QCD Evolution and TMD/Spin Experiments

J. P. Chen, Jefferson LabQCD Evolution Workshop, May 14-17, 2012

Introduction

SIDIS Transverse Experiments: Transversity and TMDs

Q2 Dependence of the Moments of Spin Structure Functions

Evolution and High-Twists

Experiments < -- > Theory (QCD)• Quarks/Gluons are fundamental degrees of freedom in QCD but they are confined in hadrons

experimental observables are on hadrons

• Hard process (factorization)example: DIS at high Q2

simplify situation to allow extraction of information on quarks/gluons • Observable depending on probing scale: Q2

power dependence (twists)logarithmic dependence (evolution)

• Initial exploration (discovery?) to precision study (full understanding?)

Unpolarized DIS: Discovery of Quarks (Partons)

J.T. Friedman R. Taylor H.W. Kendall

Nobel Prize 1990

Callan-Gross

relation:

Bjorken Scaling:

Point particles cannot be further resolved; their measurement

does not depend on wavelength, hence Q2,

Spin-1/2 quarks cannot absorb longitudinally polarized vector

bosons and, conversely, spin-0 (scalar) quarks cannot absorb

transversely polarized photons.

Unpolarized Structure Function F2

• Bjorken Scaling

• Scaling Violation

• Gluon radiation – QCD evolution

NLO: Next-to-Leading-Order

• One of the best experimental tests of QCD

Polarized DIS - Surprises with Spin

The sum of Quark Spins contribute little to the proton spin, and strange quarks are negatively polarized.

EMC: J.Ashman et al, Nucl. Phys. B328 (1989) 1

Polarized Structure functions

HERMES Collins/Sivers asymmetry data

Transverity2011 Franco Bradamante

COMPASS Sivers asymmetry 2010 datax > 0.032 region - comparison with HERMES results

NEW

NEW

JLab 12 GeV Projections: Map Collins and Sivers asymmetries in 4-D (x, z, Q2, PT):

Transverse Spin and TMDs

SIDIS Experiments with a Transversely Polarized Target

Leading-Twist TMD PDFs

f1 =

f 1T =

SiversSivers

HelicityHelicity

g1 =

h1 =TransversityTransversity

h1 =

Boer-MuldersBoer-Mulders

h1T =

PretzelosityPretzelosity

h1L =

Worm GearWorm Gear

: Survive trans. Momentum : Survive trans. Momentum integrationintegration

Nucleon Spin

Quark Spin

g1T =

Worm GearWorm Gear

Leading-Twist TMD PDFs

f1 =

f 1T =

SiversSivers

HelicityHelicityg1 =

h1 =TransversityTransversity

h1 =

Boer-MuldersBoer-Mulders

h1T =

PretzelosityPretzelosity

g1T =

Worm GearWorm Gear

h1L =

Worm GearWorm Gear

: Probed with transversely pol targetNucleon Spin

Quark Spin

Status of Transverse Spin Study • Large single spin asymmetry in pp->X (Fermi Lab, RHIC-spin)• 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), new COMPASS data - consistent with zero for - from proton and for all channels from deuteron - large for K+ ?• Collins Fragmentation from Belle• Global Fits/models: Anselmino, Prokudin et al., Vogelsang/Yuan et al.,

Pasquini et al., Ma et al., Gamberg et al.…• Very active theoretical and experimental efforts

Many workshops/conferences to discuss TMDs with QCD, evolution, … RHIC-spin, JLab (6 GeV and 12 GeV), Belle, FAIR, J-PARC, EIC, …• First neutron measurement from Hall A 6 GeV (E06-010)• SoLID (and CLAS12, …) with polarized 3He/p at JLab 12 GeV Unprecedented precision with high luminosity and large acceptance

Separation of Collins, Sivers and pretzelocity effects through angular dependence

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

E06 010 Experiment‑Spokespersons: Chen/Evaristo/Gao/Jiang/Peng

• First measurement on n (3He)• Polarized 3He Target• Polarized Electron Beam, 5.9 GeV

– ~80% Polarization– Fast Flipping at 30Hz

• BigBite at 30º as Electron Arm– Pe = 0.7 ~ 2.2 GeV/c

• HRSL at 16º as Hadron Arm– Ph = 2.35 GeV/c – Excellent PID for /K/p

• 7 PhD Thesis Students (All graduated)

15

Beam Polarimetry(Møller + Compton)

LuminosityMonitor

XeeHe ),(3

E06-010 3He Target Single-Spin Asymmetry in SIDIS

3He Sivers SSA:negative for π+,

3He Collins SSA small Non-zero at highest x for +

Blue band: model (fitting) uncertainties Red band: other systematic uncertainties

X. Qian, et al. PRL (2011) 107:072003 (2011)

Neutron Results with Polarized 3He from JLab

Collinsasymmetries are not large, except at x=0.34

Sivers negative

Blue band: model (fitting) uncertainties Red band: other systematic uncertainties

X. Qian at al., PRL 107:072003(2011)

Asymmetry ALT Result

• 3He ALT : Positive for -

hq

qTLT DgFA shsh

11)cos()cos(

LT

To leading twist:

J. Huang et al., PRL. 108, 052001 (2012).

• – Corrected for proton dilution, fp

– Predicted proton asymmetry contribution < 1.5% (π+), 0.6% (π-)

•

– Dominated by L=0 (S) and L=1 (P) interference

• Consist w/ model in signs, suggest larger asymmetry

Neutron ALT Extraction

hq

qT

n DgA 11LT Trans-helictiy

JLab 12 GeV Era: Precision Study of TMDs

• From exploration to precision study with 12 GeV JLab• Transversity: fundamental PDFs, tensor charge• TMDs: 3-d momentum structure of the nucleon Quark orbital angular momentum• Multi-dimensional mapping of TMDs

• 4-d (x,z,P┴,Q2)

• Multi-facilities, global effort

• Precision high statistics• high luminosity and large acceptance

SIDIS with SoLID

12 GeV: Mapping of Collins/Siver Asymmetries with SoLID

• Both + and -

• For one z bin

(0.4-0.45)

• Will obtain many z bins (0.3-0.7)

• Tensor charge

E12-10-006 3He(n), Spokespersons: J. P. Chen, H. Gao, X. Jiang, J-C. Peng, X. QianE12-11-007(p) , Spokespersons: K. Allda, J. P. Chen, H. Gao, X. Li, Z-E. Mezinai

Map Collins and Sivers asymmetries in 4-D (x, z, Q2, PT)

Expected Improvement: Sivers Function

• Significant Improvement in the valence quark (high-x) region• Illustrated in a model fit (from A. Prokudin)

f 1T =

E12-11-107: Worm-gear functions (“A’ rating: )

Spokespersons: Chen/Huang/Qiang/Yan

• Dominated by real part of interference between L=0 (S) and L=1 (P) states

• No GPD correspondence• Lattice QCD -> Dipole Shift in mom. space.

• Model Calculations -> h1L =? -g1T

.

h1L =

g1T =

Longi-transversityTrans-helicity

Cent

er o

f poi

nts:

)()(~ 11 zDxgA TLT )()(~ 11 zHxhA LUL

Discussion• Unprecedented precision 4-d mapping of SSA

• Collins and Sivers• +, - and K+, K-

• New proposal polarized proton with SoLID• Study factorization with x and z-dependences • Study PT dependence• Combining with the world data

• extract transversity and fragmentation functions for both u and d quarks• determine tensor charge• study TMDs for both valence and sea quarks • study quark orbital angular momentum• study Q2 evolution

• Global efforts (experimentalists and theorists), global analysis• much better understanding of multi-d nucleon structure and QCD

• Long-term future: EIC to map sea and gluon SSAs

Moments of Spin Structure Functions

Q2 Dependence, Evolution and Higher-Twists

Higher-Twist Extraction from Data

MRST, unpolarized PDF H-T coefficients

LSS, polarized PDF (NLO) H-T coefficients

First Moment of g1p/g1

n:1p /1

n

EG1b, arXiv:0802.2232 EG1a, PRL 91, 222002 (2003)

1p

Total quark contribution to nucleon spin (at high Q2)

Twist expansion at intermediate Q2, LQCD, ChPT at low Q2

E94-010, PRL 92 (2004) 022301 E97-110, preliminary, EG1a, from d-p

1n

Bjorken Sum: 1 of p-n

EG1b, PRD 78, 032001 (2008)E94-010 + EG1a: PRL 93 (2004) 212001

Higher Twist (Twist-4 f2) Extraction Color Polarizabilities/Lorentz Force

• JLab + world neutron 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/Lorentz force

= 0.033+-0.029 B = -0.001+-0.016

• Proton and p-n (A. Deur)

f2= -0.160+-0.028+-0.109 (p),

-0.101+-0.027+-0.067 (p-n)

PLB 93 (2004) 212001

Effective Coupling Extracted from Bjorken Sum

s/

A. Deur, V. Burkert, J. P. Chen and W. Korsch PLB 650, 244 (2007) and PLB 665, 349 (2008)

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.

<Resonances> = <DIS> ?

• PRL 101, 1825 02 (2008)

1 resonance comparison with pdfspartial moments

Second Spin Structure Function g2

d2: Color Polarizability/Lorentz Force Burkhardt - Cottingham Sum Rule

Precision Measurement of g2n(x,Q2): Search for Higher Twist Effects

• Measure higher twist quark-gluon correlations.• Hall A Collaboration, K. Kramer et al., PRL 95, 142002 (2005)

Color Polarizability /Lorentz Force: d2

• 2nd moment of g2-g2WW

d2: twist-3 matrix element

d2 and g2-g2WW: clean access of higher twist (twist-3) effect: q-g correlations

Color polarizabilities are linear combination of d2 and f2

Provide a benchmark test of Lattice QCD at high Q2

Avoid issue of low-x extrapolation

Relation to Sivers and other TMDs

1

0

22

21

2

1

0

22

22

222

)],(3),(2[

)],(),([3)(

dxQxgQxgx

dxQxgQxgxQd WW

d2 on neutron

E01-012

d2(Q2)

E08-027 “g2p”SANE

“d2n” new in Hall A

6 GeV Experiments

Sane: new in Hall C

“g2p” in Hall A, running now

projected

Burkhardt - Cottingham Sum Rule

P

N

3He

BC = Meas+low_x+Elastic

0<X<1 :Total Integral

very prelim

“low-x”: refers to unmeasured low x part of the integral. Assume Leading Twist Behaviour

Elastic: From well know FFs (<5%)

“Meas”: Measured x-range

Brawn: SLAC E155xRed: Hall C RSS Black: Hall A E94-010Green: Hall A E97-110 (preliminary)Blue: Hall A E01-012 (preliminary)

0)(1

0 22 dxxgΓ

BC Sum Rule

P

N

3He BC satisfied w/in errors for 3He

BC satisfied w/in errors for Neutron(But just barely in vicinity of Q2=1!)

BC satisfied w/in errors for JLab Proton2.8 violation seen in SLAC data

very prelim

Results on 2n : E01-012 and E94-010

Higher-Twist Extraction and Comparison

Extract Higher-Twist part of 2DIS

Compare with higher-twist estimated from E97-103 data

E08-027 : Proton g2 Structure Function Fundamental spin observable has never been measured at low or moderate Q2

BC Sum Rule : violation suggested for proton at large Q2, but found satisfied for the neutron & 3He.

Spin Polarizability : Major failure (>8 of PT for neutron LT. Need g2 isospin separation to solve.

Hydrogen HyperFine Splitting : Lack of knowledge of g2 at low Q2 is one of the leading uncertainties.

Proton Charge Radius : also one of the leading uncertainties in extraction of <Rp> from H Lamb shift.

BC

Su

m R

ule

Spokespersons: Camsonne, Chen, Crabb, Slifer(contact), 6 PhD students, 3 postdocs

Running until 5/18/2012

Sp

in P

ola

riza

bili

ty

LT

Summary

• Study quark-gluon structure of nucleon depends on probing scale Q2 Q2 dependence provides valuable information on QCD dynamics

• TMD study from exploration to precision: Q2 evolution critical• Q2 dependence of moments of spin structure g1/g2:

• study higher-twists• precision measurements of g2 and d2: twist-3• Extraction of f2: twist-4

d2/f2 E, B : Color polarizabilities/Lorentz forces

Announcements

End-of-run (g2p experiment in Hall A) party this afternoon 3-5 pm at CEBAF Center Atrium

KITPC (Kavli Institute for Theoretical Physics China ) Program onNucleon structure (QCD and Hadron Physics)

July 2- 20, 2012, Beijing, China http://kitpc.itp.ac.cn/program.jsp?id=PF20120611 The last week (7/16-7/20) will be for The 4th Workshop on Hadron Physics in China and Opportunities in US

http://www.ciae.ac.cn/eng/hadron2012/index.htm

The 7th International Workshop on Chiral Dynamics August 6-10, 2012, JLab http://www.jlab.org/conferences/CD12/