Transverse Spin and TMDs

Jian-ping Chen, Jefferson LabEIC Workshop at INT09, Oct.19-23, 2009

Introduction: why do we care about transverse structure?

Current status: What have we learned?

Near-future perspective: What do we expect before EIC?

Ultimate goal: What can EIC contribute?

Acknowledgement: Some plots from H. Avagyan, H. Gao, X. Jiang, X. Qian, …

Introduction

Why do we care about transverse structure?

Strong Interaction and QCD• Strong interaction, running coupling ~1 -- QCD: accepted theory for strong interaction -- asymptotic freedom (2004 Nobel) perturbation calculation works at high energy -- interaction significant at intermediate energy quark-gluon correlations -- interaction strong at low energy (nucleon size)

confinement

theoretical tools: pQCD (co-linear factorization), OPE, Lattice QCD, AdS/CFT, …

• A major challenge in fundamental physics: Understand QCD in all regions, including strong

(confinement) region E

s

Nucleon (Hadron) Structure• Colors are confined in hadronic system

• Hadron: ideal lab to study QCD

• Nucleon = u u d + sea + gluons• Mass, charge, magnetic moment, spin, axial charge, tensor charge • Decomposition of each of the above fundamental quantities

Mass: ~1 GeV, but u/d quark mass only a few MeV each! Momentum: total quarks only carry ~ 50% Spin: ½, total quarks contribution only ~30% Spin Sum Rule

Orbital Angular Momentum Relations to GPDs and TMDs Tensor charge Transverse sum rule?

• Partons and gluon field are in-separable • Multi-parton correlations are important• Beyond co-linear factorization• Multi-dimensional structure and distributions Transverse dimension is crucial for complete understanding of nucleon

structure and QCD, and help shed light in understanding confinement

Three Decades of Spin Structure Study• 1980s: EMC (CERN) + early SLAC quark contribution to proton spin is very small = (12+-9+-14)% ! ‘spin crisis’ (Ellis-Jaffe sum rule violated)

• 1990s: SLAC, SMC (CERN), HERMES (DESY) = 20-30% the rest: gluon and quark orbital angular momentum

A+=0 (light-cone) gauge (½) + Lq+ G + Lg=1/2 (Jaffe)

gauge invariant (½) + Lq + JG =1/2 (Ji) A new decomposition (X. Chen, et. al.) Bjorken Sum Rule verified to <10% level

• 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … : ~ 30%;G probably small?, orbital angular momentum important? Transversity and Transverse-Momentum Dependent Distributions Generalized Parton Distributions Orbital angular Momentum

Current Status

What have we learned?

Transversity and TMDs

• 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 integrating 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)

“Leading-Twist” TMD Quark Distributions

Quark

Nucleon

Unpol.

Long.

Trans.

Unpol. Long. Trans.

Multi-dimension Distributions

GPDs/IPDsH(x,rT),E(x,rT),..

d2kT

d2kT

TMD PDFs f1u(x,kT),

.. h1u(x,kT)

Gauge invariant definition (Belitsky,Ji,Yuan 2003)Universality of kT-dependent PDFs (Collins,Metz 2003)Factorization for small kT. (Ji,Ma,Yuan 2005)

Wpu(k,rT) “Mother” Wigner distributions

d2 r T

PDFs f1u(x), .. h1

u(x)

quark polarization

Access TMDs through Hard Processes

Partonic scattering amplitude

Fragmentation amplitude

Distribution amplitude

proton

lepton lepton

pionproton

proton lepton

antilepton

Drell-Yan

BNLJPARC

FNAL

EIC

SIDIS

electron

positron

pion

pion

e–e+ to pions

s=20 GeV, pT=0.5-2.0 GeV/c�0 – E704, PLB261 (1991) 201.�+/- - E704, PLB264 (1991) 462.

Xpp Single Spin Asymmetries in

Large transverse single-spin effects were observed at RHIC, at much higher CM energies.

• In collinear picture, the QCD predict small SSAs with transversely polarized protons colliding at high energies.

Kane, Pumplin, Repko ‘78

FermiLab E-704

FNAL

BELLE: Collins function measurements

BELLE: Asymmetries in e+e-→h1h2X (H┴1 H┴

1)_

Efremov et al. Phys.Rev.D. 73,094025 (2006)

positivity limit1

Belle detectorKEKB

Asymmetric collider8GeV e- + 3.5GeV e+

Direct indication of non-0 Collins fragmentation !

Separation of Collins, Sivers and pretzelocity effects through angular dependence in SIDIS

1( , )

sin( ) sin( )

sin(3 )

l lUT h S

h SSiverCollins

Pretzelosi

UT

tyU

sUT h S

h ST

N NA

P N

A

A

N

A

1

1 1

1

1 1

sin( )

sin(3 )

sin( )Co

PretzelosityU

SiversUT

llins

T h S T

h S

UT

UT h S

TU

UT

TA

H

f

A

D

A h H

h

AUTsin() from transv. pol. H target

`Collins‘ moments

• Non-zero Collins asymmetry

• Assume q(x) from model, then

H1_unfav ~ -H1_fav

• H1 from Belle (arXiv:0805:2975)

`Sivers‘ moments

•Sivers function nonzero (+) orbital angular momentum of quarks

•Regular flagmentation functions

Collins Moments for Kaon

S. Gliske’s talk at DNP09

Sivers Moments for Kaon

Collins asymmetries from COMPASS deuteron

Phys. Lett. B 673 (2009) 127-135

u and d cancellation?

Sivers asymmetries from COMPASS deuteron

Transversity Distributions

A global fit to the HERMES p, COMPASS d and BELLE e+e- data by the Torino group (Anselmino et al.).

PRD 75, 054032 (2007)

PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008 F. BradamanteF. Bradamante

Collins asymmetry – proton datacomparison with M. Anselmino et al. predictionsPRD 75, 054032 (2007)

Franco BradamanteTransverse2008, Beijing

PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008 F. BradamanteF. Bradamante

Sivers asymmetry – proton datacomparison with the most recent predictions from M. Anselmino et al. (arXiv 0805.2677) Franco Bradamante

Transverse2008, Beijing

2-d (x-PT) Collins Moments

S. Gliske’s talk at DNP09

2-d (x-PT) Sivers Moments

Other TMDs

xB

COMPASS 2002-2004arXiv:0705.2402

Pretzelocityg1T

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

Collins

Sivers

First measurement on the neutron with polarized 3He

With good PID, Kaon data for free

Collins, Sivers, Pretzelocity and g1

T

7 PhD Students

Completed data taking 2/09

Exceeded PAC approved goal

Summary of Current Status

• Large single spin asymmetry in pp->X• Collins Asymmetries

- sizable for the proton (HERMES and COMPASS) large at high x,- and has opposite sign unfavored Collins fragmentation as large as favored (opposite sign)? - consistent with 0 for the deuteron (COMPASS)

• Sivers Asymmetries - non-zero for + from proton (HERMES), consistent with zero (COMPASS)? - consistent with zero for - from proton and for all channels from deuteron - large for K+ ?

• Collins Fragmentation from Belle

• Global Fits/models by Anselmino et al., Yuan et al. and …

• First neutron measurement from Hall A 6 GeV (E06-010)

• Very active theoretical and experimental study RHIC-spin, JLab (6 GeV and 12 GeV), Belle, FAIR, J-PARC, … EIC

Near-future Perspective

What do we expect before EIC?

Collins and Sivers SSAs with CLAS @ 6 GeV JLab

CLAS with a transversely polarized proton target will allow measurements of Collins and Sivers asymmetries in the large-x region

Anselmino et al Vogelsang & YuanSchweitzer et al

Precision Study of Transversity and TMDs

• From exploration to precision study• Transversity: fundamental PDFs, tensor charge• TMDs provide 3-d structure information of the nucleon• Learn about quark orbital angular momentum• Multi-dimensional mapping of TMDs

• 3-d (x,z,P┴ )

• Q2 dependence • Multi-facilities, global effort

• Precision high statistics• high luminosity and large acceptance

CHL-2CHL-2

Upgrade magnets Upgrade magnets and power suppliesand power supplies

Enhance equipment in Enhance equipment in existing hallsexisting halls

6 GeV CEBAF1112Add new hallAdd new hall

12 GeV Upgrade Kinematical Reach

• Reach a broad DIS region • Precision SIDIS for

transversity and TMDs• Experimental study/test of

factorization • Decisive inclusive DIS

measurements at high-x• Study GPDs

Solenoid detector for SIDIS at 11 GeVProposed for PVDIS at 11 GeV

FGEMx4

LGEMx4 LSGas Cherenkov

HG

Aerogel

GEMx2

SH

PS

Z[cm]

Y[cm

]

Yoke

Coil

3HeTarget

3-d Mapping of Collins/Sivers Asymmetries at JLab 12 GeV

With A Large Acceptance Solenoid Detector (L=1036)

• Both + and -

• For one z bin

(0.5-0.55)

• Will obtain 8

z bins (0.3-0.7)

• Upgraded PID for K+ and K-

Power of SOLid

Discussion• Unprecedented precision 3-d mapping of SSA

• Collins and Sivers• +, - and K+, K-

• Study factorization with x and z-dependences • Study PT dependence• With similar quality SIDIS data on the proton and data from e+e-

• extract transversity and fragmentation functions for both u and d quarks• determine tensor charge• study TMDs for valence quarks• study quark orbital angular momentum

• Combining with world data, especially data from high energy facilities (future EIC)• study Q2 evolution (need theoretical development)• sea and gluon TMDs (more surprises are waiting?)

• Global efforts (experimentalists and theorists), global analysis• Precision information on multi-dimension nucleon structure

Ultimate Goal

What can EIC contribute?

Transverse Structure Study with EIC

• Much large kinematical reach Much higher Q2 range, clearly into hard scattering region

Wide Q2 range, study Q2 evolution and high-twist effects Much higher PT range, into high PT region and overlap region Much lower x range, study sea TMDs Reach current fragmentation region for flavor study (pions, Kaons, nucleons, …)

• Ultimate understanding of nucleon structure with complete 4-d (x,z,PT,Q2) mapping Model independent extractions of transversity and TMDs through global analysis Determination of tensor charge

• Study, test and understand QCD• Special universality: Sivers(SIDIS) = - Sivers(Drell-Yan)• Study QCD beyond co-linear approximation, study parton correlations• Shed light on QCD in strong region (confinement)

Sivers effect: Pion electroproduction100 days at L=1033 MEIC (4x60 GeV) (Harut Avakian)

Sivers effect: Kaon electroproduction

EIC

CLAS12

(Harut Avakian)

Summary

• Why transverse dimension? Complete understanding of nucleon structure Transverse momentum dependence - strong quark-gluon correlations Key to understanding QCD in all regions, including confinement region

• What have we learned? Non-zero Collins and Sivers asymmetries for pions and Kaons Non-favored Collins fragmentation functions as important as favored ones HERMES and COMPASS Collins asymmetries consistent, HERMES and COMPASS Sivers results on the proton might be different? First measurements of Collins and Sivers asymmetry on the neutron Explorations on other TMDs: Boer-Mulders, Pretzelocity and g1

T

Model dependent extractions of transversity, Sivers and Collins functions • What do we expect before EIC?

• Precision 3-d (x,z,PT) mapping of TMDs • What can EIC contribute?

• Ultimate coverage in kinematics, complete 4-d (x,z,PT,Q2) mapping• Lead to breakthrough in full understanding of nucleon structure and QCD