High-Energy QCD

Spin Physics

Xiangdong JiMaryland Center for Fundamental Physics

University of Maryland

DIS 2008, April 7, 2008, London

Outline

Why spin physics? Polarized parton distribution functions Spin structure of the proton, Orbital angular momentum and Generalized parton distributions (GPDs) Transverse single-spin asymmetries Conclusion

Why spin physics?

Spin is a fundamental degree of freedom originated from the space-time symmetry.

Spin plays a critical role in determining the basic structure of fundamental interactions.

Test of a theory is not complete without a full test of spin-dependent decays and scattering.

Spin provides a unique opportunity to probe the inner structure of a composite system (such as the proton) and hence testing our ability to understand the working of non-perturbative QCD.

Remarkable experimental progress in QCD spin physics in the last 20 years Inclusive spin-dependent DIS

EMC, SMC, COMPASS E142,E143,E154,E156 HERMES Jlab-Hall A, B(CLAS)

Semi-inclusive DIS SMC, COMPASS HERMES

Polarized pp collisions RHIC

PHENIX & STAR

Double-spin asymmetries in semi-inclusive processes

from HERMES & COMPASS

Recent experimental progress

Talks by Korzenev, Robinet, Stolarski, Jackson

Double spin asymmetry for pion production from PHENIX and jet production from STAR (run 5+6)

(

Recent experimental progress

Talks by Gagliardi, Hoffman, Aoki, Ellinghaus

Polarized Parton Distributions

Polarized PDFs

When the proton (or neutron) is polarized, the quarks and gluons are polarized as well,

In the large Nc limit, the mass of the nucleon is order Nc and spin is of order 1. The polarized effect is relatively small, particularly for the

gluons of order Nc squared in the vacuum. Pol. PDF can be extracted from the

experimental data through global fits.

(NLO) Global fits

Make some generic assumptions about the functional form with a few parameters and fit them to data

Many efforts in the past have been made Gluck, Reya, Stratmann, Vogelsang (2001) Blumlein and Bottcher (2003) Leader, Sidorov, Stamenov (2006) Hirai, Kumano, Saito (2006) …..

One of the most recent is the NLO fit by de Florian, Sassot, Stratmann and Vogelsang (hep-ph/0804.0422) in which pp collision jet data are first included. (Technically challenging!)

DSSV PDF

Polarized sea distributionsRHIC spin asymmetries

DSSV spin content

The gluon pol. is small, but the uncertainty is large (E. Leader’s talk). Future data will improve this

Gluon polarization and chi-squared

Future improvement

Sea-quark polarization W production at RHIC EIC

Gluon pol. Direct photon production Higher precision in jet and pion

Spin Structure of the Nucleon

The nucleon spin

The driving question for QCD spin physics is where the nucleon spin come from?

Spin budget of the proton

25%

75%

Total proton spin = 1/2

Quark spin measuredIn DIS

“Dark” angular momentum?

Spin of the proton in QCD

The spin of the nucleon can be decomposed into contributions from quarks and gluons

Further decomposition of quark contribution

Further decomposition of gluon contribution

1/ 2 ( ) ( )q gJ J J

1[ ( ) ]2

v sq f f qf

f

J q q L

g gJ g L Infinite momentum frame

There is no analogous sum rule involving transversity!

Spin in asymptotic limit

Scale evolution equation

Asymptotic solution

Roughly half of the angular momentum is carried by gluons!

OAM must be important

2

2

2

2

2 316

316

92g

q

f

fs

g

q

J

J

n,

n,

J

J

lnd

d

f

gf

fq n

J,n

nJ

316

16

2

1

316

3

2

1

Argument for large orbital motion

Quarks are essentially massless. A relativistic quark moving in a small region of space must have non-zero orbital angular momentum. (MIT bag model)

Finite orbital angular momentum is essential for Magnetic moment of the proton. g2 structure function Asymmetric momentum-dependent parton distribution

in a transversely polarized nucleon …

Total quark angular momentum

The total angular momentum is related to the GPDs by the following sum rule

Where E and H are GPDs defined for unpolarized quarks.

Contribution from H is related to the momentum fraction carried by quarks.

E is similar to Pauli form factor F2, can best be determined with a trans. pol. target.

0

1lim [ ( , , ) ( , , )]

2q q qtJ dxx H x t E x t

Talk by D. Mueller

DVCS with transversely polarized target from HERMES & Jlab

Talk by P. Haegler

Looking forward

Jlab 12 GeV upgradeA comprehensive program to study GPDs

EIC

Vanderhaeghen et al.

EIC: 5 GeV e on 50 GeV proton: Much large range possible….

D. Hasell, R. Milner et al.Vanderheaghen et al

Transverse Single-Spin Asymmetries

Session talks by F. Yuan, Radici, Lu, MuldersGoldstein, Sozzi, Ogawa, Videbaek, Fields, Melis,Tanaka

Transverse-Spin Related Distributions

Transversity distribution q(x) or h(x) (twist-2) the density of transversely polarized quarks in a transversely

polarized nucleon chirally-odd

Sivers function qT(x, kT) (twist-2 at small k) Asymmetric distribution of quarks with T-momentum kT in a

transversely polarized nucleon T-odd, depends on ISI/FSI

Twist-3 quark-gluon correlation functions Polarized gluons!

Related Fragmentation functions

What have we learned from data?

SSA in PP scattering is large, even at RHIC energy. Consistent with twist-3 expectation.

SSA in eP scattering is large at HERMES, becomes small at COMPASS. The Collins function is

consistent with e+e- data, but with interesting/strange charge dependence. (Ogawa)

Siver’s function has interesting flavor dependence.

Talk by Ogawa

First extraction of transversity

From semi-inclusive DIS asymmetry measured by HERMES &COMPASS (Anselmino et al, 2007)

A unified picture for SSA

In DIS and Drell-Yan processes, SSA depends on Q and transverse-momentum PT

At large PT, SSA is dominated by twist-3 correlation effects (Afremov& Teryaev, Qiu & Sterman)

At moderate PT, SSA is dominated by the kT-dependent parton distribution/fragmentation functions

Ji, Qiu, Vogelsang, & Yuan, Phys.Rev.Lett.97:082002,2006

The two mechanisms at intermediate PT generate the same physics! However, this does not generalize to higher order in 1/Q (Bacchetta et al, 0803.0227)Baccetta’s talk

Future Challenge?

PQCD & Factorization? Is PT =1-2 GeV high enough to use pQCD ? (a twist-3

effect, scaling, maybe ok for total cross section.) Is the peculiar flavor dependence in HERMES data due to

non-perturbative physics? Or imprecise data? (g2)

Transverse-spin effort small at high energy? Jaffe & Saito, QCD selection rule (1996) Vogelsang & others, small double asymmetry for Drell-Yan PAX collaboration at GSI, PP-bar scattering at lower energy

The ultimate goal? Can one extract transversity to a good precision? Can one calculate TMD & Twist-3 correlations?

Conclusion

We have learned a lot about pol. PDF in the last 20 years. The quantitative gluon and sea quark polarizations need high-precision measurement.

Significant orbital angular momentum contribution to the spin of the proton. Must find way to expose them. DVCS and other related process are unique way to do this (GPDs).

Much theoretical progress has been made in understanding the physical mechanisms of single spin asymmetries. It yet becomes the useful tool to learn about the spin structure of the nucleon.