Study Neutron Spin Structure with a Solenoid

Jian-ping Chen, Jefferson LabHall A Collaboration Meeting

June 22-23, 2006

Inclusive DIS:

Valence quark spin structure: A1 at high x

g2, d2 and higher-twist effects (twist-3)

g3, f2 (twist-4)

Semi-inclusive DIS

Example: transversity.•Acknowledgement: E. Chudakov (simulation), X. Zheng, W. Korsch,

Z. Meziani, K. Kumar, P. Souder, …

Introduction

• DIS provided rich information on quark-gluon structure of the nucleon and the strong interaction (QCD)

• High energy: asymptotic freedom

perturbative QCD calculation works, QCD well tested

parton distributions functions (PDFs) extracted from DIS data

quark-parton models

large-x region, spin-flavor decomposition• Low-to-intermediate energy: confinement

quark-gluon correlations: higher twists

test QCD in the strong interaction (non-perturbative) region?• Semi-inclusive DIS

a new window to study nucleon structure and QCD

Unpolarized and Polarized Structure functions

Unpolarized Parton Distributions (CTEQ6)• After 40 years DIS experiments, unpolarized structure of the nucleon reasonably

well understood.• High x valence quark dominating

NLO Polarized Parton Distributions (BB)

Neutron Spin Structure with JLab 12 GeV

• DIS program on neutron spin structure:

A1n at high-x, d2

n, g3n

SIDIS: transversity, and …

high luminosity and large acceptance• Polarized 3He target

effective polarized neutron

highest polarized luminosity• A solenoid with detector package

large acceptance

Valence Quark Spin Structure

A1 at high-x

JLab E99-117 A1n Results

• First precision A1n data at x > 0.3

• Comparison with model calculations• SU(6) symmetry• Valence quark models• pQCD (with HHC) predictions• Other models: Statistical model,

Chiral Soliton model, PDF fits, …

• Crucial input for pQCD fit to PDF

• PRL 92, 012004 (2004)

PRC 70, 065207 (2004)

Polarized Quark Distributions

• Combining A1n and A1

p results

• Valence quark dominating at high-x

• u quark spin as expected• d quark spin stays negative!

• Disagree with pQCD model calculations assuming HHC (hadron helicity conservation)

• Quark orbital angular momentum

• Consistent with valence quark models and pQCD PDF fits without HHC constraint

• x high enough?

Solenoid Option with 11 GeV beam

• Acceptance 10-30 times HMS+SHMS

• Low energy particles cut off (~1.7 GeV)

• PID: Gas Cherekov + Shower Counter

• Challenge: polarized 3He target inside the solenoid

• 100 hours beam time, a precision measurement of A1n at high-x

up to ~0.8

• Can do Q2 study for high-x up to 0.75

• Definitive measurements to shed lights on valence quark picture

• Solenoid,

200 hours

• HMS+SHMS,

1800 hours

(X. Zheng)

g2, d2 and higher-twist

twist-3: quark-gluon correlations

Nucleon Structure Beyond Simple Parton Models

• Naïve quark-parton models

no interactions between quarks

reasonable at high Q2 due to asymptotic freedom

• Interaction important at low to intermediate Q2

quantify the interaction

1st step beyond parton distributions: quark-gluon correlations

how to measure q-g correlations?

Operator Product Expansion

• In QCD framework: Operator Product Expansion

1/Q expansion (twist expansion)

twist is related to (mass dimension – spin)

contains twist- matrix elements

22

2 )(

Q

Qg

Twist-2 and Twist-3

-- twist-2: parton (quark, gluon) distributions

-- no interactions

-- twist-3: quark-gluon correlations

-- one gluon

one additional 1/Q

g2: twist-3, q-g correlations• experiments: transversely polarized target

SLAC E155x, JLab Hall A

g2 leading twist related to g1 by Wandzura-Wilczek relation

• g2 - g2WW: a clean way to access twist-3 contribution

quantify q-g correlations

1

21

21

22

22

22

22

),(),(),(

),(),(),(

x

WW

WW

y

dyQygQxgQxg

QxgQxgQxg

d2: twist-3 matrix element

• 2nd moment of g2-g2WW

d2: twist-3 matrix element

Provide a benchmark test of Lattice QCD

Avoid issue of low-x extrapolation (as in the lower moments)

Needs precision data at high-x

1

0

22

21

2

1

0

22

22

222

)],(3),(2[

)],(),([3)(

dxQxgQxgx

dxQxgQxgxQd WW

E97-103(Q2~1 GeV2), K. Kramer et al., PRL 95, 142002 (2005) E99-117(Q2~3-5 GeV2), X. Zheng et al., PRC70, 065207 (2004)

g2n: JLab and world data

d2n: JLab and world data

• E99-117+SLAC (high Q2) E94-010 (low Q2)

• Twist-3 matrix element

• ChPT (low Q2) MAID model • Lattice QCD (high Q2) other models

g2n/d2

n with the solenoid

• Transversely polarized target target in front of the solenoid• Angular range 10o-22o,

• Acceptance is ~ 10-30 times higher than SHMS+HMS with W2 > 4 GeV2

Q2 = 3 GeV2, x: 0.1- 0.55 4 0.15 – 0.6 5 0.2 - 0.65 6 0.3 – 0.7

In ~100 hours, map of Q2 dependence of d2n.

Benchmark test of Lattice QCD calculations.

JLab 12 GeV Projection for x2g2n

Solenoid (100 hours) (W >2 GeV) SHMS+HMS (500 hours) (W. Korsch)

d2n with JLab 12 GeV

• Projection with Solenoid, Statistical only, will be systematic limited? Improved Lattice Calculation (QCDSF, hep-lat/0506017)

g3: Parity Violating Spin Structure Functionf2: twist-4, color polarizabilities

Color “Polarizabilities”Color “Polarizabilities”

f2 and Color Polarizabilities Extraction

• JLab + world n data,

4 = (0.019+-0.024)M2

• Twist-4 term 4 = (a2+4d2+4f2)M2/9

• extracted from 4 term f2 = 0.034+-0.005+-0.043

• Color polarizabilities

= 0.033+-0.029

B = -0.001+-0.016

Z. Meziani et al. PLB 93 (2004) 212001

g3: Parity Violating Spin Structure Function

• f2 can be directly measured from:

1

0

23

22

21

222 )),(9),(12),(7(

2

1)( dxQxgQxgQxgxQf

g3 is a parity violating spin structure function.

• Never been measured so far

• g3: unpolarized beam and polarized target

ZZA

ZZV ggyxyggy

dxdy

d

dxdy

d 13

2

)2()1(~

g3 in Naïve Parton Model

• Naïve Parton Model:

•Provide a clean way to measure sea-quark spin•Asymmetry expected to be at the same level as the other DIS parity asymmetry (~10-5 Q2 – 10-4 Q2)•Need high luminosity and large acceptance

)()(23 qqgexgq

qAqZ

Measurement of g3n

• Rate estimation with the Solenoid detector: polarized 3He target in front the solenoid 1036 neutron/s luminosity, 50% target polarization 11 GeV beam, 10o - 22o, W > 2 GeV x: 0.1 - 0.65, Q2: 2 – 8 GeV2, <x> ~ 0.25, <Q2> ~ 4 GeV2

rate is 3.3 KHz 1000 hours beam, statistical precision for asymmetry will be 1.8x10-5. A significant first measurement (~ a few )

Semi-inclusive Deep Inelastic Scattering

Transversity, …

Transversity

• Three twist-2 quark distributions:• Momentum distributions: q(x,Q2) = q↑(x) + q↓(x)• Longitudinal spin distributions: Δq(x,Q2) = q↑(x) - q↓(x)

• Transversity distributions: δq(x,Q2) = q┴(x) - q┬(x)

• Some characteristics of transversity:• δq(x) = Δq(x) for non-relativistic quarks• δq and gluons do not mix → Q2-evolution different• Chiral-odd → not accessible in inclusive DIS

• It takes two chiral-odd objects to measure transversity• Semi-inclusive DIS

Chiral-odd distributions function (transversity)

Chiral-odd fragmentation function (Collins function)

JLab 6 GeV Projections (n) and World Data (p, d)

π- π+The errors with approved beam time will be 33% higher.

COMPASS (d)

HERMES (p)

JLab 6 GeV (n)

Collins CollinsSivers Sivers

Collins and Sivers Asymmetries

• Projections with MADII (1200 hours)

• Solenoid option:

-- Acceptance for both e

and improved by

~ 1 order of magnitude

-- Total improvement

~ 2 orders of magnitude

• + case

Two halves different

baffles

• Simulations to be done

- +

Collins

Sivers

Summary

• A powerful tool for inclusive DIS study at high-x • Improvement of a factor of 10-30 in acceptance

• A1n at high-x

• Crucial input to fundamental understanding of valence quark picture

• d2n

• twist-3 matrix element: q-g correlations• direct comparison with Lattice QCD

• First g3n measurement

• Twist-4 (f2n), color polarizabilities, sea-quark spin

• Even better for semi-inclusive DIS• An example: transversity: 2 orders of magnitude improvement