Parton Distributions at High x

J. P. Chen, Jefferson Lab DNP Town Meeting, Rutgers, Jan. 12-14, 2007

Introduction

Unpolarized Parton Distribution at High x

Polarized Parton Distributions at High x

New Vista: Transversity at High x

Summary

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 (AAC06)

Why Are PDFs at High x Important?

• Valence quark dominance: simpler picture

-- direct comparison with nucleon structure models

SU(6) symmetry, broken SU(6), diquark• x 1 region amenable to pQCD analysis

-- hadron helicity conservation?• Clean connection with QCD, via lattice moments• Input for search for physics beyond the Standard Model at high

energy collider

-- evolution: high x at low Q2 low x at high Q2

-- small uncertainties amplified

-- example: HERA ‘anomaly’ (1998) • Input to nuclear, high energy and astrophysics calculations

Predictions for High x

Nucleon Model F2n/F2

p d/u u/u d/d A1n A1

p

SU(6) 2/3 1/2 2/3 -1/3 0 5/9

Scalar diquark 1/4 0 1 -1/3 1 1

pQCD 3/7 1/5 1 1 1 1

Proton Wavefunction (Spin and Flavor Symmetric)

11

110

)(3

2)(

3

1

)(3

1)(

18

1)(

2

1

SS

SSS

uuduud

uduuduudup

Unpolarized Parton Distribution at High x

and Moments of Structure Functions

d/u Extraction from F2n/F2

p

• No ‘free’ neutron target (life time ~ 12 minutes)

-- deuteron (or 3He) used as ‘effective’ neutron target• However, deuteron is a nucleus, F2d ≠ F2p + F2n• Nuclear effects (nuclear binding, Fermi motion, shadowing)

obscure neutron structure information

-- ‘nuclear EMC effect’

Unpolarized Neutron to Proton ratioUnpolarized Neutron to Proton ratio

Unpolarized Neutron to Proton ratioUnpolarized Neutron to Proton ratio

• Mirror symmetry of A=3 nuclei Extract F2

n/F2p from ratio of 3He/3H

structure functions

Super ratio R = ratio of ”EMC ratios” for 3He

and 3H Calculated to within 1%

• Most systematic and theoretical uncertainties cancel

• Nearly free neutron target by tagging low-momentum proton from deuteron at backward angles

• Small p (70-100 MeV/c) Minimize on-shell extrapolation

(neutron only 7 MeV off-shell)

• Backward angles (pq> 110o)

Minimize final state interactions

Spectator tagging

DIS from A=3 nuclei

Unpolarized Neutron to Proton Ratio

Hall A 11 GeV with HRSBONUS at Hall B 11 GeV with CLAS12

At high x

F2p

F2p

High-x PDFs- p Scattering

=d

u

F2p - xF3

p = 4xu

F2p + xF3

p = 4xu Unprecedented valence / sea separation

MINERAMain INjector ExpeRiment for v-A

• MINERvA is a compact, fully active neutrino detector designed to study neutrino-nucleus interactions with unprecedented detail

• MINERvA is unique in worldwide program• Opportunity for precision neutrino interaction measurements• Wide range of neutrino energies

• MINERvA Schedule– late 2007-2008: construction begins– 2009: complete construction, installation

• Helium target approved. H/D still need approval.

Separated Structure Functions at Large x and Duality

Data from JLab Hall C E94-110

The resonance region is, on average, well described by NNLO QCD fits.

The result is a smooth transition from Quark Model Excitations to a Parton Model description, or a smooth quark-hadron transition.

FF22

FFLL

FF11

F2, F1 in excellent agreement with NNLO + TM above Q2 = 2 GeV2

Remove known HT, the elastic, and duality works down to Q2 = 0.5 GeV2

The case looks different for FL

FL related to the gluon contribution

n = 2 Cornwall-Norton Momentsn = 2 Cornwall-Norton Moments

FF22

FFLL

2xF2xF11

Extracting d-bar/-ubar From Drell-Yan Scattering (E866/E906)

Ratio of Drell-Yan cross sections Fermilab E906/Drell-Yan will extend these measurements and reduce statistical uncertainty.

Semi-Inclusive DIS at 11 GeV JLab

x

x

Valence Quark Spin Structure

A1 at high x and flavor decomposition

Polarized quarks as x--> 1

SU(6) symmetry: A1

p = 5/9 A1n = 0 d/u=1/2

∆u/u = 2/3 ∆d/d = -1/3 Broken SU(6) via scalar diquark

dominance

A1p 1 A1

n 1 d/u 0 ∆u/u 1 ∆d/d -1/3

Broken SU(6) via helicity conservation

A1p 1 A1

n 1 d/u 1/5 ∆u/u 1 ∆d/d 1

Note that ∆q/q as x--> 1 is more sensitive to spin-flavor symmetry breaking effects than A1

World data for A1 World data for A1

Proton Neutron

Precision A1n at High x from Hall A

E99-117

• First precision A1

n data at high x

• Extracting valence quark spin distributions

• Test our fundamental understanding of valence quark picture

• SU(6) symmetry• Valence quark models• pQCD (with HHC) predictions

• Quark orbital angular momentum• Crucial input for pQCD fit to PDF• PRL 92, 012004 (2004)

• PRC 70, 065207 (2004) • Physics News Update, Science Now,

Science News, Physics Today Update, APS-DNP web, …

A1p/A1

d Results from CLAS

xbj

A 1p

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 1xbj

A 1d ( D

-sta

te c

orre

cted

) 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 - 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

Naïve Extraction of 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

A1p at 11 GeV

Projections for JLab at 11 GeV

A1n at 11

GeV

u and d at JLab 11 GeV

Flavor decomposition with SIDISFlavor decomposition with SIDIS

Polarized Sea

JLab @11 GeV

Duality in Spin-Structure: Hall A E01-012 Results

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

• Study quark-hadron duality in spin structure. • Access even higher x region?

A13He (Resonance vs DIS) 1

n resonance comparison with pdfs

xQ2

d2: Quark-gluon Correlations and Color Polarizabilities

d2: color polarizability, q-g correlations

Wandzura-Wilczek relation

• d2: 2nd moment, twist-3 matrix element, q-g correlations

• Color polarizability, benchmark test of Lattice QCD

1

21

21

22 ),(),(),(

x

WW

y

dyQygQxgQxg

1

0

22

21

2

1

0

22

22

222

)],(3),(2[

)],(),([3)(

dxQxgQxgx

dxQxgQxgxQd WW

Proton Results: d2p (Hall C and SLAC)

d2p

Q2

Neutron Results: d2n (Hall A and SLAC)

Planned d2n with JLab 6 GeV and 12 GeV

• Projections with planned 6 GeV and 12 GeV experiments Improved Lattice Calculation (QCDSF, hep-lat/0506017)

Transversity at High x

Semi-inclusive Deep Inelastic Scattering

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)

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

Chiral-odd distributions function (transversity) Chiral-odd fragmentation function (Collins function)

• TMDs: (without integration over PT)

• Distribution functions depends on x, k┴ and Q2 : δq, f1T┴ (x,k┴ ,Q2), …

• Fragmentation functions depends on z, p┴ and Q2 : D, H1(x,p┴ ,Q2)• Measured asymmetries depends on x, z, P┴ and Q2 : Collins, Sivers, …

(k┴, p┴ and P┴ are related)

• HERMES measurement on p: non-zero Collins (+/-) and Sivers (+) moments• COMPASS measurement on d: consistent with zero

E06-010/06-011 Single Target-Spin Asymmetry in Semi-Inclusive n↑(e,e′π+/-) Reaction on a Transversely Polarized 3He Target

Collins

Sivers

First neutron measurement planned at 6 GeV JLab

JLab 12 GeV with large accpetance: precision measurement of transversity and tensor charge

Summary• High x is a clean region to understand valence quark structure• Good progress in the last 5-10 years• JLab 12 GeV will make unique contributions to high-x PDF study• Unpolarized PDFs at high x

• d/u at high x: 3He/3H, BONUS, PV-DIS• Duality, FL, neutrino reactions, sea quarks

• Polarized PDFs at high x• A1 at high x: valence structure, flavor decomposition• d2: color polarizability, test Lattice QCD

• Transversity at high x• New dimension• JLab 12 GeV will make significant contributions

• Next decade: • Complete a chapter on unpolarized and polarized PDF study at high x• Open a new chapter on transversity study