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Spin Structure of the Proton andDeuteron
K. GriffioenCollege of William & Mary
griff@physics.wm.edu
Spin Structure at Long Distances
Jefferson Lab
12 March 2009
12 March 2009 SS@LD (JLab) 2
Inelastic Scattering
Q2 increases
12 March 2009 SS@LD (JLab) 3
F2p(x,Q2) and g1
p (x,Q2)
12 March 2009 SS@LD (JLab) 4
g1p(x,Q2)
12 March 2009 SS@LD (JLab) 5
g1p(x,Q2)
12 March 2009 SS@LD (JLab) 6
The Q2 Map
• Infinite Q2 Parton Model, PDF(x)
• Large Q2 pQCD, PDF(x,log(Q2))
• Medium Q2 Higher twist, target mass correct.
• Low Q2 Resonances (complexity)
• Tiny Q2 Chiral perturbation theory
• Zero Q2 Real photons• Complexity, as measured by γ0, δLT, d2 and Γ1,
disappears rapidly at high and low Q2
12 March 2009 SS@LD (JLab) 7
Regions of Q2
scaling: lnQ2
higher twist: (1/Q2)n
χPT: (Q2)n
no nice expansion
CLAS EG1 Data
12 March 2009 SS@LD (JLab) 8
Spin Structure with CLAS
• Long-standing programin Hall-B at JLab tomeasure longitudinaldouble spin asymmetriesA|| on 15NH3 and 15ND3
• EG1: 0.05<Q2<3.5 GeV2
– data (2001); anal (2008)
• EG4: 0.01<Q2<1 GeV2
– data (2006); anal (2009)
• EG12: 0.5<Q2<7 GeV2
– data (2012?); anal (2014)
12 March 2009 SS@LD (JLab) 9
CLAS EG1 g1p (Q2<0.7)
• At low Q2 the Δ resonance drives g1 negative• Extensive x-range at fixed Q2 allows integration over x• Red curve is the EG1 model used for radiative corrections
12 March 2009 SS@LD (JLab) 10
CLAS EG1 g1p (Q2>0.7) & g1/F1
• At higher Q2, g1 becomes positive everywhere• g1/F1 falls far below the DIS extrapolation at low Q2
• Red curve is the EG1 model (dashed: DIS extrapolation)
12 March 2009 SS@LD (JLab) 11
A1 Data from EG1
xbj
A1d ( D-state corrected ) HF perturbed QM
World Data Parm + d WF Q2 = 4.2 GeV2
World Data parm Q2 = 10 GeV2
Spin 3/2 suppression
Helicity 3/2 suppression
Symmetric Q Wave function suppression
SLAC - E143
SMC
HERMES
SLAC - E155
CLAS-EG1b Q2 = 1.0 - 4.52 GeV2
SU(6)
pQCD
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Isgur, PRD 59, 034013 (2003)
Close and Melnitchouk, PRC68, 035210 (2003)
xbj
A1p
HF perturbed QM
World Data parm Q2 = 10 GeV2
Spin 3/2 suppression Helicity 3/2 suppression
Symmetric Q Wave function
SLAC - E143
SMC
HERMES
SLAC - E155
CLAS-EG1b Q2 = 1.0 - 4.52 GeV2
SU(6)
pQCD
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ProtonDeuteron
W > 2; Q2 > 1
~g1/F1
12 March 2009 SS@LD (JLab) 12
Quark polarization in the valence limit
CLAS EG1 Data
Simulated Data for EG12Extracted from A1
p, A1d and d/u
12 March 2009 SS@LD (JLab) 13
PDFs and CLAS
• Error envelopes for PDFs from LSS05 global analysis (green)• CLAS EG1 data significantly improve errors on Δu, Δd, Δx and ΔG (blue)
• CLAS EG12 (12 GeV upgrade) will especially improve ΔG (red)
12 March 2009 SS@LD (JLab) 14
Higher Twist from g1 in CLAS
•F1 from NMC fit to F2 and 1998 SLAC fit to R•g1 (leading twist) from NLO fit at high Q2
•h from fit to all data, especially CLAS in the pre-asymptotic region•d2: twist-3, f2: twist-4
EG1
12 March 2009 SS@LD (JLab) 15
Bjorken Sum & Higher Twist
Bjorken Sum Rule:
Fit Γ1p-n to powers of
1/Q2 and extract f2p-n
CLAS: Deur
12 March 2009 SS@LD (JLab) 16
Nachtmann Moments
CLAS, Osipenko
PLB609(05)259
12 March 2009 SS@LD (JLab) 17
Color Polarizability
• Osipenko, CLAS, proton, PLB609(05)249– f2 = 0.039(39) χE = 0.026(27) χB = -0.013(13)
• E94-010, Hall A, neutron– f2 = 0.034(43) χE = 0.033(29) χB = -0.001(16)
• Deur, CLAS, Bjorken (p-n)– f2 = -0.101(74) χE = -0.077(50) χB = 0.024(28)
• More accurate determinations are needed.
12 March 2009 SS@LD (JLab) 18
RSS g2p
€
2Γ =0
1
∫ g2(x,Q2)dx = 0
€
2
WWg = −1g +
g1yx
1
∫ dy
€
2g =2
WWg +2g Hall C: Slifer et al. arXiv:0812.0031
Burkhardt-Cottingham Sum RuleWandzura-Wilczek
Q2=1.28 GeV2
12 March 2009 SS@LD (JLab) 19
Duality
Hall CPRL85(00)1182Global duality to 10%Local duality to 10%W=1.232, 1.535, 1.680 GeV
Duality - structure functionsaveraged over resonancesbehave according to DISsystematicsGlobal - all resonancesLocal - one resonance
12 March 2009 SS@LD (JLab) 20
Polarized Duality
GRSV: Phys. Rev. D 53, (1996) 4775
BSB : Eur. Phys. J. C 41, (2005) 327
AAC : Phys. Rev. D 62, (2000) 034017.
Hall CRSS, Wesselmann, SliferQ2=1.379 GeV2
Target Mass Corrections applied to PDFsNo duality for ΔPRL98(07)132003
12 March 2009 SS@LD (JLab) 21
Duality at CLAS (EG1)
Δ (1232)S11 (1535)
F15 (1680)
Global
Δ (1232)S11 (1535)
F15 (1680)
Global
Proton Deuteron
12 March 2009 SS@LD (JLab) 22
CLAS Moments Γ1p,d
low Q2 fit
GDH + χpT
PRELIMINARY PRELIMINARY
12 March 2009 SS@LD (JLab) 23
Forward Spin Polarizability
real photon point
PRELIMINARY
CLAS EG1 Data
12 March 2009 SS@LD (JLab) 24
γ0p-n and γ0
p+n
A DeurCLAS + Hall A
For isovector (p-n) caseΔ contribution cancels
12 March 2009 SS@LD (JLab) 25
Latest CLAS Data
• Recent results from CLAS EG1b
• Uses data from all 4 beam energies
12 March 2009 SS@LD (JLab) 26
EG1b Fitting A1 + ηA2
12 March 2009 SS@LD (JLab) 27
EG1b A1 vs. x
Blue line:DIS model of A1
at Q2=10 GeV2
Δ dip is stillsignificant atQ2 ~ 2 GeV2
12 March 2009 SS@LD (JLab) 28
EG1b A2
Black points: extraction from EG1bBlack line: eg1b model for A2
Blue points: RSS data
12 March 2009 SS@LD (JLab) 29
EG1b g1p for Various Q2s
12 March 2009 SS@LD (JLab) 30
EG1b g1d
g2 extractedfrom A1 & A2
vs. x (left)vs. Q2 (right)for W<2 GeV
PRELIMINARY
Bjorken x
PRELIMINARYg1D
Q2=0.07
Q2=4
12 March 2009 SS@LD (JLab) 31
EG1b A1d
A1/2 transition is dominant
_(1232)P33
N(1520-35)D13/S13
A3/2 transition is dominant
PRELIMINARY
12 March 2009 SS@LD (JLab) 32
EG1b A1d
g2 extractedfrom A1 & A2
vs. x (left)vs. Q2 (right)for W<2 GeV
PRELIMINARY
W(GeV)
A1
PRELIMINARY
12 March 2009 SS@LD (JLab) 33
EG1b g1p/F1
p vs. Q2
Scaling starts at:x Q2
0.085 0.10.125 0.20.175 0.30.250 0.60.350 0.80.500 1.0
12 March 2009 SS@LD (JLab) 34
EG1b g2
g2 extractedfrom A1 & A2
vs. x (left)vs. Q2 (right)for W<2 GeV
12 March 2009 SS@LD (JLab) 35
EG1b Γ2 & d2
12 March 2009 SS@LD (JLab) 36
EG1b Γp1,3,5
12 March 2009 SS@LD (JLab) 37
EG4 Γ1p Expected
12 March 2009 SS@LD (JLab) 38
EG1b γ0p
Error est. on g2 (100%)
PRELIMINARY
PRELIMINARY
12 March 2009 SS@LD (JLab) 39
EG1b γ0d
PRELIMINARY PRELIMINARY
Error est. on g2 (100%)
12 March 2009 SS@LD (JLab) 40
Higher Twist d2
Hall A (neutron)E94-010Amarian, PRL92(04)022301
CLAS EG1 (proton)Osipenko, PRD71(05)054007Model-dependent determination
12 March 2009 SS@LD (JLab) 41
R = σL/σT (DIS)
Hall C: E99-118Tvaskis, PRL98(07)142301
12 March 2009 SS@LD (JLab) 42
Hydrogen Hyperfine Splitting
= 6.48(89)
= -0.57(57)
Δpol = 1.34(24) ppm from CLAS
12 March 2009 SS@LD (JLab) 43
EG1b B1 and B2
g2 extractedfrom A1 & A2
vs. x (left)vs. Q2 (right)for W<2 GeV
12 March 2009 SS@LD (JLab) 44
Moments
• Elastic and resonant scattering are higher twists• One must be careful when to include elastic• WW (leading twist) [does not]• Γ1,2
(n) = <xng1,2(x)> [does not]• Γ2
(0) = 0 (Burkardt-Cottingham) [does]• Γ2
(0)WW = 0 (thus elastic cancels higher twist)• Γ2
(2)WW = -(2/3)Γ1(2)
• d2 = 3Γ2(2) + 2Γ1
(2) (higher twist) [does (not)]• d2 = 0 if Γ2
(2) = Γ2(2)WW (no higher twist)
• B1,2 [do not]
12 March 2009 SS@LD (JLab) 45
Commensurate ScalingBrodsky, Lu, PRD51(95)3652; Deur, PLB650(07)244
12 March 2009 SS@LD (JLab) 46
Conclusions
• A wealth of data exists for g1, g2
• What’s still missing:– high x: A1
p,d (CLAS12)
– g2p on the proton (transverse target); SANE (Hall C) covers
Q2>1 GeV2; nobody’s measuring Q2<1 GeV2
– precision and full kinematic coverage for 1< Q2<10(CLAS12)
– low Q2 evolution of g1p,d (EG4)
• What’s gained:– understanding three regions
• Q2 near 0 (χPT)
• Q2 from 0.1-10 GeV2 (TMC, higher twists, resonances, the transition)
• Q2 near infinity (pQCD)
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