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A New Spin on the Neutron Spin W. Korsch Department of Physics and Astronomy University of Kentucky Lexington, KY 40506 [email protected] BNL, Nuclear Seminar, Jan. 30, 2007
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Page 1: A New Spin on the Neutron Spin · 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

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

Page 2: A New Spin on the Neutron Spin · 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

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

Page 3: A New Spin on the Neutron Spin · 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

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

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

Page 4: A New Spin on the Neutron Spin · 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

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

Page 5: A New Spin on the Neutron Spin · 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

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

Page 6: A New Spin on the Neutron Spin · 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

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

Page 7: A New Spin on the Neutron Spin · 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

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

Page 8: A New Spin on the Neutron Spin · 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

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

Page 9: A New Spin on the Neutron Spin · 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

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

Page 10: A New Spin on the Neutron Spin · 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

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

Page 11: A New Spin on the Neutron Spin · 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

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

Page 12: A New Spin on the Neutron Spin · 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

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

Page 13: A New Spin on the Neutron Spin · 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

Spin Physics in Hall A

Reconstruction and PID

W. Korsch (Univ. of Kentucky) Spin Physics at JLab BNL, January 2007 12

Page 14: A New Spin on the Neutron Spin · 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

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

Page 15: A New Spin on the Neutron Spin · 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

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

Page 16: A New Spin on the Neutron Spin · 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

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

Page 17: A New Spin on the Neutron Spin · 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

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

Page 18: A New Spin on the Neutron Spin · 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

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

Page 19: A New Spin on the Neutron Spin · 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

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

Page 20: A New Spin on the Neutron Spin · 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

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

Page 21: A New Spin on the Neutron Spin · 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

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

Page 22: A New Spin on the Neutron Spin · 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

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

(

)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

Page 23: A New Spin on the Neutron Spin · 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

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

Page 24: A New Spin on the Neutron Spin · 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

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

Page 25: A New Spin on the Neutron Spin · 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

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

Page 26: A New Spin on the Neutron Spin · 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

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

Page 27: A New Spin on the Neutron Spin · 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

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

Page 28: A New Spin on the Neutron Spin · 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

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

Page 29: A New Spin on the Neutron Spin · 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

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

Page 30: A New Spin on the Neutron Spin · 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

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

Page 31: A New Spin on the Neutron Spin · 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

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

Page 32: A New Spin on the Neutron Spin · 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

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

Page 33: A New Spin on the Neutron Spin · 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

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

Page 34: A New Spin on the Neutron Spin · 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

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

Page 35: A New Spin on the Neutron Spin · 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

Spin Physics in Hall B

Higher Twist Contributions to Γp1(Q2)

a

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1 100

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Yy CD)©4fg5D)©]D47l1¡5DZOiD7©]65D)©4'Da1¡5^57©]6eD© Df 4K1¡C8= Ru6 y yYy gy y > y 13£ ¤ 6% 1|l6 0Fl9;Y9DF#9%MhY5DcO@:#U"59kE;=J:#UÆ9;YY=JY5OiY95DZO@D685D68EROiCèOi:#U"5^5

D9;M OiD68EJ?lDF#9DF#68YU685BÑY=JM DF#95DN9*8yDYZOi7h=C OiD68=J:!?hO@:lUDF#9C Oi5D685U#H#9D=cDF#9H#:#Ek9;YDGO@68:D^68:~£V¤3$0Fl9+C89ROiU#68:)D 0685DEk=J:DY6lH#D68=J:*D=r > 685c6:lU#68ERO@D9;U^ÚDF#9NUhO@5F#9;UE;H#Y,9N68:T!6h3)Ql3

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

Page 36: A New Spin on the Neutron Spin · 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

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

Page 37: A New Spin on the Neutron Spin · 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

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

Page 38: A New Spin on the Neutron Spin · 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

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

Page 39: A New Spin on the Neutron Spin · 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

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

Page 40: A New Spin on the Neutron Spin · 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

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

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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

Page 42: A New Spin on the Neutron Spin · 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

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

Page 43: A New Spin on the Neutron Spin · 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

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

Page 44: A New Spin on the Neutron Spin · 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

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

Page 45: A New Spin on the Neutron Spin · 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

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

Page 46: A New Spin on the Neutron Spin · 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

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

Page 47: A New Spin on the Neutron Spin · 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

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

Page 48: A New Spin on the Neutron Spin · 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

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

Page 49: A New Spin on the Neutron Spin · 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

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

Page 50: A New Spin on the Neutron Spin · 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

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


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