1. Spin Study at JLab: from Longitudinal to Transverse
J. P. Chen, Jefferson Lab
Berkeley Summer Spin Program, 2009, LBNL, California
Introduction
Longitudinal and transverse spin
Selected results from JLab
Recently completed and planned measurements
12 GeV plan

2. 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 as E

3. 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

4. Three Decades of Spin Structure Study
1980s: EMC (CERN) + early SLAC
quark contribution to proton spin is very small
DS = ( )% ! ‘spin crisis’
(Ellis-Jaffe sum rule violated)
1990s: SLAC, SMC (CERN), HERMES (DESY)
DS = 20-30%
the rest: gluon and quark orbital angular momentum
A+=0 (light-cone) gauge (½)DS + Lq+ DG + Lg=1/ (Jaffe)
gauge invariant (½)DS + Lq + JG =1/ (Ji)
A new decomposition (X. Chen, et. al)
Bjorken Sum Rule verified to <10% level
2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … :
DS ~ 30%; DG probably small, orbital angular momentum probably significant
Transversity, Transverse-Momentum Dependent Distributions
Generalized Parton Distributions

5. Unpolarized and Polarized Structure functions

6. Parton Distributions (CTEQ6 and DSSV)
Polarized PDFs
Unpolarized PDFs
CTEQ6, JHEP 0207, 012 (2002)
DSSV, PRL101, (2008)

7. Jefferson Lab Experimental Halls
6 GeV polarized
CW electron beam
Pol=85%, 180mA
Will be upgraded to 12 GeV by ~2014
HallA: two HRS’ Hall B:CLAS Hall C: HMS+SOS

8. Jefferson Lab Hall A Experimental Setup for inclusive polarized n (3He) Experiments

9. 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

10. 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)

11. JLab Spin Experiments Results: Just completed: Planned Future: 12 GeV
Moments: Spin Sum Rules and Polarizabilities
Higher twists: g2/d2
Quark-Hadron duality
Spin in the valence (high-x) region
Just completed:
d2p (SANE) and d2n
Transversity (n)
Planned
g2p at low Q2
Future: 12 GeV
Inclusive: A1/d2,
Semi-Inclusive: Transversity, TMDs, Flavor-decomposition
Review: Sebastian, Chen, Leader, arXiv: , PPNP 63 (2009) 1

12. Longitudinal Spin (I)
Spin in Valence (high-x) Region

13. Valence (high-x) A1p and A1n results
Hall A E99-117, PRL 92, (2004)
PRC 70, (2004)
Hall B CLAS, Phys.Lett. B641 (2006) 11

14. pQCD with Quark Orbital Angular Momentum
F. Yuan, H. Avakian, S. Brodsky, and A. Deur, arXiv:
Inclusive Hall A and B and Semi-Inclusive Hermes
BBS
BBS+OAM

15. Projections for JLab at 11 GeV
A1p at 11 GeV

16. Flavor decomposition with SIDIS
Du and Dd at JLab 11 GeV
Polarized Sea
GeV

17. Longitudinal Spin (II)
Quark Hadron Duality in Spin Strcuture Function

18. Duality in Spin-Structure: Hall A E01-012 Results
A13He (resonance vs DIS)
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, (2008)

19. Duality in Spin-Structure: Partial Moment Results
G1 resonance comparison with pdfs

20. Spin Sum Rules: Zeroth Moments
Moments of Spin Structure Functions 
Global Property

21. Bjørken Sum Rule
gA: axial vector coupling constant from neutron b-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
Valid at large Q2 (higher-twist effects negligible)
Data are consistent with the Bjørken Sum Rule at 5-10 % level

22. Gerasimov-Drell-Hearn Sum Rule Circularly 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), …

23. 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,n), S2(Q2, n)
Same assumptions: no-subtraction dispersion relation
optical theorem
(low energy theorem)
Generalized GDH Sum Rule

24. 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 ~ k  GDH
High Q2 (> ~1 GeV2): Operator Product Expansion
Intermediate Q2 region: Lattice QCD calculations
Low Q2 region (< ~0.1 GeV2): Chiral Perturbation Theory
Calculations: HBcPT: Ji, Kao, Osborne, Spitzenberg, Vanderhaeghen
RBcPT: Bernard, Hemmert, Meissner
Reviews: Theory: Drechsel, Pasquini, Vanderhaeghen, Phys. Rep. 378,99 (2003)
Experiments: Chen, Deur, Meziani, Mod. Phy. Lett. A 20, 2745 (2005)

25. Q2 evolution of neutron spin structure moments
JLab E (Hall A) Neutron spin structure moments and sum rules at Low Q2
GDH integral on neutron
Q2 evolution of neutron spin structure moments
(sum rules) with pol. 3He
transition from quark-gluon to hadron
Test cPT calculations
Results published in several PRL/PLB’s Q2
PRL 89 (2002)

26. First Moment of g1p and g1n : G1p and G1n
Test fundamental understanding
ChPT at low Q2, Twist expansion at high Q2, Future Lattice QCD
G1p
G1n
E94-010, from 3He, PRL 92 (2004)
E97-110, from 3He, preliminary
EG1a, from d-p
EG1b, arXiv:
EG1a, PRL 91, (2003)

27. G1 of p-n
EG1b, PRD 78, (2008)
E EG1a: PRL 93 (2004)

28. Effective Strong Coupling
A new attempt at low Q2
Experimental Extraction from Bjorken Sum

29. The strong coupling constant from pQCD
as (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 LQCD

30. Definition of effective QCD couplings
G. Grunberg, PLB B95 70 (1980); PRD (1984); PRD (1989).
Prescription:
Define effective couplings from a perturbative series truncated to the first term in as.
Generalized Bjorken sum rule:
Use
to define an effective asg1.
Process dependent. But can be related through
“Commensurate scale relations”
S.J. Brodsky & H.J Lu, PRD (1995)‏
S.J. Brodsky, G.T. Gabadadze, A.L. Kataev, H.J Lu, PLB (1996)‏
Extend it to low Q2 down to 0: include all higher twists.

31. Effective Coupling Extracted from Bjorken Sum
A. Deur, V. Burkert, J. P. Chen and W. Korsch
PLB 650, 244 (2007) and PLB 665, 349 (2008)
as/p

32. “Comparison” with theory ↔
Fisher et al.
Bloch et al.
Maris-Tandy
Bhagwat et al.
Cornwall
Godfrey-Isgur: Constituant Quark
Model
Furui & Nakajima: Lattice
Schwinger
-Dyson
Furui & Nakajima

33. Transverse Spin (I): Inclusive
g2 Structure Function and Moments
Burkhardt - Cottingham Sum Rule

34. 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

35. 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, (2005)

36. BC Sum Rule BC = Meas+low_x+Elastic P N 3He
0<X<1 :Total Integral P
Brawn: SLAC E155x
Red: Hall C RSS
Black: Hall A E94-010
Green: Hall A E (preliminary)
Blue: Hall A E01-012
(very preliminary) N
very prelim
BC = Meas+low_x+Elastic
“Meas”: Measured x-range
3He
“low-x”: refers to unmeasured low x part
of the integral.
Assume Leading Twist Behaviour
Elastic: From well know FFs (<5%)

37. BC Sum Rule P N 3He BC satisfied w/in errors for JLab Proton
2.8 violation seen in SLAC data N
BC satisfied w/in errors for Neutron
(But just barely in vicinity of Q2=1!)
very prelim
3He
BC satisfied w/in errors for 3He

38. BC Sum Rule What can BC tell us about Low-X? P N 3He Unmeasured Low-X
Measured x
0<x<1
What can BC tell us about Low-X? P N
Unmeasured Low-X
very prelim
“DIS” = -(RES+ELAS)
3He

39. Spin Polarizabilities
Higher Moments of Spin Structure Functions at Low Q2

40. Higher Moments: Generalized Spin Polarizabilities
generalized forward spin polarizability g0
generalized L-T spin polarizability dLT

41. Neutron Spin Polarizabilities
dLT insensitive to D resonance
RB ChPT calculation with resonance for g0 agree with data at Q2=0.1 GeV2
Significant disagreement between data and both ChPT calculations for dLT
Good agreement with MAID model predictions
g dLT
E94-010, PRL 93 (2004) Q2 Q2

42. CLAS Proton Spin Polarizability
g0p
g0p Q6
EG1b, Prok et al.
arXiv:
Large discrepancies with ChPT!
Only longitudinal data, model for transverse (g2)
g0 sensitive to resonance

43. Summary of Comparison with cPT
IAn G1P G1n G1p-n g0p g0n dLTn
Q2 (GeV2)
HBcPT poor poor good poor good good good bad poor bad
RBcPT/D good fair fair fair good poor fair bad good bad
dLT puzzle: dLT not sensitive to D, one of the best quantities to test cPT,
it disagrees with neither calculations by several hundred %!
A challenge to cPT 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

44. New Experiment: Proton g2 and LT
g2 : central to knowledge of Nucleon Structure
but remains unmeasured at low Q2
E : A- rating by PAC33
K. Slifer, A. Camsonne, ,J. P. Chen
Critical input to Hydrogen Hyperfine Calculations
Violation of BC Sum Rule suggested at large Q2
State-of-Art PT calcs fail dramatically for LT
Septa Magnets for low Q2
Transverse bPolarized Proton Target n
LT Spin Polarizability
BC Sum Rule

45. Color Polarizabilities
Higher Moments of Spin Structure Functions at High Q2

46. 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 cE,cB 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?

47. Measurements on neutron: d2n (Hall A and SLAC)

48. d2(Q2) BRAND NEW DATA! Very Preliminary Proton MAID Model
RED : RSS. (Hall C, NH3,ND3)
BLUE: E (Hall A, 3He)
Neutron
very prelim
GREEN: E (Hall A, 3He)
stat only

49. d2(Q2) Sane: just completed in Hall C “g2p” in Hall A, 2011
E “g2p”
SANE
6 GeV Experiments
Sane: just completed in Hall C
“g2p” in Hall A, 2011
projected
“d2n” just completed in Hall A

50. Planned d2n with JLab 12 GeV
Projections with 12 GeV experiments
Improved Lattice Calculation (QCDSF, hep-lat/ )

51. Color “Polarizabilities”

52. f2 Extraction and Color Polarizabilities
JLab + world n data,
m4 = ( )M2
Twist-4 term
m4 = (a2+4d2+4f2)M2/9
extracted from m4 term f2 =
f2 can be measured from g3
Color polarizabilities
cE =
cB =
Proton and p-n
f2= (p),
(p-n)
PLB 93 (2004)

53. Transverse Spin (II): Single Spin Asymmetries in SIDIS
Transversity and TMDs

54. 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)

55. “Leading-Twist” TMD Quark Distributions
Nucleon
Unpol.
Long.
Trans.
Quark
Unpol.
Long.
Trans. 55 55

56. Current Status Large single spin asymmetry in pp->pX
Collins Asymmetries
- sizable for proton (HERMES and COMPASS)
large at high x, p- and p+ has opposite sign
unfavored Collins fragmentation as large as favored (opposite sign)?
- consistent with 0 for deuteron (COMPASS)
Sivers Asymmetries
- non-zero for p+ from proton (HERMES), consistent with zero (COMPASS)?
- consistent with zero for p- 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

57. E Single Target-Spin Asymmetry in Semi-Inclusive n↑(e,e′π+/-) Reaction on a Transversely Polarized 3He Target
First neutron measurement
7 PhD Students
Completed data taking in Feb.
Exceeded PAC approved goal
Collins
Sivers

58. Hall-A Transversity: en→e’pX en→e’KX
Polarized 3He: effective polarized neutron target
World 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

59. Target Performance Online Preliminary
Online preliminary EPR/NMR analysis shows a stable 65% polarization with 15 mA beam and 20 minute spin flip
Cell: Astral
Cell: Maureen
Online Preliminary

60. Projections of g1T First Neutron (3He) Measurement
With Fast Beam Helicity Flip (30Hz)
Projected Uncertainties (Stat. Only):
2.3% at low x
3.4% at high x

61. 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

62. Upgrade magnets and power supplies
Add new hall 12 11
6 GeV CEBAF
Upgrade magnets and power supplies
CHL-2
Enhance equipment in existing halls
INFO FOR ME, BUT DO NOT SAY UNLESS ASKED!!!!!
Cost range (from Mission Needs Statement) $170M-$250M
This includes $30-50 M that could come from redirection of the present JLab Ops budget, and
~$20M that might come from foreign contributors (if they match what they did for the original project)
About $47M of the total could come from a redirection of present operating funds over the duration of the project."

63. 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

64. Solenoid detector for SIDIS at 11 GeV
Proposed for PVDIS at 11 GeV
GEMs

65. 3-D Mapping of Collins/Siver Asymmetries at JLab 12 GeV With A Large Acceptance Solenoid Detector
Both p+ and p-
For one z bin
( )
Will obtain 4
z bins ( )
Upgraded PID for K+ and K-

66. 3-D Projections for Collins and Sivers Asymmetry (p+)

67. Discussion Unprecedented precision 3-d mapping of SSA
Collins and Sivers
p+, p- 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

68. 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
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
transversity and TMDs,
spin-flavor decomposition (~2 orders improvement)
Unpolarized luminosity: 5x1038 , acceptance ~ 300 msr (with baffles)
Parity-Violating DIS
Boer-Mulders function

69. Single Spin Asymmetries in (Qausi-)Ealstic
Two-photon Exchange and GPDs

70. 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.

71. E05-015 Projection Measurements at Q2=0.5, 1.0 GeV2 (and 2 GeV2).
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 @ 10s level
 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.

72. 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 cPT calculations,  ‘dLT 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