Spin Physics Program in Jefferson Lab's Hall C
Oscar A. RondónINPP - University of Virginia
DIFFRACTION 2014 - 8th International Workshop on Diffraction in High-Energy Physics
Primošten, CroatiaSeptember 13, 2014
9/13/14 2
Probing Nucleon Structure withPolarized Electromagnetic Scattering
9/13/14 3
Inelastic e-nucleon Scattering
● Inclusive EM scattering is described by hadronic and leptonic tensors
● Symmetries reduce hadronic tensor to four structure functions (SF's):
– Symmetric part: unpolarized W1, W
2
– Anti-symmetric part: spin-dependent G
1, G
2
WμνA= 2ϵμνλ σqλ
{M 2 S σ G1(ν ,Q2)+ [M ν Sσ
−pσS⋅q ]G 2(ν ,Q2)}
e- e-
Target fragments Current jet
Inclusive scattering: undetected final state
● * hadronic structure does not contribute for Bjorken x > ~ 0.1
– JLab's domain is best region for illuminating nucleon structure
(http://www.desy.de/~gbrandt/feyn/)
9/13/14 4
Structure Functions in Inclusive DIS
● G1, G
2, W
1 and W
2, contain all the information on nucleon
structure that can be extracted from inclusive data
● In high energy DIS, g1 and g
2 scale like F
1 and F
2 (up to log
violations)
● In the quark parton model g1 and F
1 are also related to parton
distribution functions - PDF's:
limQ 2 , ν→∞M 2
νG1(ν ,Q2)=g1( x)
limQ 2 , ν→∞
M ν2 G2(ν ,Q2
)=g 2( x)
limQ 2 , ν→∞M W 1(ν ,Q2
)=F1(x )
limQ2 , ν→∞
νW 2(ν ,Q2)=F 2(x)
Bjorken x=Q2/(2 M ν)
F1( x)=12∑ e f
2(q f
↑(x )+q f
↓(x)) g1( x)=
12∑ e f
2(q f
↑(x )−q f
↓(x))
9/13/14 5
Virtual Compton Asymmetries
● SA A1 is defined in terms of
the difference for 3/2 and ½ helicity cross sections
● A2 represents the interference
between initial transverse and final longitudinal amplitudes
– obeys Soffer-Teryaev bound
A2=σTL
(1/2)
σT(3/2)+σT
(1/2) ≤√ A1+1
2R≤ R=
σ LσT
A2=γ
F 1( g1+ g2)=
γ
F1
g T
A1=σT
(3/2)−σT(1/2)
σT(3/2)+σT
(1/2)
A1=1F1
(g1−γ2 g 2) ; γ=2 x M
√Q 2
● The spin SF's are also related to virtual photon cross-sections and spin asymmetries (SA)
– the helicity of the virtual photon-nucleon system is 3/2 or ½ for transverse photons, ½ for longitudinal ones
9/13/14 6
Model Independent Extraction of Spin Structure Functions
● G1 and G
2 can be separated by measuring cross section differences
for opposite beam helicities with target spins parallel and transverse to the beam
,N ,=42 E '
Q2 E[ E cosNE ' cos M G12 E E ' cos−cosN G 2]
cos=sin N sincoscosN cos , , : final lepton angles
● transverse target spin N: comparable G
1, G
2 terms
– G1 is twist-2 (plus corrections)
– G2 has both twist-2 and twist-3 contributions
d2
d dE '−
d 2
d dE '=
42 E '
Q2 EE ' sin cos[M G1 ,Q2
2 E G2 ,Q2]
9/13/14 7
Transverse Polarized Scattering:Unlocking Twist-3
● Twist-2 and twist-3 operators contribute at same order in transverse polarized scattering
– twist-2: handbag diagram
– twist-3: qgq correlations
● direct access to twist-3 via g2:
– interacting qgq, beyond asymptotically free partons, is first step to understanding confinement
– "Unique feature of spin-dependent scattering" (R. Jaffe)
twist-2
log Q2 αQCD
twist-3 (twist-2 corrections)
(Comments NPP 19, 239 (1990))
9/13/14 8
g2 and g
T Spin Structure Functions
[1] hep-ph/9408305v1[2] JHEP 0911 (2009) 093
Experimentally measured quantitiesg T ( x)=g1( x)+g2( x)=
12∑ eq
2 gTq( x)
gTq in terms of Transverse Momentum Dependent distributions [1]
gT (x )=∫ d 2 k t
k t2
2 M 2
g1Tq(x , k t
2)
x+
mM
h1(x)x
+ gT (x)
twist-3 TMD quark mass term qgq interaction
Applying twist-2 Wandzura-Wilczek approximation of g2
g2WW
(x )=−g 1( x)+∫x
1 dyy
g1( y)
Twist-3 for the nucleon (neglecting quark mass)
g2=12∑ eq
2[ gTq−∫x
1 dyy( gT
q( y)− gT
q( y ))]; gT=qg term, gT = Lorentz invariance [2]
9/13/14 9
Hall C Spin Experiments
9/13/14 10
Hall C Spin Structure Program
Spin Structure Functions at 6 GeV:
Inclusive measurements
SSF's in the Nucleon Resonances - RSS (published)PRL 98, 132003 (2007), PRL 105, 101601 (2010), PRC 74, 035201 (2006)
Proton SSF at high Bjorken x - SANE (preliminary results)
Precision Deuteron spin structure - g1
d/F1
d (Hall B eg1/DVCS)
Semi-inclusive measurements
Flavor Decomposition of Spin - SemiSANE (12 GeV)
Real Polarized Photons:
Polarized Compton Scattering - WACS (12 GeV)
9/13/14 11
RSS - Resonances Spin Structure
Measure proton and deuteron spin asymmetries A1(W, Q²) and A
2(W, Q²)
at Q² ≈ 1.3 GeV² and 0.8 ≤ W ≤ 1.91 GeV
Goals: study W dependence of asymmetries, onset of polarized local duality, and twist-3 effects
Precision Measurement of the Nucleon Spin Structure Functionsin the Region of the Nucleon Resonances
TJNAF E01-006
U. Basel, Florida International U., Hampton U., U. Massachusetts, U. Maryland,Mississippi S. U., North Carolina A&T U., U. of N. C. at Wilmington,Norfolk S. U., Old Dominion U., S.U. New Orleans, U. of Tel-Aviv,
TJNAF, U. of Virginia, Virginia P. I. & S.U., Yerevan Physics I.
Spokesmen: Oscar A. Rondon (U. of Virginia) and Mark K. Jones (Jefferson Lab)
9/13/14 12
SANE - Spin Asymmetries of the Nucleon Experiment
(TJNAF E07-003)
SANE CollaborationArgonne National Lab., Christopher Newport U., Florida International U.,
Hampton U., Jefferson Lab., U. of New Hampshire, Norfolk S. U., North Carolina A&T S. U., Mississippi S. U., Ohio U., IHEP - Protvino, U. of Regina, Rensselaer Polytechnic I., Rutgers U., Seoul National U., Southern U. New Orleans,
Temple U., Tohoku U., U. of Virginia , Yerevan Physics I., Xavier U.
Spokespersons: S. Choi (Seoul), M. Jones (JLab), Z-E. Meziani (Temple), O. A. Rondon (U. of Virginia)
Measure the proton spin structure function g2(x, Q²) and spin
asymmetry A1 (x, Q²) for 2.5 Q² 6.5 GeV² and 0.3 x 0.8
Goal: Learn all we can about proton spin structure from an inclusive double polarization measurement
9/13/14 13
Layout in JLab's Hall C: RSS
Hall CHall C
CEBAF CEBAF South LinacSouth Linac
High MomentumSpectrometer
HMS
9/13/14 14
ee-- Beam Beam<P> ~ 73%<P> ~ 73%
HMSHMS
PolarizedPolarizedTargetTarget
Hall CHall C
CEBAF CEBAF South LinacSouth Linac
Layout in JLab's Hall C: SANE
[1] Big Electron Telescope Array ~ 190 msr; = ± 10°
[1]
9/13/14 15
BETA with DIS electron simulation
BigCal Pb glassCalorimeter [1]
B field: 80°, 180°
BeamBeam
[2] [3]
[4]
[5]
[4] Norfolk State U. and U. of Regina[5] UVA- JLab
[1] BigCal Collaboration[2] North Carolina A&T U.[3] Temple U
(W. Armstrong)
9/13/14 16
Polarized Target
Ammonia + LHeAmmonia + LHe
● Dynamic Nuclear Polarized ammonia NH
3, ND
3, at 5T and 1K
– Proton <P> ~70% in beam
– Deuteron <P> ~20% in beam
– Proton luminosity ~1035 Hz cm-2
● Target used in multiple experiments:
– SLAC: E143, E155, E155x (g2)
– JLab: GEn98, GEn01, RSS, SANE
9/13/14 17
Data
9/13/14 18
ExperimentExperiment DetectorDetector Detected Detected particleparticle
Scattering Scattering TypeType
Beam Beam Energy Energy [GeV][GeV]
Field Field DirectionDirection
TargetTarget
RSS HMS e- Inclusive inelastic &
elastic
5.76 180°, 90° NH3ND3
C, LHe [1]
SANE BETA e, 0 Inclusive inelastic
5.9, 4.7 180°, 80° NH3
HMS e Inclusive inelastic
5.9, 4.7 180°, 80° NH3C, LHe [1]
Inclusive elastic
5.9 80° NH3
BETA - HMS e - p Coincidence elastic
5.9 80° NH3
Hall C Spin Structure Program
[1] Unpolarized, for dilution factor
9/13/14 19
BETA and HMS data
● Q 2 – x phase space of BETA's 80° data (SANE)
– cut on E' 1.3 GeV
● Central kinematics of HMS inclusive asymmetry data
(RSS and SANE)
0
0.5
1
1.5
2
2.5
3
0.5 1 1.5 2 2.5
Q2
[GeV
2 ]
W [GeV]
RSS 5.75 GeV, 90o
180o
SANE 5.9 GeV 80o
4.7 GeV 180o
5.9 GeV 80o
180o
4.7 GeV 80o
180o
DIS Resonances
9/13/14 20
Measured Asymmetries A∥, A
⊥ (RSS)
Am=ϵ
f Pb P t C N
+C D ; ϵ =N -
−N +
N -+N +
Aphys=Am
f rc
+Arc
● N +,- = charge normalized, dead time corrected yields
● Pb, P
t = beam, target polarizations
● f = polarized dilution factor
● CN, C
D = N polarization corrections
● Arc, f
rc= radiative corrections
(Proton: PRL 98, 132003 (2007))
9/13/14 21
Measured Asymmetries A(80°), A(180°)
Am=ϵ
f Pb P t C N
; ϵ =N -
−N +
N -+N +
Aphys=1f rc
(Am− f b Ab
1− f b
)+Arc
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.80.0
0.2
0.4
0.6
0.8
W [GeV]
A 1
80°
1.4 1.6 1.8 2 2.2 2.4 2.6 2.80.00
0.05
0.10
0.15
0.20
0.25
W [GeV]
A 9
0°
SANE
Preliminary
SANE
Preliminary
A ⊥ =(A180 cos80o+A80)/sin 80o
● N +,- = charge normalized, dead time corrected yields
● Pb, P
t = beam, target polarizations
● f = polarized dilution factor
● CN = N polarization corrections
● Arc, f
rc= radiative corrections
● Ab, f
b = background corrections
9/13/14 22
Sample of Normalizations and corrections
Pbeam
Ptarget
Run No.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 30
0.05
0.1
0.15
0.2
0.25
W[GeV]
f
Q²[GeV²]2.4 3.03.7 4.5
E [GeV]● 4.7 ■ 5.9
Data
MCfb
9/13/14 23
Results
9/13/14 24
Spin Asymmetries A1 and A
2
(H-y. Kang)
● HMS single arm data in the resonances, Q² ~1.3 GeV²
– Model independent separation from measured asymmetries
W [GeV]
A1
p
SANE Preliminary
W [GeV]
A2
p
SANE Preliminary
RSS: PRL 98, 132003 (2007)
9/13/14 25
Spin Asymmetries A1 and A
2
W [GeV]
A1
p
Preliminary
W [GeV]
A2
p
Preliminary
(H-y. Kang)
● HMS single arm data in the resonances, Q² ~1.8 GeV²
– Model independent separation from measured asymmetries
9/13/14 26
A 1p
DIS Spin Asymmetry A1
A 1p
● BETA data - Statistical errors only
● CLAS data of same W but different Q2 are merged in A1
p
(W)
APS 2012 (Preliminary)
9/13/14 27
g2 Spin Structure Functions
● First world data for g2
p,d in the
resonances
● Twist-2 g2
WW computed using
RSS fit to g1 point by point
● Clear difference between proton data and twist-2 part
PRL 105, 101601 (2010)
9/13/14 28
g2 in DIS and Resonances
(W. Armstrong)
(Curves are twist-2 g
2
WW from PDF's)
● BETA proton data
– DIS and resonances
0.3 < x < 0.8, 2.5 < Q2 < 6., E' 1.3 GeV (more data available down to 0.9 GeV)
– Twist-2 g2
WW(4 GeV²) from
PDF's
● SLAC E143, E155, E155x DIS data
9/13/14 29
DIS Transverse Spin SF gT
p
● Bag Model (1990's)
– Data scaled 2.5
– Model updates needed
● gT
p = F1 A
2 / measures spin
distribution normal to *
● SANE gT
p(x >.3) = 0.023±0.006
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.2
0
0.2
0.4
0.6
0.8
SANE 2-3 GeV² 3-4 GeV² 4-5 GeV²SLAC .8-3 GeV² 3-4 GeV² 4-9 GeV²
x
g
T JLab 2012 (Preliminary)SANE 2-3 GeV² 3-4 GeV² 4-5 GeV²SLAC .8-3 GeV² 3-4 GeV² 4-9 GeV²
g TTangerman & Mulders hep-ph/9408305v1
twist-2
twist-3
full gT
0 0.7-1
2
Bag Model (Jaffe & Ji)
9/13/14 30
Operator Product Expansion for Spin SF's
● OPE connects SF's Cornwall-Norton moments to twist-2, twist-3 matrix elements a
N, d
N
– d2 is mean color-magnetic
field along spin
● Nachtmann moments needed to get twist-3 free of tmc
∫0
1
x N g 1( x ,Q2)dx=
aN
2+ tmc , N=0, 2,4, ..
∫0
1
x N g 2( x ,Q2)dx=
N (d N−aN )
2(N+1)+ tmc , N=2, 4,..
(tmc: target mass corrections)
d 2(Q2) =∫
0
1
dx ξ2(2ξ
xg1+3(1−
ξ2 M 2
2 Q2) g2) ⇒
Q 2→∞∫
0
1
dx x2(2 g1+3 g 2)
Proton Deuteron NeutronMeasured
CN
Nachtmann
CN
Nachtmann
RSS d2 twist-3 matrix elements
x ranges
0.0060.001 0.0080.002 0.0030.002
0.0040.001 0.0050.002 0.0020.001Full 0< x <1
0.0360.003 0.0170.004 -0.0180.003
0.010 0.001 0.003 0.002 -0.008 0.002
Moments at Q2 1.3 GeV2
– measured range 0.32< x<.8 plus elastic (quasi-elastic for deuteron)
– unmeasured low x <0.32 suppressed by x2 weight
(OPE valid to N=2 < Q2/M0
2 ~ 1.3/0.52
per DIS – resonances duality)
(Ji & Unrau, PR D52 (1995) 72)
9/13/14 31
Operator Product Expansion for Spin SF's
● OPE connects SF's Cornwall-Norton moments to twist-2, twist-3 matrix elements a
N, d
N
– d2 is mean color-magnetic
field along spin
● Nachtmann moments needed to get twist-3 free of tmc
∫0
1
x N g 1( x ,Q2)dx=
aN
2+ tmc , N=0, 2,4, ..
∫0
1
x N g 2( x ,Q2)dx=
N (d N−aN )
2(N+1)+ tmc , N=2, 4,..
(tmc: target mass corrections)
d 2(Q2) =∫
0
1
dx ξ2(2ξ
xg1+3(1−
ξ2 M 2
2 Q2) g2) ⇒
Q 2→∞∫
0
1
dx x2(2 g1+3 g 2)
SANE's measured C-N d 2
(all data E '>1.3GeV, W >2GeV.Only projected error shown.)
9/13/14 32
Operator Product Expansion for Spin SF's
● OPE connects SF's Cornwall-Norton moments to twist-2, twist-3 matrix elements a
N, d
N
– d2 is mean color-magnetic
field along spin
● Nachtmann moments needed to get twist-3 free of tmc
∫0
1
x N g 1( x ,Q2)dx=
aN
2+ tmc , N=0, 2,4, ..
∫0
1
x N g 2( x ,Q2)dx=
N (d N−aN )
2(N+1)+ tmc , N=2, 4,..
(tmc: target mass corrections)
d 2(Q2) =∫
0
1
dx ξ2(2ξ
xg1+3(1−
ξ2 M 2
2 Q2) g2) ⇒
Q 2→∞∫
0
1
dx x2(2 g1+3 g 2)
SANE
● SANE analysis near final version
● Publication in preparation
9/13/14 33
Hall C 12 GeV Spin PhysicsExperiment Title Beam days Rating
Measurement of the Charged Pion Form Factor to High Q2 52 AMeasurement of the Ratio R=sigmaL/sigmaT in Semi-Inclusive Deep-Inelastic Scattering 40 A-Inclusive Scattering from Nuclei at $x > 1$ in the quasielastic and deeply inelastic regimes 32 A-The Search for Color Transparency at 12 GeV 26 B+
E12-06-101 36 A
E12-06-12129 A-
13 B+Deuteron Electro-Disintegration at Very High Missing Momentum 21 B+Detailed studies of the nuclear dependence of F2 in light nuclei. 23 A-Proton Recoil Polarization in the 4He(e,e'p)3H, 2H(e,e'p)n, and 1H(e,e'p) Reactions 37 B+
50 B+
Scaling Study of the L-T Separated Pion Electroproduction Cross Section at 11 GeV 36 A-22 A-
Studies of the L-T Separated Kaon Electroproduction Cross Section from 5-11 GeV 40 B+Transverse Momentum Dependence of Semi-Inclusive Pion Production 32 A-In Medium Nucleon Structure Functions, SRC, and the EMC effect 40 B+Measurement of Semi-Inclusive Àæ Production as Validation of Factorization 25 A-Exclusive Deeply Virtual Compton and Neutral Pion Cross-Section Measurements in Hall C 53 A
E12-13-011 The Deuteron Tensor Structure Function b1 30 A-
E12-14-002 Precision Measurements and Studies of a Possible Nuclear Dependence of R 22 B E12-14-003 Wide-angle Compton Scattering at 8 and 10 GeV Photon Energies 18 A- E12-14-005 Wide Angle Exclusive Photoproduction of pi-zero Mesons 18 B E12-14-006 Initial State Helicity Correlation in Wide Angle Compton Scattering 15 B
Total Spin Physics days 95
E12-06-101 E12-06-104 E12-06-105 E12-06-107
Measurement of Neutron Spin Asymmetry A1n in the Valence Quark Region Using an 11 GeV Beam and a Polarized 3He Target in Hall CA Path to 'Color Polarizabilities' in the Neutron:A Precision Measurement of the Neutron $g_2$ and $d_2$ at High $Q^2$ in Hall C
E12-10-002 Precision measurements of the F_2 structure function at large x in the resonance region and beyondE12-10-003
E12-10-008 E12-11-002 E12-11-009 The Neutron Electric Form Factor at Q^2 up to 7 (GeV/c)^2 from the Reaction d(e,e'n)p
via Recoil PolarimetryE12-07-105 E12-09-002 Precise Measurement of pi+/pi- Ratios in Semi-inclusive Deep Inelastic Scattering PartI:
Charge Symmetry violating Quark DistributionsE12-09-011 E12-09-017 E12-11-107 E12-13-007 E12-13-010
(Conditionally approved)
9/13/14 34
Extras
9/13/14 35
GE
p/G
M
p from inclusive and coincidence
dataRatio from:
● SANE inclusive HMS data at Q² = 2.06 GeV²
– Ael
p = -0.20 ± 0.02
– GE
p/G
M
p = 0.60 ± 0.18 ± 0.06
(statistical + systematic error)
● BETA–HMS e–p coincidences at Q² = 5.66 GeV²
– GE
p/G
M
p = 0.67 ± 0.36
(statistical error only)
Preliminary
(SANE stat. errors only)
(A. Liyanage)
RSS
9/13/14 36
SANE Collaboration (E-07-003)
P. SolvignonArgonne National Laboratory, Argonne, IL
E. Brash, P. Carter, A. Puckett, M. VeilleuxChristopher Newport University, Newport News, VA
W. Boeglin, P. Markowitz, J. Reinhold Florida International University, Miami, FL
I. Albayrak, O. Ates, C. Chen, E. Christy, C. Keppel, M. Kohl, Y. Li, A. Liyanage, P. Monaghan, X. Qiu,
L. Tang, T. Walton, Z. Ye, L. Zhu Hampton University, Hampton, VA
P. Bosted, J.-P. Chen, S. Covrig, W. Deconink, A. Deur, C. Ellis, R. Ent, D. Gaskell, J. Gomez, D. Higinbotham,
T. Horn, M. Jones, D. Mack, G. Smith, S. WoodThomas Jefferson National Accelerator Facility, Newport News, VA
J. Dunne, D. Dutta, A. Narayan, L. Ndukum, Nuruzzaman Mississippi State University, Jackson. MI
A. Ahmidouch, S. Danagoulian, B. Davis, J. German, M. Jones North Carolina A&T State University, Greensboro, NC
M. Khandaker Norfolk State University, Norfolk, VA
A. Daniel, P.M. King, J. RocheOhio University, Athens, OH
A.M. Davidenko, Y.M. Goncharenko, V.I. Kravtsov, Y.M. Melnik, V.V. Mochalov, L. Soloviev, A. Vasiliev
Institute for High Energy Physics, Protvino, Moscow Region, Russia
C. Butuceanu, G. HuberUniversity of Regina, Regina, SK
V. KubarovskyRensselaer Polytechnic Institute, Troy, NY
L. El Fassi, R. GilmanRutgers University, New Brunswick, NJ
S. Choi, H-K. Kang, H. Kang, Y. KimSeoul National University, Seoul, Korea
M. ElaasarState University at New Orleans, LA
W. Armstrong, D. Flay, Z.-E. Meziani, M. Posik, B. Sawatzky, H. Yao
Temple University, Philadelphia, PA
O. Hashimoto, D. Kawama, T. Maruta, S. Nue Nakamura, G. Toshiyuki
Tohoku U., Tohoku, Japan
K. SliferUniversity of New Hampshire
H. Baghdasaryan, M. Bychkov, D. Crabb, D. Day, E. Frlez, O. Geagla, N. Kalantarians, K. Kovacs, N. Liyanage, V. Mamyan, J. Maxwell, J. Mulholland, D. Pocanic,
S. Riordan, O. Rondon, M. Shabestari University of Virginia, Charlottesville, VA
L. PentchevCollege of William and Mary, Williamsburg, VA
F. WesselmannXavier University, New Orleans, LA
A. Asaturyan, A. Mkrtchyan, H. Mkrtchyan, V. TadevosyanYerevan Physics Institute, Yerevan, Armenia
Ph.D. student, M.S. Student, Student
9/13/14 37
9/13/14 38
Why is g2 interesting?
● tests twist-3 effects = quark-gluon correlations
● higher twist corrections to g1 with 3rd moment d
2 matrix element
● test of lattice QCD, QCD sum rules, quark models from moments
● polarizabilities of color fields (with twist-4 matrix element f2)
● magnetic B= (4d
2+ f
2)/3 and electric
E= (4d
2 - 2 f
2)/3.
● 3rd moment related to color Lorentz force on transverse polarized quark (M. Burkardt, AIP Conf.Proc. 1155 (2009) 26)
– sign of d2 related to sign of transverse deformation (anomalous q)
● contains chiral odd twist-2 = quark transverse spin (mass term)
– test quark masses (covariant parton models)
9/13/14 39
RSS Spin Structure Functions g1
p,d
F. Wesselmann et al.,Phys.Rev.Lett. 98, 132003 (2007)(including spin asymmetries A
1, A
2)
In preparation
9/13/14 40
RSS Proton Spin Asymmetries
Fit A1 and A
2 independently
– Four Breit-Wigner resonance shapes plus DIS background
– Reduced 2 = 1.2 - 1.4 for 12 d.o.f.
9/13/14 41
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-0.1
-0.05
0
0.05
0.1
E143 (SANE Q² range) SANE (E'>=1.3)E155x (SANE Q² range)
xx g
2
g2 in DIS and Resonances
● SLAC x g2(2< Q² < 6 GeV²)
● Total errors SANE & E143, statistical only E155x
● Proton (NH3)
– Hall C SANE (E07-003)
– 0.3 < x < 0.8 2.5 < Q2 < 6.5
APS Spring 2012 (Preliminary)
(H. Baghdasaryan)
Preliminary
9/13/14 42
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.2
-0.1
0
0.1
0.2
0.3
0.4
SANE 2-3 GeV²
3-4 GeV² 4-5 GeV² SLAC
x
A
2
p
DIS Spin Asymmetry A2
● DIS A2
p not zero is signal of parton transverse momentum
– connection to transverse twist-3 TMD g1T
:
JLab 2012 (Preliminary)
g 2( x)=d
dxg1T(1)(x )+ gT ( x)
9/13/14 43
Nucleon Spin beyond G1 and G
2
● Need to go beyond a0 to
understand nucleon spin
– Orbital angular momentum (OAM) L is needed.
● Partons have transverse momentum, implies OAM
– Muller, Ji, Radyushkin, Generalized Parton Distributions – GPDs
– functions of Mandelstam t, light cone momentum ξ
– exclusive scattering, DV Compton, meson
H x ,=t=0 =q x = f 1 xH x ,=t=0 = q x=g 1 x
E x , , t , E x , , t (no partonic analogs)
J q=12 ∫−1
1 dx x [H q x , , t=0
Eq x , , t=0](Ji's sum rule)
∑ J q=∑ qLq
9/13/14 44
Nucleon Spin beyond G1 and G
2
● Need to go beyond a0 to
understand nucleon spin
– Orbital angular momentum (OAM) L is needed.
● Partons have transverse momentum, implies OAM
– Mulders et al., Transverse Momentum dependent Distributions – TMDs
– functions of x and kt
– Semi-inclusive scattering (detect final e, one hadron)
Transverse Momentum Distributionsby Polarization
Target ↓ \ quark → U L TU f1(x, kt) h1
_|_
L g1 h1L_|_
T f1T _|_ g1T
_|_ h1 h1T _|_
Longitudinal SSF (leading twist)
g1(x )=∑ g1q(x)=∑∫ d
2k t g1 L( x , k t
2)
Transverse SSF (twist-3)
g1T(1 )( x)=∑ g1T
q (1)( x)=∑∫ d 2 k t
k t2
2M 2 g1Tq( x , k t
2)
gT (x)=g1(x )+ddx
g1T(1)=g 1( x)+g2( x)
9/13/14 45
Double Spin SIDIS ALT
● g1T
(x, kt) is chiral-even TMD
for quarks with longitudinal helicity in a transverse polarized target
● Weighted by kt
2/2M2 and
integrated over kt, generates a
cos(-s) azimuthal A
LT,
measurable in SIDIS
Hall A E06-010,PRL 108 (2012) 05200
ALT x , y , z
∣PT∣/M cos −s=
C x , y∑ e2 g1T1x Dh
z
C ' x , y∑ e2 f 1 x Dh z
9/13/14 46
1
n
E01-012E94-010Curves from TM corrected PDF's
Duality in g1
● Bloom – Gilman duality for spin SF's
– Local Duality only above (1232)
– Global duality (for W > threshold, or from elastic) obtains above Q2 > 1.8 GeV2
– seen in p, d, and 3He
– DIS SSF's from PDF's extrapolated with target mass corrections
9/13/14 47
Duality in g1
● Bloom – Gilman duality for spin SF's
– Local Duality only above (1232)
– Global duality (for W > threshold, or from elastic) obtains above Q2 > 1.8 GeV2
– seen in p, d, and 3He
– DIS SSF's from PDF's extrapolated with target mass corrections
CLAS eg1bBands: DIS g
1
9/13/14 48
