Highlights of Spin Study at JLab Hall A: Longitudinal and Transverse

J. P. Chen, Jefferson LabPacific-Spin2011, Cairns, Australia

Introduction

Longitudinal and transverse spin

Selected results from JLab Hall A

SSA in SIDIS: Transversity and TMDs

g2 (d2) at intermediate to high Q2: higher-twists, B-C sum rule

g1/g2 at low Q2: GDH sum/spin polarizabilities

Future experiments (6 GeV and 12 GeV)

Spin Milestones (I)

• Nature: (www.nature.com/milestones/milespin) 1896: Zeeman effect (milestone 1) 1922: Stern-Gerlach experiment (2) 1925: Spinning electron (Uhlenbeck/Goudsmit)(3) 1928: Dirac equation (4) Quantum magnetism (5) 1932: Isospin(6) 1935: Proton anomalous magnetic moment 1940: Spin–statistics connection(7) 1946: Nuclear magnetic resonance (NMR)(8) 1950s: Development of magnetic devices (9) 1950-51: NMR for chemical analysis (10) 1951: Einstein-Podolsky-Rosen argument in spin variables(11) 1964: Kondo Effect (12) 1971: Supersymmetry(13) 1972:Superfluid helium-3 (14)

Spin Milestones (II) 1973: Magnetic resonance imaging(15) 1975-76:NMR for protein structure determination (16) 1978: Dilute magnetic semiconductors (17) 1980s: “Proton spin crisis or puzzle” 1988: Giant magnetoresistance(18) 1990: Functional MRI (19) Proposal for spin field-effect transistor (20) 1991: Magnetic resonance force microscopy (21) 1996: Mesocopic tunnelling of magnetization (22) 1997: Semiconductor spintronics (23) (Spin-polarized suprecurrents for spintronics, 1/2011) 2000s: “Nucleon transverse spin puzzle”? ?: More puzzles in nucleon spin? …… ?: Breakthroughs in nucleon spin/nucleon structure study? …… ?: Applications of nucleon spin physics?

Nucleon Structure, Moments 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% Energy-Momentum Sum Rule

Spin: ½, quarks contribution ~30% Spin Sum Rule(s)

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) What observable directly corresponds to Lz~ bx X py ? Bjorken Sum Rule verified to <10% level

• 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … : ~ 30%;G probably small, orbital angular momentum probably significant Sum Rules at low Q2

Higher-Twists Transversity, Transverse-Momentum Dependent Distributions

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

JLab Polarized 3He Target

longitudinal, transverse and vertical

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

High in-beam polarization ~ 60%

Effective polarized neutron target

13 completed experiments 7 approved with 12 GeV (A/C)

15 uA

JLab 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/A)

~ 1034 (Hall B)

JLab Spin Experiments

• Results:• SSA in SIDIS: Transversity (n)/ TMDs• g2/d2: Higher twists, B-C sum rule• Spin Moments: Spin Sum Rules and Polarizabilities• Quark-Hadron duality• Spin in the valence (high-x) region

• 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

Single Target-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 PDFs

f1 =

f 1T =

SiversSivers

HelicityHelicity

g1 =

h1 =TransversityTransversity

h1 =

Boer-MuldersBoer-Mulders

h1T =

PretzelosityPretzelosity

h1L =

Worm GearWorm Gear(Kotzinian-Mulders)(Kotzinian-Mulders)

: Survive trans. Momentum : Survive trans. Momentum integrationintegration

Nucleon Spin

Quark Spin

g1T =

Worm GearWorm Gear

Leading-Twist TMD PDFs

f1 =

f 1T =

SiversSivers

HelicityHelicityg1 =

h1 =TransversityTransversity

h1 =

Boer-MuldersBoer-Mulders

h1T =

PretzelosityPretzelosity

g1T =

Worm GearWorm Gear

h1L =

Worm GearWorm Gear(Kotzinian-Mulders)(Kotzinian-Mulders)

: Probed by E06-010Nucleon Spin

Quark Spin

Separation of Collins, Sivers and pretzelocity effects through angular dependence

1( , )

sin( ) sin( )

sin(3 )

l lUT h S

h SSiverCollins

Pretzelosi

UT

tyU

sUT h S

h ST

N NA

P N

A

A

N

A

1

1 1

1

1 1

sin( )

sin(3 )

sin( )Co

PretzelosityU

SiversUT

llins

T h S T

h S

UT

UT h S

TU

UT

TA

H

f

A

D

A h H

h

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 Experiment ‑• First measurement on n (3He)• Polarized 3He Target• Polarized Electron Beam, 5.9 GeV

– ~80% Polarization– Fast Flipping at 30Hz

• BigBite at 30º as Electron Arm– Pe = 0.7 ~ 2.2 GeV/c

• HRSL at 16º as Hadron Arm– Ph = 2.35 GeV/c – Excellent PID for /K/p

• 7 PhD Thesis Students (5 graduated)

16

Beam Polarimetry(Møller + Compton)

LuminosityMonitor

XeeHe ),(3

History of Figure of Merit of Polarized 3He Target

• High luminosity: L(n) = 1036 cm-2 s-1

• Record high in-beam ~ 60% polarization with 15 A beam with automatic spin flip every 20 minutes

Performance of 3He Target

In-beam 3He pol. 55-60%

3He Target Single-Spin Asymmetry in SIDIS

3He Sivers SSA:negative for π+,

3He Collins SSA small Non-zero at highest x for +

Blue band: model (fitting) uncertainties Red band: other systematic uncertainties

arXiv: 1106.0363, submitted to PRL

Results on Neutron

Collinsasymmetries are not large, except at x=0.34

Sivers negative

Blue band: model (fitting) uncertainties Red band: other systematic uncertainties

Asymmetry ALT Result

• 3He ALT

Positive for -

hq

qTLT DgFA shsh

11)cos()cos(

LT

To leading twist:

Preliminary

• – Corrected for proton dilution, fp

– Predicted proton asymmetry contribution < 1.5% (π+), 0.6% (π-)

• – Dominated by L=0 (S) and L=1 (P) interference

• Consist w/ model in signs, suggest larger asymmetry

Neutron ALT Extraction

Preliminary

hq

qT

n DgA 11LT

JLab 12 GeV Era: Precision Study of TMDs

• From exploration to precision study with 12 GeV JLab• Transversity: fundamental PDFs, tensor charge• TMDs: 3-d momentum structure of the nucleon Quark orbital angular momentum• Multi-dimensional mapping of TMDs

• 4-d (x,z,P┴,Q2)

• Multi-facilities, global effort

• Precision high statistics• high luminosity and large acceptance

Solenoid detector for SIDIS at 11 GeVAlso for PVDIS at 11 GeV

Approved SIDIS experiments: E10-006 & E11-007

SSA in SIDIS Pion Production Transversely/ Longitudinally Polarized 3He Target at 8.8 and 11 GeV.

Large acceptance: >100 msr

High luminosity : > 1036

Mapping of Collins/Siver Asymmetries with SoLID

• Both + and -

• For one z bin

(0.4-0.45)

• Will obtain many z bins (0.3-0.7)

• Upgraded PID for K+ and K-

Map Collins and Sivers asymmetries in 4-D (x, z, Q2, PT)

Worm-gear functions:• Dominated by real part of interference

between L=0 (S) and L=1 (P) states• No GPD correspondence• Lattice QCD -> Dipole Shift in mom. space.• Model Calculations -> h1L

=? -g1T .

h1L =

g1T =

Worm Gear

Cent

er o

f poi

nts:

)()(~ 11 zDxgA TLT )()(~ 11 zHxhA LUL

Discussion• Unprecedented precision 4-d mapping of SSA

• Collins and Sivers• +, - and K+, K-

• New proposal polarized proton with SoLID• Study factorization with x and z-dependences • Study PT dependence• Combining with the 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• study Q2 evolution

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

• Longer-term future: EIC to map sea and gluon SSAs

Inclusive Transverse Spin

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

Results on 2n : E01-012 and E94-010

Higher-Twist Extraction and Comparison

Extract Higher-Twist part of 2DIS

Compare with higher-twist estimated from E97-103 data

Color Polarizability (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

d2(Q2) d2(Q2)

E08-027 “g2p”SANE

“d2n” new in Hall A

6 GeV Experiments

Sane: new in Hall C

“g2p” in Hall A, 2011

projected

Spin Sum Rules: Moments of SFs

Moments of Spin Structure Functions

Sum Rules

Global Property

Generalized GDH Sum RuleConnecting 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 Theory

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

RBPT: Bernard, Hemmert, MeissnerReviews: Chen, Deur, Meziani, Mod. Phy. Lett. A 20, 2745 (2005)

J.P. Chen, Int. J. Mod. Phys. E19, 1893 (2010).

el v

dvvQGQS

),(4)(

212

1

JLab E94-010 and E97-110

Genaralized GDH sum on neutron at Low Q2

0.1 < Q2 < 1 GeV2, resonance region

PRL 89 (2002) 242301

Q2

E97-110

Q2

E94-010

0.02 < Q2 < 0.3 GeV2, resonance region

First Moment of g1p :1

p

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

First Moment of g1n :1

n

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

1n

1 of p-n

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

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)

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

Preliminary Results from E97-110• Significant disagreement between data and both ChPT calculations for LT

• Good agreement with MAID model predictions

0 LT

Q2

Q2

Axial Anomaly and the LT Puzzle

N. Kochelev and Y. Oh; arXiv:1103.4891v1

E08-027 : Proton g2 Structure Function Fundamental spin observable has never been measured at low or moderate Q2

BC Sum Rule : violation suggested for proton at large Q2, but found satisfied for the neutron & 3He.

Spin Polarizability : Major failure (>8 of PT for neutron LT. Need g2 isospin separation to solve.

Hydrogen HyperFine Splitting : Lack of knowledge of g2 at low Q2 is one of the leading uncertainties.

Proton Charge Radius : also one of the leading uncertainties in extraction of <Rp> from H Lamb shift.

BC

Su

m R

ule

Spokespersons: Camsonne, Crabb, Chen, Slifer(contact), 6 PhD students, 3 postdocs

Scheduled to run 11/2011-5/2012

Sp

in P

ola

riza

bili

ty

LT

Summary

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

• first neutron transversity/TMD measurement• precision measurements of g2/d2: high-twist• spin sum rules and polarizabilities• test PT calculations, ‘LT puzzle’ • valence spin structure, quark-hadron duality

• Bright future• complete a chapter in spin structure study with 6 GeV JLab• 12 GeV Upgrade will greatly enhance our capability

• Precision determination of the valence quark spin structure• Precision multi-d map of TMDs/transverse spin/tensor charge• Precision extraction of GPDs, 3-d structure

• EIC: precision determination of sea and gluon in multi-d• Goal: a full understanding of nucleon structure and QCD• Lead to breakthrough in strong interaction?