overview of jefferson lab’s spin physics programme

Overview of Jefferson Lab’s Spin Physics Programme

Stephen Bültmann - ODU RHIC/AGS Users Meeting, June 2007

• Introduction• Experimental Setup• Asymmetry Measurement• Moments of Structure Functions• Outlook

Spin structure vs distance scale

magnetic moment(GDH SR)

pions, nucleon

constituentquarks, N*

multiple partons

single partonsQ2

Q2=0

phot

on in

tera

cts

with

Bjorken Sum Rule Asymptotic freedom

Perturbative QCD

GDH Sum Rule

Chiral Perturbation Theory


The CEBAF AcceleratorElectron beam• Energy up to 5.7 GeV • Current 1 - 100 µA (Hall B 50 nA) • Polarization > 0.8


Experimental Halls


Hall A HRS + HRSHall B CLAS

Hall C HMS + SOSPolarized Targets:H2 and D2 (Hall B + C)3He (Hall A)

Polarized Targets in Halls B & C


• Dynamically polarized targets of solid (deuterated) ammonia• 5 Tesla magnetic field• 140 GHz polarizing microwaves• 1 Kelvin superfluid helium• Longitudinal polariztion

P1 < 0.9 P1 ave = 0.7 - 0.8

P2 < 0.4 P2 ave = 0.2 - 0.3

measured by NMR• Also transverse

polarization in Hall C• Current

3 nA in Hall B100 nA in Hall C

• Luminosity < 1035 cm-2 sec-1

Polarized Target in Hall A


• Polarized 3He gas target• Optical pumping and spin

exchange• Longitudinal and transverse

polarizationP3 < 0.5 P1 ave = 0.4

measured by NMR and EPR• Current 12 µA• Luminosity < 1036 cm-2 sec-1

CLAS Detector in Hall B


DIS of lepton off nucleon

€

Q2 = −q2 = 4EE 'sin2 θ2

€

W 2 = M 2 + 2Mν − Q2

€

x = Q2

2Mν

€

d2σdΩdE '

= σ Mott1ν

F2(x,Q2) + 2M

F1(x,Q2)tan2 θ2

⎡ ⎣ ⎢

⎤ ⎦ ⎥

€

d2σ ↑⇑

dΩdE '− d2σ ↓⇑

dΩdE '= 4α 2E '

νEQ2 E + E 'cosθ( )g1(x,Q2) − 2Mxg2(x,Q2)[ ]

Virtual photon scatters off partonk k’

qp

p’

PxP=

Elastic

W

xP=p

q

P

p’

kk’


Kinematic Coverage


EG1 EG4

Status of g1(x,Q2)

• Existing data mostly for DIS and low x• Remaining

– G (RHIC, COMPASS)– L (COMPASS, HERMES, Jlab)– Transversity (HERMES, Jlab, RHIC)– Large x precision measurements

(Jlab)– Measurement in non-perturbative

region (Jlab)


the asymmetries A1 and A2 can be extracted by varying the direction of the nucleon polarization

where D, , d, are function of Q2, W, E0, R

the structure functions g1 and g2 are linear combination of A1 and A2

ee’

Pe Pt

e

nucleon ( )

( )21

21||

AAdA

AADA

ζ

η

+=

+=⊥

( )( )[ ]σεεσεεσσσ sin12cos1' 21

2TTteLTv AAPP

ddEd −+−++Γ=

Ω

T

LT

T

AAσσ

σσσ '

22/32/1

1 =−

=A1 A2

A1 A2

( ) ( )

( ) ( )2112

2

222

22

2

21221222

22

1

,24

,

,24

,

QxFAAMxQ

xMQQQxg

QxFAQ

MxAxMQ

QQxg

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+=g1(x,Q2

)

g2(x,Q2

)Stephen Bültmann - ODU RHIC/AGS Users Meeting, June 2007

Asymmetry Measurement



Simultaneous extraction of A1 and A2 from measured asymmetry

A|| = D ( A1 + A2 ) with = and D =ε √ Q2

E - ε E’

1 - ε E’ / E

1 + ε R

DFPPAC

Ate

rawback×

=||

A1+A2 for proton

Parametrization of previous world data (including CLAS) by S. Kuhn , L. Stuart, et al. including “AO” and “MAID2000” for resonance regionBlue solid line = Estimated contribution from AA22 to AA11++AA22

1.7 GeV (proton) 5.7 GeV (proton)


gg11 forfor the pthe protonroton

Parameterization of previous world data (including CLAS)g1(x,Q2) = [(A1+´ A2)+(°-´)A2]F1

1+°2

g1(x,Q2) for the proton


Proton/Deuteron Comparison

In the ¢(1232) region and at low Q2, g1

d/2 is consistent with g1p

At high Q2, g1p is significantly

larger than g1d/2 , indicating a

negative contribution from the neutron




• Very preliminary result• A2 is larger than previously used EG1 model, basing on MAID and AO• Same result reported by RSS experiment from JLab Hall C (2007)

Asymmetry Measurement in Hall C (RSS)


Q2 range from 0.8 to 1.4 GeV2/c2

• Polarized longitudinal and transverse ammonia target

• 100 nA electron beam• Both polarizations average

between 0.6 and 0.7• HMS spectrometer at 13.5º• 160 million events

Asymmetry A1


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 - E143SMC

HERMESSLAC - 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 1xbj

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

Proton Deuteron

g2 from Hall C (RSS)


Twist-2 Wandzura-Wilcek approximation



d2 = 0.0057 ± 0.0009 stat. ± 0.0007 sys. for 0.29 < x < 0.84d2 = 0.0029 at Q2 = 5 GeV2/c2

Compared to SLAC d2 = 0.0032 ± 0.0017

Twist-3 matrix element d2 representing quark-gluon correlation

Polarized PDF’s


• Inclusion of large amount of low-Q2 data from CLAS EG1 by Leader, Siderov, and Stamenov

• Simultaneous extraction of polarized parton densities and higher twist corrections

Polarized PDF’s


Error envelopes LSS05 LSS06 (EG1) CLAS12

overall improved by EG1 data

(1232)S11 (13)

F1 (1)

Global

Test of Quark-Hadron Duality


Proton



Q2 range from 0.8 to 1.4 GeV2/c2

Integration over resonance region 1.09 GeV < W < 1.91 GeVof NLO PDFs and comparison with measurement gives a ratio of1.17 ± 0.08

Global duality only at 2 sigma levelLocal duality not observed

QQ22 dependence of dependence of gg11/F/F11 Q2 dependence of g1 at

fixed x is very similar to F1

in the DIS region

EG1 data show a decrease

in g1/F1 even in the DIS

region

Resonance region

different Q2 dependence

goes negative at

High Q2 results agree with

SLAC data


Assuming the naïve parton model with no sea contribution, quark polarizations in the valence region can be estimated directly from the data:

¢u/u = [5g1p-2g1

d/(1-1.5wD)]/[5F1p-2F1

d]

¢d/d = [8g1d/(1-1.5wD)-5g1

p]/[8F1d-5F1

p]

¢u /u ! 1 as x ! 1Consistent with pQCD and QMDisagrees with SU(6)

¢d /d < 0 up to the highest x ~0.6Consistent with Hyperfine Perturbed QM Disagrees with pQCD w/o orbital angular momentum


Quark polarization in the valence region

Moments and Sum Rules

∫=1

0

21

21 dx)Q,x(g)Q( Γ

QPM


1p = 3

36436

136

a3 + a8 + a0

1n = - 3

36436

136

a3 + a8 + a0

= 0.186 +QCD corr

= - 0.025 +QCD corr

Ellis-Jaffe Sum Rule

Bjorken Sum Rule (pre QCD) evolution Q2+=−611Anp g

GDH Sum Rule( ) 2

2/32/12

2

41

8κ

ννσσ

απ−=−= ∫

∞

thrGDH

dMI

relates the difference of the photo-absorption cross section for helicity 1/2 and 3/2 to the nucleon magnetic moment, i.e. a connection between dynamic and static properties. Recent measurements at Bonn and Mainz, ongoing efforts at other labs

based on very general principles, as gauge invariance, dispersion relation, low energy theorem

at finite Q2 can be related to the integral of the spin structure function g1

strong variation of nucleon spin properties as a function of Q2

IGDH

( ) GDHQI

MQdxQxg 2

2

02

11 2, 2 ⏐⏐ →⏐=Γ

→∫

GDH sum rule

DISpQCD

Transition Region

Q2 (GeV2)1

1


Generalized GDH IntegralA generalization of the GDH sum rule has been suggested by Ji and Osborne by relating the virtual-photon forward Compton amplitude S1 to the nucleon structure function G1 X.Ji et al., Phys.Lett.B472 (2000) 1

∫IGDH (Q2) = dx g1(x,Q2)

x0

Q2 < 0.1 GeV2

0.1 < Q2 < 0.5 GeV2

Q 2 > 0.5 GeV 2

GDH sum rule and Chiral Perturbation Theory

- — + cQ2 + O (Q4)

Lattice?

Ellis-Jaffe Sum rule and Operator Product Expansion

~

2

M2

(Q2)Q-2=2,4,…

Calculable

16Q2

S1 (0,Q2)


Measurable

11 for the proton and deuteron for the proton and deuteron

Xmin=0.001, x_max= pion production threshold shows strong Q2 dependence varying from negative to positive values as Q2

increases

1 1proton deuteron

Q2(GeV2)Q2(GeV2)


Low Q2 behavior of 1 - PT

proton deuteron

preliminary preliminar

y


EG4 projection

• Extends to very low Q2 of 0.015 GeV2 both proton and deuteron

• Data taken earlier this year


Hall A Measurement on 3He


Preliminary1

nE94-110 Q2 range 0.1 - 1 GeV2

Hall A Measurement on 3He E01-012


1n

• g1/g2 and A1/A2 (3He/n) in resonance region, 1 < Q2 < 4 GeV2

• Study quark-hadron duality in spin structure

Bjorken Sum Q2 Evolution


Combined data fromEG1a and Hall A E94-010A. Deur, et al., PRL 93, 212001 (2004)

JLab Upgrade: EG12 projections

W > 2; Q2 > 1

Allows access to higher x values


Summary A wealth of new data on the nucleon spin structure in the

non-perturbative regime has been produced at Jefferson Lab as part of a broad spin physics program, still in progress

These measurements provide new information for understanding the transition between hadronic and partonic degrees of freedom by investigating spin structure functions, related sum rules and moments, asymmetries, …

A new measurement to cover the very low momentum transfer region and provide a bridge to the GDH sum rule at the photon point has just been completed recently

12 GeV program at Jlab will offer the opportunity to extend these measurements into new kinematic regions


overview of jefferson lab’s spin physics programme

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