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A New Spin on the Neutron Spin
W. Korsch
Department of Physics and AstronomyUniversity of KentuckyLexington, KY [email protected]
BNL, Nuclear Seminar, Jan. 30, 2007
Outline
Outline
1 Introduction to Polarized Inclusive DIS
2 The Role of Jefferson Lab
3 Spin Physics in Hall A
4 Spin Physics in Hall B
5 Combining Halls A and B
6 Summary and Outlook
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 2
Introduction to Polarized Inclusive DIS
Polarized (Deep-)Inelastic Inclusive Scattering
Unpolarized DIS:
k) (E, µk k’) (E’, µk’
q),ν (µq
µ, SµP
X (W)
Kinematic variables:W = invariant massQ2 = −q2 = 4EE′sin2(θ/2)
ν = E− E′ =P · q
M
x =Q2
2Mν(Bjorken Scaling Variable)
y =P · qP · K =
ν
Eγ =
2Mx√Q2
Spin-averaged cross section
dσ
dx dy=
e4
4π2Q2
(y2
F1(x , Q2) +1
2xy
(1− y − y2
4γ2
)F2(x , Q2)
)W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 3
Introduction to Polarized Inclusive DIS
Polarized DIS:
ϕαk
k’
P,S
θ
Spin-dependent cross section
d∆σ(α,ϕ)
dx dy=
e4
4π2Q2
(cosα
((1− y
2− y2
4γ2)g1(x , Q2)− y
2γ2g2(x , Q2)
))−sinα cosϕ
√γ2
(1− y − y2
4γ2
)(y2
g1(x , Q2) + g2(x , Q2)))
α, ϕ refer to target spin orientationtwo new (spin) Structure Functions: g1(x , Q2), g2(x , Q2)
α = 0 ⇒ longitudinally polarized targetα = 90, ϕ = 0(180) ⇒ transversely polarized target (note: d∆σchanges sign for ϕ : 0 ↔ 180)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 4
Introduction to Polarized Inclusive DIS
Experiment ⇒ measure scattering asymmetries:
Beam: longitudinally polarizedTarget: longitudinally or transversely polarized
Measure scattering asymmetries ⇒ virtual photon asymmetries:
A1(x , Q2) =σ 1
2− σ 3
2
σ 12
+ σ 32
=g1(x , Q2)− γ2g2(x , Q2)
F1(x , Q2)
A2(x , Q2) =2σTL
σ 12
+ σ 32
=γ[g1(x , Q2) + g2(x , Q2)]
F1(x , Q2)
F1(x , Q2) for neutron:
“well” known in DIS region (SLAC, CERN, DESY)“poorly” known in resonance region⇒ need to measure spin dependent cross sections
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 5
Introduction to Polarized Inclusive DIS
World Data on g1,2(x, Q2) (in DIS region)World data on
0
0.02
0.04
0.06
xg1
proton
E142E154
HERMES
E143E155
SMC
-0.04
-0.02
0
0.02
0.04deuteron
-0.04
-0.02
0
0.02
x
neutron
0.01 0.1 1
Given at experimental .
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 6
Introduction to Polarized Inclusive DIS
World Data on g1,2(x, Q2) (in DIS region)World data on
0
0.02
0.04
0.06
xg1
proton
E142E154
HERMES
E143E155
SMC
-0.04
-0.02
0
0.02
0.04deuteron
-0.04
-0.02
0
0.02
x
neutron
0.01 0.1 1
Given at experimental .
x10-2
10-1
1
p 2xg
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
E143E155E155x
Proton
x10-2
10-1
1
d 2xg
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
E143E155E155x
Deuteron
x10-2
10-1
1
(x)
n 2xg
-1
-0.5
0
0.5
1
E142E143E154E155E155x
Neutron
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 6
The Role of Jefferson Lab
What can Jefferson Lab Contribute?
ë E . 5.7GeV á Parton -Hadron Transition
ë C.W. beam, Ip ≈ 40µA(or more)
ë Pe ≈ 80%
ë ~e− spin flip rate: 30 Hz
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 7
The Role of Jefferson Lab
Spin Structure Studies at Jefferson Lab
Hall A kinematic coverage:
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 8
The Role of Jefferson Lab
2 High Resolution Spectrometers∆Ω ≈ 5 msr (ext. tgt. accep.)∆pp≈ ± 4 %
δpp≈ 3· 10-4
π-/e- < 10-4
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 9
Spin Physics in Hall A
Hall A Polarized 3He Program
3 ~He Target
Pt ≈ 35 → 45%spin orientation: ‖ or ⊥(any horizontal direction)
fast polarization reversal(few mins.)
high pressure (≈ 10 atm)spin-exchange target.
high pol. L ≈ 6× 1035/cm2/s
Photo−Diode for EPR
@ I = 12 µAP = 45 %
Diode Laser
Diode Laser
Diode Laser
3 x 30W @ 795nm
Coils
~100 µ m L = 40 cmCell:
windows:
NMR RF Drive Coils
e − beame−beam
Oven
Pickup Coils
Helmholtz
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 10
Spin Physics in Hall A
Contents
[Rb] ~ 10 cm-314
[ He] ~ 10 cm-3203
[N ] ~ 10 cm-3182
Electron Beam
40 cm
Pumping Lasers6 cm
Windows : 130 - 150 mµ6 cm
+ Q2 evolution of moments of gn1,2 in resonance region
+ “large” x (& 0.2), measurements in resonance and DIS regimes+ transverse asymmetries in DIS regime (small)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 11
Spin Physics in Hall A
Reconstruction and PID
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 12
Spin Physics in Hall A
From 3He to the Neutron
In general:
g
3He1,2 (x , Q2) = Pngn
1,2(x , Q2) + 2Ppgp1,2(x , Q2)
* spin depolarization → S′ -, D - states → Pn = 0.86+0.036−0.020,
Pp = −0.028+0.094−0.004
* nuclear binding, Fermi motion −→ ∆ isobar, pions, vectormesons, off-shell effects
* small-x-effects (nuclear shadowing, nuclear anti-shadowing:0.05 . x . 0.2)
In resonance region: nuclear binding and Fermi motion significant:gn
1,2 ⇒ (20-30)% uncertainty, but effects on integrals smaller (.10%)
Γn(Q2) =1
PnΓ
3He(Q2)− 2Pp
PnΓp(Q2) Proton: MAID or CLAS (Hall B)
J.L. Friar et al., PRC42, 2310 (1990)C. Ciofi degli Atti et al., PRC48, R968 (1993)F. Bissey et al., PRC65, 064317 (2002)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 13
Spin Physics in Hall A
g3He
1,2 at low Q2 and low W
0 0.5 1x
−0.2
0
0.2
−0.1
0
0.1
−0.1
0
−0.1
0
0.1
−0.1
0
−0.1
0g
1(x)
g2(x)
0.10 GeV2
0.26 GeV2
0.42 GeV2
0.58 GeV2
0.74 GeV2
0.90 GeV2
Hall A: g3He
1 and g3He
2
pronounced ∆ resonance
g2 ≈ -g1 ⇒ g2 is not small !!note: σLT ∝ (g1 + g2), ∆ is M1transition
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 14
Spin Physics in Hall A
Extension of pQCD to Resonance Regime
Relation between 1st Cornwall-Norton moment of (spin-dependent)scaling function (N =p,n) and the OPE:
ΓN1 (Q2) ≡
∫ 1
0dx gN
1 (x , Q2) =∑
τ=2,4,...
µNτ (Q2)
Qτ−2 = µN2 (Q2) +
µN4 (Q2)
Q2 +µN
6 (Q2)
Q4 + . . .
µτ contain nucleon matrix elementsµ2 Û incoherent scattering of partons (+ perturbative QCDcorrections) Û large Q2
µτ>2 Û coherent scattering of several (few) partons (+ pertubativeQCD corrections), measure of quark-gluon and quark-quarkcorrelationsmeasure of “Initial(Final) State Interactions” Û should becomemore important at lower Q2
related to quark-hadron duality
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 15
Spin Physics in Hall A
Look at µ2:
µ2(Q2 →∞) =
∫ 1
0dx g1(x) = ±a3 + a8 + a0
Axial charges:a3 → gA|np = 1.2670(35) 4
a8 → hyperon weak decay (0.579(25))4a0 → ∆Σ =
∑u,d ,s(∆q + ∆q), from fit to high Q2 data 4
(SU(3)f symmetry assumed)finite Q2: use Q2 dependence of coefficient functionsAccessing higher twist terms:
⇒ ∆Γ1(Q2) ≡ Γ1(Q2)− µ2(Q2)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 16
Spin Physics in Hall A
µ4 =M2
9(a2 + 4d2 + 4f2)
twist-2 ( target mass correction): a2 = 2∫ 1
0dx x2g1(x) 4
twist-3: d2 =
∫ 1
0dx x2(2g1(x) + 3g2(x)) = 3
∫ 1
0dx x2gτ=3
2 (x)
twist-4: f2 →extract from fit
X. Ji and P. Unrau, Phys. Lett. B333 (1994)E. Stein et al., Phys. Lett. B353 (1995)X. Ji and W. Melnitchouk, Phys. Rev. D56 (1997)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 17
Spin Physics in Hall A
µ4 =M2
9(a2 + 4d2 + 4f2)
twist-2 ( target mass correction): a2 = 2∫ 1
0dx x2g1(x) 4
twist-3: d2 =
∫ 1
0dx x2(2g1(x) + 3g2(x)) = 3
∫ 1
0dx x2gτ=3
2 (x)
twist-4: f2 →extract from fit
X. Ji and P. Unrau, Phys. Lett. B333 (1994)E. Stein et al., Phys. Lett. B353 (1995)X. Ji and W. Melnitchouk, Phys. Rev. D56 (1997)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 18
Spin Physics in Hall A
µ4 =M2
9(a2 + 4d2 + 4f2)
twist-2 ( target mass correction): a2 = 2∫ 1
0dx x2g1(x) 4
twist-3: d2 =
∫ 1
0dx x2(2g1(x) + 3g2(x)) = 3
∫ 1
0dx x2gτ=3
2 (x)
twist-4: f2 →extract from fit
X. Ji and P. Unrau, Phys. Lett. B333 (1994)E. Stein et al., Phys. Lett. B353 (1995)X. Ji and W. Melnitchouk, Phys. Rev. D56 (1997)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 19
Spin Physics in Hall A
µ4 =M2
9(a2 + 4d2 + 4f2)
twist-2 ( target mass correction): a2 = 2∫ 1
0dx x2g1(x) 4
twist-3: d2 =
∫ 1
0dx x2(2g1(x) + 3g2(x)) = 3
∫ 1
0dx x2gτ=3
2 (x)
twist-4: f2 →extract from fit
X. Ji and P. Unrau, Phys. Lett. B333 (1994)E. Stein et al., Phys. Lett. B353 (1995)X. Ji and W. Melnitchouk, Phys. Rev. D56 (1997)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 20
Spin Physics in Hall A
Higher Twist Contributions to Γn1(Q2)
pol. 3He from Hall A
1 10-0.10
-0.05
0
0.05
2(GeV )
2Q
nΓ
(
)1
Q2
SLAC E154SMC
HERMES
SLAC E142
SLAC E143
JLab E94010
Γ1(Q2) =∫ 1
0 dxg1(x , Q2)
Elast. contribution included
twist-2: ∆Σn = 0.35 ± 0.08note: ∆Σp = 0.145 ± 0.113 !!! Q2> 5 GeV2
Z.-E. Meziani et al., Phys. Lett. B 613 (2005)M. Osipenko et al., Phys.Lett. B 609 (2005)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 21
Spin Physics in Hall A
0 0.5 1 1.5 2
1/Q2 (GeV
−2)
−0.08
−0.04
0
0.04
0.08
∆Γ
1
n
SLAC E154SMC
HERMES
SLAC E142
SLAC E143
JLab E94010
an2= −0.0031(20)
dn2= 0.0079(48) (E155x)
Z.-E. Meziani et al., Phys. Lett. B 613 (2005)
Fitted range:0.5 GeV2 < Q2 < 10 GeV2
fn2 = 0.034± 0.043 (tot. uncert.)µn
6/M4 = −0.019± 0.017
(Values for Q2 = 1 GeV2)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 22
Spin Physics in Hall A
The Spin Structure Function gn2
8 s.s.f. g2(x, Q2) has no interpretation in the parton model !8 related to the “transverse” spin structure function
gT(x,Q2) = g1(x, Q2) +g2(x, Q2)8 higher-twist structure function ⇒ coherent lepton-parton scattering
with more than one parton involved in scattering process.8 twist-2 part of g2(x, Q2) is completely determined by twist-2 part of
g1 (x, Q2):
gWW2 (x , Q2) = −g1(x , Q2) +
∫ 1
x ′dx ′
g1(x ′, Q2)
x ′S. Wandzura and F. Wilczek, Phys. Lett. B72 (1977)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 23
Spin Physics in Hall A
8 twist-2 and twist-3 contributions are leading twist8 higher twist (twist-3 and higher) contributions can be directly
separated. → g2(x, Q2) is a unique structure function!!!
γγ γ γ
twist-2 twist-3
T TL L
↑ ↓
T
↑ ↑
⇒ sensitive to quark-gluon correlations.
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 24
Spin Physics in Hall A
Q2 Dependence of gn2 at x ≈ 0.2
E97-103: 1.92 GeV < W < 2.48 GeV
]2/c2
[GeV2Q0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.40
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1n2g
n,WW2g
B & B, scenario 2
0.2≈Bj
x
ë higher twist (twist-3?) increase for Q2 . 1 GeV2, but not huge (h.t.> 0)K. Kramer et al., Phys. Rev. Lett. 95 (2005)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 25
Spin Physics in Hall A
Higher Twist Contributions to gn1 at x≈ 0.2
Evolve Blümlein and Böttcher pol. parton distribution functions down tolow Q2: twist-2 evolution
]2/c2
[GeV2Q0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0n1g
0.2≈Bjx
B & B , scenario 2
ë higher twist contributions appear to be small (or cancel) down toQ2 ≈ 0.54 GeV2
K. Kramer et al., Phys. Rev. Lett. 95 (2005)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 26
Spin Physics in Hall A
x-110 1
)2(x
,Qn 2
g
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
JLab E97-103JLab E97-103 Systematic ErrorsSLAC E155XJLab E99-117
2 from B&B scen. 1 @ 1.0 GeVWW
2g2
from B&B scen. 1 @ 5.0 GeVWW2g
d2
n = 0.0062 ± 0.0028
Q2 ≈ 5 GeV2
(w/o E97-103)X. Zheng et al., Phys.Rev.C 70 (2004)P.L. Anthony et al., Phys. Lett. B553 (2003)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 27
Spin Physics in Hall A
x-110 1
)2(x
,Qn 2
g
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
JLab E97-103JLab E97-103 Systematic ErrorsSLAC E155XJLab E99-117
2 from B&B scen. 1 @ 1.0 GeVWW
2g2
from B&B scen. 1 @ 5.0 GeVWW2g
d2
n = 0.0062 ± 0.0028
Q2 ≈ 5 GeV2
(w/o E97-103)X. Zheng et al., Phys.Rev.C 70 (2004)P.L. Anthony et al., Phys. Lett. B553 (2003)
StratmannWeigel and Gamberg
Soffer and Bourelly
g2_WW
SLAC E155x
JLab E99-117
JLab E97-103
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 27
Spin Physics in Hall A
Theoretical Predictions for d2
Neutron
Proton
SLAC E155XLattice
QCD Sum Rules
Bag Model Chiral soliton
Predictions and data
0.00
-0.02
-0.04
d2
0.03
-0.02
0.01
0.00
-0.01
-0.03
0.02
0.02
SLAC E155x +
JLab E99-117
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 28
Spin Physics in Hall B
Hall B Polarized p, d Program
15N~H3, Pt . 70% (‖), solid15N~D3, Pt . 45% (‖), solidSpectrometer: CLAS,∆Ω ≈ 1.5 sr
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 29
Spin Physics in Hall B
New Results on gp1 from Hall B
-0.8
0.8
0.045<Q2<0.054g1p
-0.8
0.8
0.054<Q2<0.065
-0.8
0.8
0.065<Q2<0.077
-0.8
0.8
0.077<Q2<0.091
-0.8
0.8
0.09<Q2<0.11
-0.8
0.8
0.11<Q2<0.13
-0.8
0.8
0.13<Q2<0.16
-0.8
0.8
0.16<Q2<0.19
-0.8
0.8
0.19<Q2<0.22
-0.8
0.8
0.22<Q2<0.27
-0.8
0.8
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.26<Q2<0.32
xBj
0
0.251.10<Q2<1.31g
1p
0
0.251.31<Q2<1.56
0
0.251.56<Q2<1.87
0
0.251.87<Q2<2.23
0
0.252.23<Q2<2.66
0
0.252.66<Q2<3.17
0
0.253.17<Q2<3.79
0
0.25
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
3.79<Q2<4.52
xBj
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 30
Spin Physics in Hall B
New Results on gd1 from Hall B
-0.5
0
-0.5
0
-0.5
0
-0.5
0
-0.5
0
-0.5
0
g1d
Q2 = 0.2 GeV2
Q2 = 0.24 GeV2
Q2 = 0.3 GeV2
Q2 = 0.35 GeV2
Q2 = 0.42 GeV2
Q2 = 0.5 GeV2
xbj
Q2 = 0.6 GeV2
-0.5
0
0.070.080.090.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-0.25
0
0.25
-0.25
0
0.25
-0.25
0
0.25
-0.25
0
0.25
-0.25
0
0.25g
1d Q2 = 1.4 GeV2
Q2 = 1.7 GeV2
Q2 = 2.0 GeV2
Q2 = 2.4 GeV2
Q2 = 3.0 GeV2
xbj
Q2 = 3.5 GeV2
-0.25
0
0.25
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 31
Spin Physics in Hall B
Γp1(Q2) and Γd
1(Q2) from Hall B
€ Dodge, Old Dominion University
∫
Ph.D. work:
V. Dharmawardane – ODU
`p 1(Q
2)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 32
Spin Physics in Hall B
Higher Twist Contributions to Γp1(Q2)
a
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1 100
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EG1a Collaboration
fp2 = 0.039± 0.022(stat.)± 0.0000.018(sys.)± 0.030(low x)± 0.007
0.011(αs)
µp6 = 0.011± 0.013(stat.)± 0.010
0.000(sys.)± 0.011(low x)± 0.000(αs)
Values at Q2 = 1 GeV2M. Osipenko et al., Phys.Lett. B 609 (2005)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 33
Combining Halls A and B
Γn1(Q2) from 3He (Hall A) and D (Hall B)
Γ1(Q2) =∫ 1
0 dx g1(x, Q2)
Low x extrapolation:
Hall A: 2 GeV < W < 32 GeVÛ Bianchi & Thomas
Hall B: own model
Determination of Γn1 very consistent ⇒ nuclear effects are
understood G. Dodge, talk at GDH2004M. Amarian et al., Phys. Rev. Lett. 92 (2004)N. Bianchi and E. Thomas, Phys. Lett. B450 (1999)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 34
Combining Halls A and B
Color Polarizabilities of the Proton and the Neutron
Color polarizabilites: Response of color electric and magnetic fields tospin orientation.
χE = 23(2d2 + f2)
χB = 13(4d2 − f2)
E. Stein et al., Phys. Lett. B 353 (1995)X. Ji, hep-ph/9510362 (1995)
Proton (Q2 = 1 GeV2)
χpE = 0.026± 0.015(stat .)±0.021
0.024 (sys.)
χpB = −0.013∓ 0.007(stat .)∓0.010
0.012 (sys.)
Neutron (Q2 = 1 GeV2)
χnE = 0.033± 0.029
χnB = −0.001± 0.016
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 35
Combining Halls A and B
Future Higher Twist Studies in Hall A
0.01 0.1 10Q2 (GeV
2)
−0.005
0.000
0.005
0.010
0.015
d 2 E94010 Neutron
E155x NeutronChPT
MAID
Lattice QCD
1
E99−117 + E155x Neutron
Proposal
2008: d2(〈Q2〉 = 3GeV 2)JLab at 12 GeV: d2(〈Q2〉 = 3, 4, 5GeV 2)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 36
Combining Halls A and B
Higher Twist Contributions to the Bj Integral
at infinite Q2:Bjorken integral: Hall A and Hall B data combined
Γp−n1 ≡ Γp
1 − Γn1 ≡
∫ 1
0dx (gp
1 (x)− gn1(x)) =
gA
6
at finite (large) values of Q2 and leading twist ( = twist-2), MSscheme:
Γp−n1 (Q2) =
gA
6
[1− αs
π− 3.58
(αs
π
)2
− 20.21(
αs
π
)3
+ . . .
]= µp−n
2 (Q2)
at finite (small) values of Q2 and power corrections (OPE):
Γp−n1 (Q2) =
∞∑i=1
µp−n2i (Q2)
Q2i−2 = µp−n2 (Q2) +
µp−n4 (Q2)
Q2 +µp−n
6 (Q2)
Q4 + . . .
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 37
Combining Halls A and B
The Bjorken Integral in the Transition Regime
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 38
Combining Halls A and B
Fitted range:0.8 GeV2 < Q2 < 10 GeV2
fp−n2 = −0.11± 0.15(uncor)+0.04
−0.03(cor)µp−n
6 /M4 = 0.08± 0.06(uncor)± 0.01(cor)
Fitted range:0.66 GeV2 < Q2 < 10 GeV2
fp−n2 = −0.17± 0.05(uncor)+0.04
−0.05(cor)µp−n
6 /M4 = 0.12± 0.02(uncor)± 0.01(cor)
(Values for Q2 = 1 GeV2)
Low x extrapolation consistently done → Bianchi & Thomas (2 GeV < W < 32 GeV) +Regge parameterization for W > 32 GeV (Note: Bj integral is flavor non-singlet)A. Deur et al., Phys. Rev. Lett. 93 (2004)
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 39
Combining Halls A and B
Extraction of αeffs at Low Q2
Define αeffs using the Bjorken integral
Γp−n1 (Q2) = gA
6
(1− αeff
s (Q2)π
) ß absorb power and pQCD correc-tions in αeff
s
S. Brodsky, hep-ph/0310289G. Grunberg, Phys. Rev. D29 (1984)G. Grunberg, Phys. Lett. B95 (1980)
αeffs stays finite as Q → 0 !!
EG1b data consistentwith Burkert-Ioffe curve !
Bj = Q2× GDH
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 40
Summary and Outlook
Summary
7 Polarized 3He program in Hall A has been successfully taking datafor ≈8 years.
7 High luminosity ⇒ Q2 evolution of moments can be measured.7 Higher twist effects in spin structure g1 and g2 functions appear to
be small for the proton and the neutron down to Q2 < 1 GeV2.
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 41
Summary and Outlook
Outlook
3 ~He Program
gDGH : Q2 < 0.5 GeV 2
3 ~He(~e, e′n) ⇒ GnE : Q2 ≤ 3.4 GeV 2
SSAs: 3 ~He(~e, e′π∓)X
3 ~He(~e, e′d(n)) ⇒ 3He w.f., GnE
d2 @ Q2 = 3 GeV 2, Ay
JLab @ 11 GeV
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 42
Summary and Outlook
Outlook
3 ~He Program
gDGH : Q2 < 0.5 GeV 2
3 ~He(~e, e′n) ⇒ GnE : Q2 ≤ 3.4 GeV 2
SSAs: 3 ~He(~e, e′π∓)X
3 ~He(~e, e′d(n)) ⇒ 3He w.f., GnE
d2 @ Q2 = 3 GeV 2, Ay
JLab @ 11 GeV
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 43
Summary and Outlook
Outlook
3 ~He Program
gDGH : Q2 < 0.5 GeV 2
3 ~He(~e, e′n) ⇒ GnE : Q2 ≤ 3.4 GeV 2
SSAs: 3 ~He(~e, e′π∓)X
3 ~He(~e, e′d(n)) ⇒ 3He w.f., GnE
d2 @ Q2 = 3 GeV 2, Ay
JLab @ 11 GeV
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 44
Summary and Outlook
Outlook
3 ~He Program
gDGH : Q2 < 0.5 GeV 2
3 ~He(~e, e′n) ⇒ GnE : Q2 ≤ 3.4 GeV 2
SSAs: 3 ~He(~e, e′π∓)X
3 ~He(~e, e′d(n)) ⇒ 3He w.f., GnE
d2 @ Q2 = 3 GeV 2, Ay
JLab @ 11 GeV
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 45
Summary and Outlook
Outlook
3 ~He Program
gDGH : Q2 < 0.5 GeV 2
3 ~He(~e, e′n) ⇒ GnE : Q2 ≤ 3.4 GeV 2
SSAs: 3 ~He(~e, e′π∓)X
3 ~He(~e, e′d(n)) ⇒ 3He w.f., GnE
d2 @ Q2 = 3 GeV 2, Ay
JLab @ 11 GeV
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 46
Summary and Outlook
Outlook
3 ~He Program
gDGH : Q2 < 0.5 GeV 2
3 ~He(~e, e′n) ⇒ GnE : Q2 ≤ 3.4 GeV 2
SSAs: 3 ~He(~e, e′π∓)X
3 ~He(~e, e′d(n)) ⇒ 3He w.f., GnE
d2 @ Q2 = 3 GeV 2, Ay
JLab @ 11 GeV
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 47
Summary and Outlook
Outlook
3 ~He Program
gDGH : Q2 < 0.5 GeV 2
3 ~He(~e, e′n) ⇒ GnE : Q2 ≤ 3.4 GeV 2
SSAs: 3 ~He(~e, e′π∓)X
3 ~He(~e, e′d(n)) ⇒ 3He w.f., GnE
d2 @ Q2 = 3 GeV 2, Ay
JLab @ 11 GeV
W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 48