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
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6
2
3
22
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0
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2
0
0
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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?