): Inclusive

g2 Structure Function and Moments Burkhardt - Cottingham Sum Rule

g2: twist-3, q-g correlations• experiments: transversely polarized target

SLAC 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

1

21

21

22

22

22

22

),(),(),(

),(),(),(

x

WW

WW

y

dyQygQxgQxg

QxgQxgQxg

Precision Measurement of g2n(x,Q2): Search for Higher Twist Effects

• Measure higher twist quark-gluon correlations.• Hall A Collaboration, K. Kramer et al., PRL 95, 142002 (2005)

BC Sum Rule BC Sum Rule

P

N

3He

BC = Meas+low_x+Elastic

0<X<1 :Total Integral

very prelim

“low-x”: refers to unmeasured low x part of the integral. Assume Leading Twist Behaviour

Elastic: From well know FFs (<5%)

“Meas”: Measured x-range

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

0)(1

0 22 dxxgΓ

BC Sum Rule BC Sum Rule

P

N

3He BC satisfied w/in errors for 3He

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

BC satisfied w/in errors for JLab Proton2.8 violation seen in SLAC data

very prelim

BC Sum RuleBC Sum Rule

P

N

3He

Measured x 0<x<1

Unmeasured Low-X

“DIS” = -(RES+ELAS)

What can BC tell us about Low-X?

very prelim

Spin Polarizabilities

Higher Moments of Spin Structure Functions at Low Q2

Higher Moments: Generalized Spin Polarizabilities

• generalized forward spin polarizability 0

generalized L-T spin polarizability LT

dxxQgxQ

MxQgx

Q

M

dQQK

Q

x

TT

)],(4

),([16

),(),()

2

1()(

22

2

0 2

22

12

6

2

3

22

22

0

0

0

0

2

0

0

221

26

2

2

22

22

),(),([16

),(),()

2

1()(

x

LTLT

dxxQgxQgxQ

M

dQ

QQKQ

Neutron Spin Polarizabilities LT insensitive to resonance• RB ChPT calculation with resonance for 0 agree with data at Q2=0.1 GeV2 • Significant disagreement between data and both ChPT calculations for LT

• Good agreement with MAID model predictions

0 LT

Q2

Q2

E94-010, PRL 93 (2004) 152301

CLAS Proton Spin Polarizability

• EG1b, Prok et al. arXiv:0802.2232

Large discrepancies with ChPT!

Only longitudinal data, model for transverse (g2)

0 sensitive to

resonance

0p 0

p Q6

Summary of Comparison with PT

IAn 1

P 1n 1

p-n 0p 0

n LTn

Q2 (GeV2) 0.1 0.1 0.05 0.1 0.05 0.16 0.05 0.05 0.1 0.1

HBPT poor poor good poor good good good bad poor bad

RBPT/good fair fair fair good poor fair bad good bad

LT puzzle: LT not sensitive to , one of the best quantities to test PT,

it disagrees with neither calculations by several hundred %!

A challenge to PT theorists.

Very low Q2 data g1/g2 on n(3He) (E97-110)

g1 on p and d available soon (EG4)

Recently approved: g2 on proton E08-027

BC

Su

m R

ule

LT S

pin

Pola

riza

bili

ty

E08-027 : A- rating by PAC33K. Slifer, A. Camsonne, ,J. P. Chen

Septa Magnets for low Q2

Transverse bPolarized Proton Target

pg2 : central to knowledge of Nucleon Structure but remains unmeasured at low Q2

—Critical input to Hydrogen Hyperfine Calculations—Violation of BC Sum Rule suggested at large Q2

—State-of-Art PT calcs fail dramatically for LT

New Experiment: Proton g2 and LT

n

Color Polarizabilities

Higher Moments of Spin Structure Functions at High Q2

Color Polarizability (or Lorentz Force): d2

• 2nd moment of g2-g2WW

d2: twist-3 matrix element

d2 and g2-g2WW: clean access of higher twist (twist-3) effect: q-g correlations

Color polarizabilities are linear combination of d2 and f2

Provide a benchmark test of Lattice QCD at high Q2

Avoid issue of low-x extrapolation

Relation to Sivers and other TMDs?

1

0

22

21

2

1

0

22

22

222

)],(3),(2[

)],(),([3)(

dxQxgQxgx

dxQxgQxgxQd WW

Measurements on neutron: d2n (Hall A and SLAC)

d2(Q2) d2(Q2)

ProtonMAID Model

stat only

very prelim

GREEN: E97-110. (Hall A, 3He)

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

BLUE: E01-012. (Hall A, 3He)

BRAND NEW DATA!Very Preliminary

Neutron

d2(Q2) d2(Q2)

E08-027 “g2p”SANE

“d2n” just completed in Hall A

6 GeV Experiments

Sane: just completed in Hall C

“g2p” in Hall A, 2011

projected

Planned d2n with JLab 12 GeV

• Projections with 12 GeV experiments Improved Lattice Calculation (QCDSF, hep-lat/0506017)

Color “Polarizabilities”Color “Polarizabilities”

f2 Extraction and Color Polarizabilities• JLab + world n data, 4 = (0.019+-0.024)M2

• Twist-4 term 4 = (a2+4d2+4f2)M2/9

• extracted from 4 term f2 = 0.034+-0.005+-0.043

f2 can be measured from g3

• Color polarizabilities

= 0.033+-0.029 B = -0.001+-0.016

• Proton and p-n

f2= -0.160+-0.179 (p), -0.136+-0.109 (p-n)

PLB 93 (2004) 212001

Transverse Spin (II): Single Spin Asymmetries in SIDIS

Transversity and TMDs

Transversity

• Three twist-2 quark distributions:• Momentum distributions: q(x,Q2) = q↑(x) + q↓(x)• Longitudinal spin distributions: Δq(x,Q2) = q↑(x) - q↓(x)• Transversity distributions: δq(x,Q2) = q┴(x) - q┬(x)

• It takes two chiral-odd objects to measure transversity• Semi-inclusive DIS

Chiral-odd distributions function (transversity) Chiral-odd fragmentation function (Collins function)

• TMDs: (without integrating over PT)

• Distribution functions depends on x, k┴ and Q2 : δq, f1T┴ (x,k┴ ,Q2), …

• Fragmentation functions depends on z, p┴ and Q2 : D, H1(x,p┴ ,Q2)• Measured asymmetries depends on x, z, P┴ and Q2 : Collins, Sivers, …

(k┴, p┴ and P┴ are related)

“Leading-Twist” TMD Quark Distributions

Quark

Nucleon

Unpol.

Long.

Trans.

Unpol. Long. Trans.

Current Status• Large single spin asymmetry in pp->X• Collins Asymmetries

- sizable for proton (HERMES and COMPASS) large at high x,- and has opposite sign unfavored Collins fragmentation as large as favored (opposite sign)? - consistent with 0 for deuteron (COMPASS)

• Sivers Asymmetries - non-zero for + from proton (HERMES), consistent with zero (COMPASS)? - consistent with zero for - from proton and for all channels from deuteron - large for K+ ?

• Very active theoretical and experimental study RHIC-spin, JLab (Hall A 6 GeV, CLAS12, HallA/C 12 GeV), Belle, FAIR (PAX)

• Global Fits/models by Anselmino et al., Yuan et al. and …

• First neutron measurement from Hall A 6 GeV (E06-010)

• Solenoid with polarized 3He at JLab 12 GeV Unprecedented precision with high luminosity and large acceptance

E06-010 Single Target-Spin Asymmetry in Semi-Inclusive n↑(e,e′π+/-) Reaction on a Transversely Polarized 3He Target

Collins

Sivers

First neutron measurement

7 PhD Students

Completed data taking in Feb.

Exceeded PAC approved goal

Hall-A Transversity: en→e’Xen→e’X

Polarized 3He: effective polarized neutron targetWorld highest polarized luminosity: 1036

New record in polarization: >70% without beam ~65% in beam and with spin-flip (proposal 42%)

HRSL for hadrons (p+- and K+-), new RICH commissioned

BigBite for electrons, 64 msr, detectors performing well

Cell: AstralCell: Astral Cell: MaureenCell: Maureen

Target PerformanceOnline preliminary

EPR/NMR analysis shows a stable 65% polarization with 15 A beam and 20 minute spin flip

Projections of g1T First Neutron (3He) MeasurementWith Fast Beam Helicity Flip (30Hz)Projected Uncertainties (Stat. Only):

2.3% at low x3.4% at high x

Precision Study of Transversity and TMDs

• From exploration to precision study• Transversity: fundamental PDFs, tensor charge• TMDs provide 3-d structure information of the nucleon• Learn about quark orbital angular momentum• Multi-dimensional mapping of TMDs

• 3-d (x,z,P┴ )

• Q2 dependence • Multi-facilities, global effort

• Precision high statistics• high luminosity and large acceptance

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

12 GeV Upgrade Kinematical Reach

• Reach a broad DIS region • Precision SIDIS for

transversity and TMDs• Experimental study/test of

factorization • Decisive inclusive DIS

measurements at high-x• Study GPDs

Solenoid detector for SIDIS at 11 GeV

GEMs

Proposed for PVDIS at 11 GeV

3-D Mapping of Collins/Siver Asymmetries at JLab 12 GeVWith A Large Acceptance Solenoid Detector

• Both + and -

• For one z bin

(0.5-0.6)

• Will obtain 4

z bins (0.3-0.7)

• Upgraded PID for K+ and K-

3-D Projections for Collins and Sivers Asymmetry (+)

Discussion• Unprecedented precision 3-d mapping of SSA

• Collins and Sivers• +, - and K+, K-

• Study factorization with x and z-dependences • Study PT dependence• Combining with CLAS12 proton and world data

• extract transversity and fragmentation functions for both u and d quarks• determine tensor charge• study TMDs for both valence and sea quarks • study quark orbital angular momentum

• Combining with world data, especially data from high energy facilities• study Q2 evolution

• Global efforts (experimentalists and theorists), global analysis• much better understanding of 3-d nucleon structure and QCD

Spin Structure with the Solenoid at JLab 12 GeV

• Program on neutron spin structure with polarized 3He and solenoid Polarized 3He target

effective polarized neutron highest polarized luminosity: 1036

A solenoid with detector package (GEM, EM calorimeter+ Cherenkov large acceptance: ~700 msr for polarized (without baffles) high luminosity and large acceptance

Inclusive DIS: improve by a factor of 10-100

A1 at high-x: high precision d2 at high Q2: very high precision parity violating spin structure g3/g5 : first significant measurement

SIDIS: improve by a factor of 100-1000 transversity and TMDs, spin-flavor decomposition (~2 orders improvement)• Unpolarized luminosity: 5x1038 , acceptance ~ 300 msr (with baffles)

Parity-Violating DIS Boer-Mulders function

Single Spin Asymmetries in (Qausi-)Ealstic

Two-photon Exchange and GPDs

E05-015: Target Single Spin Asymmetry Ay

• Inclusive quasi-elastic electron scattering on vertically polarized 3He target

•Target Single Spin Asymmetry Ay=0 in one-photon approximation, two-photon exchange gives non-zero Ay.

• Elastic contribution is well-known, inelastic response provides a new way to access the Generalized Parton Distributions.

E05-015 Projection

• Neutron data provide unique new constraints on GPDs.

• Measurements at Q2=0.5, 1.0 GeV2

(and 2 GeV2).

• GPD model prediction and expected uncertainty (~2x10-3) at Q2=1.0 GeV2.

• Data taken competed two weeks ago, exceeded approved goal.

•First clear non-zero asymmetry measurement @ 10level Established quantitatively the 2-photon-exchange mechanism. Established it as a tool to precisely probe hadron structure.

Blue curve = elastic contrib.Black curve = inelastic contrib.Red point = total contrib.

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 and polarizabilities• test PT calculations, ‘LT puzzle’• precision measurements of g2/d2: high-twist• first neutron transversity measurement• first quasi-elastic target SSA: 2-photon to probe GPDs

• JLab played a major role in recent experimental efforts • shed light on our understanding of STRONG QCD • lead to breakthrough?

• Bright future• complete a chapter in spin structure study with 6 GeV JLab• 12 GeV Upgrade will greatly enhance our capability • Goal: a full understanding of nucleon structure and strong interaction