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Nucleon g2 Structure Function at Large x: Probing Color Forces
Outline:
Introduc/on
Quark-‐gluon correla/ons and color forces
JLab d2n and SANE experiments
Physics results
Summary
September 20, 2015 Erice
Zein-‐Eddine Meziani
Temple University
1
On behalf of the d2n and the SANE collabora/ons
Q2 :Four-momentum transfer x : Bjorken variable : Energy transfer M : Nucleon mass W : Final state hadrons mass
Inclusive Deep Inelastic Scattering: 1-D View
2
U
Unpolarized structure func/ons F1(x,Q2) and F2(x,Q2)
Polarized structure func/ons g1(x,Q2) (parton model interpreta6on) g2(x,Q2) (quark-‐gluon correla6ons)
L
T
September 20, 2015 Erice
Spin Polarizabilities γ0(Q2),δLT (Q2 )
Burkhardt-Cottingham sum rule Γ2 (Q2)=0
Higher twists & color Polarizabilities d2(Q2) , f2 (Q2)
First moments
Higher moments
Bjorken Sum Rule Γ1
p-n
Generalized GDH Integral
IGDH (Q2 )
Moments of Spin Structure Func/ons
GDH Sum Rule IGDH (0)
Operator product Expansion Bjorken result for (p-n) at finite Q2 Chiral Perturbation Theory
!2
8M2Q2 + cQ4 + O(Q6)-
0 1 10 ∞ Q2 pQCD χPT La@ce QCD OPE
DSE MODELS AdS/CFT
Moments of Structure Functions: Probing Color Forces
τ ≡ twist ≡ operator dimension− spin
4 September 20, 2015 Erice
Moment of spin structure function g1
September 20, 2015 5 Erice
dynamical twist-3 matrix element
dynamical twist-4 matrix element
target mass correction term
Moments of Structure Functions (continued)
12�N |ψγ{αg �Gβ}γψ|N� = d2
�p{αpβ}Sγ − pγp{βSγ}
�
d2(Q2) =� 1
0dxx2g2(x,Q2)
6
12�N |ψγαgGβαψ|N� = f2S
β
September 20, 2015 Erice
a twist-2 term (Wandzura & Wilczek, 1977):"
a twist-3 term with a suppressed twist-2 piece (Cortes, Pire & Ralston, 1992):"
Twist -2 Twist -3
Transversity q-‐g correlations"
g2 and quark-‐gluon correla/ons
d2 = 3� 1
0dxx2g2(x) =
� 1
0dxx2 [3g2(x) + 2g1(x)]
7 September 20, 2015 Erice
“Color Polarizabili/es” X.Ji 95, E. Stein et al. 95
d2 = (χE + 2χB)/4f2 = χE − χB
September 20, 2015 8 Erice
Lorentz Color Force (M. Burkardt)
September 20, 2015 Erice 9
Consider a charge e moving near speed of light (�v = (0, 0,−1)) along the −zdirection. The electromagnetic Lorentz force is written as:
F y = e��E × �v �B
�y= e(Ey −Bx) = −e
�(2)F+y
F y = −√
22P+
�P, S|qG+yγ+q|P, S�
= − 12P+
�P, S|q(Bx − Ey)γ+q|P, S�
= −M2d2
Color Lorentz force reads:
M. Burkardt, Phys. Rev. D 88, 114502 (2013) and Nucl. Phys. A 735, 185 (2004).
Average Color Lorentz Force (M. Burkardt)
FEy(0) = −M2
4χE = −M2
4
�23
(2d2 + f2)�
FBy(0) = −M2
2χB = −M2
2
�13
(4d2 − f2)�
September 20, 2015 10 Erice
Earlier nucleon world results of g2
• SLAC E155x (proton and deuteron) • JLab E99-‐117(helium-‐3), A1
n in DIS • Jlab E97-‐103 (helium 3) Q2 dependence below 1 GeV2 SLAC E155x (proton and deuteron)
September 20, 2015 11 Erice
Neutron
Recent work on g2: V. Braun et al. Phys. Rev. D83 (2011) 094023
Models and Lattice evaluations of d2 Quark Bag Models"M.Stratmann, Z.Phys.C60,763(1993)."X.Song, Phys.Rev.D54,1955(1996)."X.Ji and P.Unrau, Phys.Lett.B333,228(1994)."
Chiral Soliton Model!H.Weigel and L.Gamberg, "Nucl. Phys. A680, 48 (2000)."M.Wakamatsu, Phys. Lett. B487,118(2000)."
Lattice QCD !M.Gockeler et al., Phys.Rev.D72:054507,(2005)
September 20, 2015 12 Erice
Hall A d2n and Hall C SANE
experiments Neutron and Proton
Spokespeople: B. Sawatzky, S. Choi, X. Jiang and Z.-E.M
Students: D. Flay, D. Parno, M. Posik
and the Hall A collaboration
Spokespeople: O. Rondon, S. Choi, M. Jones and Z.-E. M
Students: W. Armstrong, H. Kang, A. Liyanage, J. Maxwell, J. Mulholland
and the Hall C collaboration
Two Jefferson lab experiments dedicated to measure the g2 structure function
September 20, 2015 13 Erice
Posik, Flay, Parno et al., Phys.Rev.Le*. 113 (2014) 2, 022002 Phys.Le*. B744 (2015) 309-‐314
Analysis close to comple/on: Preliminary results
Jefferson Lab Polarized DIS experiments at 6 GeV
September 20, 2015 14
HallA: two HRS’ Hall B:CLAS Hall C: HMS+SOS
6 GeV pol. e beam Pol=85%, 100mA
Erice
The JLab E06-‐014 (d2n) Experiment Polarized electron beam: E=4.74,
5.89 GeV, polariza/on ~ 71% Polarized 3He target ~ 50% HRS used for absolute cross
sec/on measurements at 450
Bigbite used for asymmetries measurements at 450
September 20, 2015 15 Erice
Spin Asymmetries of the Nucleon Experiment (SANE)
16 September 20, 2015 Erice
3He g2 structure function
September 20, 2015 17
x0 0.2 0.4 0.6 0.8 1
He
3 2g2 x
-0.01
-0.005
0
0.005
This Work (E = 4.7 GeV)This Work (E = 5.9 GeV)
Global Analyses
E142E155E01-012 (Resonance)E99-117E97-103
He
3 2g2 x
-0.05
0
0.05
0.1
!"#$%&"'
!"#$%&('
Erice
V. Braun et al. Nucl. Phys. B603 (2001) 69-‐124
M. Posik, D. Flay, D. Parno et al. Phys.Rev.Le*. 113 (2014) 2, 022002
3He g2 structure function
September 20, 2015 18 Erice
d2n results compared to calculations
September 20, 2015 Erice 19
Proton g2 spin structure function (SANE)
• Beta proton data – DIS and Resonance data
– g2WW curves using g1 at Q2 = 4 GeV2
– E’> 0.6 GeV
– More data at Q2 = 1.6 GeV2
September 20, 2015 Erice 20
(W. Armstrong)
Proton d2 compared to calculations
21
Nachtmann moments are needed to get twist-‐3 free of target mass correc/ons
d2(Q2) =� 1
0dxξ2
�2ξ
xg1 + 3(1− ξ2M2
2Q2)g2
�
(W. Armstrong)
September 20, 2015 Erice
Flavor separated color forces
September 20, 2015 Erice 22
Will finalize the SANE proton results …
Extraction of Twist-4 f2 n 2f
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
n 2f
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
TheoryExperiment
)2 = 0.40 GeV2Instanton Model [Balla et al., Lee et al.] (Q)2 = 1 GeV2QCD Sum Rules [Stein et al.] (Q
)2 = 1 GeV2QCD Sum Rules [Balitsky et al.] (Q)2 = 1 GeV2Meziani et al. (Q
)2> = 3.21 GeV2This Work (<Q)2> = 4.32 GeV2This Work (<Q
September 20, 2015 Erice 23
Color Electric and Mgnetic Components
September 20, 2015 Erice 24
Col
or F
orce
(MeV
/fm)
-50
0
50
100
150
200
Col
or F
orce
(MeV
/fm)
-50
0
50
100
150
200
TheoryExperiment
)2 = 0.40 GeV2Instanton Model [Balla et al., Lee et al.] (Q)2 = 1 GeV2QCD Sum Rules [Stein et al.] (Q
)2 = 1 GeV2QCD Sum Rules [Balitsky et al.] (Q)2> = 3.21 GeV2This Work (<Q)2> = 4.32 GeV2This Work (<Q
nEFnBF
Need d2 and f2 to perform the Electric and Magne/c components separa/ons
Virtual-Photon Nucleon Asymmetry A1
x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
n 1A
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1SLAC E142 SLAC E154
HERMES JLab E99-117
This Work Isgur
Bourrely et al. t et al.eClo
Leader et al. Avakian et al.
DSE (realistic)
DSE (contact)
September 20, 2015 Erice 25
Phys.Len. B744 (2015) 309-‐314
Flavor decomposition
x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)u)/(
u +
uu
+ (
00.10.20.30.40.50.60.70.80.9
1
x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)u)/(
u +
uu
+ (
00.10.20.30.40.50.60.70.80.9
1
DSE (realistic)
DSE (contact)
x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)d)/(
d +
dd
+ (
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
1
x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)d)/(
d +
dd
+ (
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
1HERMES (SIDIS) COMPASS (SIDIS)JLab E99117 (DIS) JLab CLAS EG1b (DIS)This Work Bourrely et al.
t et al.eClo Leader et al.Avakian et al.
DSE (realistic)
DSE (contact)
September 20, 2015 Erice 26
Summary The neutron was measured with precision and found consistent with
Laoce and in contrast with previous results.
The proton d2 is measured with reasonable precision and found to be consistent with Laoce QCD calcula/ons and consistent with the SLAC data around 5 GeV2. The results need to be finalized.
Using the proton and neutron data a preliminary flavor decomposi/on of the color forces is carried out.
The helicity contribu/on of the up and down quarks at large x s/ll exhibits a behavior consistent with quark models and not pQCD predic/ons.
This program will be pursued at JLab 11 GeV for higher precision and greater Q2 and x coverage.
September 20, 2015 Erice 27
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