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Transverse Spin Physics: Recent Developments

Feng Yuan Lawrence Berkeley National Laboratory

RBRC, Brookhaven National Laboratory

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Outline Introduction Great progress in the last few years

Underlying physics unrevealedConnections to other phenomena

Higher-twist effects Generalized Parton Distributions

QCD dynamics: Factorization, Universality, … Future: Puzzle and Challenges remain

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What’s Single spin asymmetry?

Single Transverse SpinAsymmetry (SSA)

Final state particle isAzimuthal symmetric

Transverse plane

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SSAs in Modern era : RHIC, JLab, HERMES, …

Central rapidity!!

BRAHMS

STAR

Large SSA continues at DIS epLarge SSA continues at DIS epand collider pp experiments!!and collider pp experiments!!

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Why Does SSA Exist? Single Spin Asymmetry requires

Helicity flip: one must have a reaction mechanism for the hadron to change its helicity (in a cut diagram)

A phase difference: the phase difference is needed because the structure S ·(p × k) violate the naïve time-reversal invariance

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Naïve parton model fails If the underlying scattering mechanism is

hard, the naïve parton model generates a very small SSA: (G. Kane et al, 1978),

It is in general suppressed by αSmq/Q See also, Ma-Sang, arXive: 0809.1791

We have to go beyond this naïve picture

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Two mechanisms in QCD Spin-dependent transverse

momentum dependent (TMD) function Sivers 90 Brodsky,Hwang,Schmidt, 02 (FSI) Gauge Property: Collins 02;Belitsky-Ji-Yuan,03 Boer-Mulders-Pijlman,03 Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04

Twist-3 quark-gluon correlations (coll.) Efremov-Teryaev, 82, 84 Qiu-Sterman, 91,98

P

kTST

Sivers function ~ ST (PXkT).

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Polarized TMD Quark Distributions

Quark

Nucleon

Unpol.

Long.

Trans.

Unpol. Long. Trans.

Boer, Mulders, Tangerman (96&98)

Three classes in the view of a quark model S-wave

Unpolarized, helicity, transversity S-P interference

g_1T,h_1Lf_1T^\perp, h_1^\perp

P-P or S-D interferenceh_1T^\perp

Miller 07, Burkardt 07, Avakian et al 08, Pasquini et al 08, …

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Pasquini’s talk

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Lz≠0 Amplitude and Sivers Function All distributions can be calculated

using the wave function. Sivers function:

Similar expressions for othersJi, Ma, Yuan, Nucl. Phys. B (2003)Ji, Ma, Yuan, Nucl. Phys. B (2003)

Lz=0 Lz=1

Where can we learn TMDs

Semi-inclusive hadron production in deep inelastic scattering (SIDIS)

Drell-Yan lepton pair production in pp scattering

Relevant e+e- annihilation processes …

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Quark-gluon correlations (twist-three) Have long been studied

F-type and D-type are related to each other, Eguchi-Koike-Tanaka 06

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TMDs and Quark-gluon Correlations (twist-3) Kt-odd distribution

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A unified picture for SSA In DIS and Drell-Yan processes, SSA depends on

Q and transverse-momentum P

At large P, SSA is dominated by twist-3 correlation effects

At moderate P, SSA is dominated by the transverse-momentum-dependent parton distribution/fragmentation functions

The two mechanisms at intermediate P generate the same physics! Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006

Initial vs Final State Interactions

Double Initial State Interactions in Drell-Yan Azimuthal asymmetry Jian Zhou’s talk on Friday

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Drell-Yan DIS

TMDs vs GPDs

See Burkardt’s talk

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Nontrivial feature for the TMDs: Universality

Universality of the Collins Mechanism Non-universality of the Sivers effects

Universality of the Collins Fragmentation

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Simple model a la Collins 93

e+e- annihilation Semi-inclusive DIS Hadron in a jet in pp

Phase information in the vertexor the quark propagatorCollins-93

Universality of the Collins Function!!

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One-gluon exchange (gauge link)?

Metz 02, Collins-Metz 02:Gamberg-Mukherjee-Mulders, 08Universality of the Collins function!!

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Similar arguments for pp collisions

Conjecture: the Collins function will be the same as e^+e^- and SIDIS

By using the Ward Identity:

same Collins fun.

Extend to two-gluon exchange

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Universality preserved

Key observations

Final state interactions DO NOT provide a phase for a nonzero SSA

Eikonal propagators DO NOT contribute to a pole

Ward identity is applicable to warrant the universality arguments

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Sivers effect is different

It is the final state interaction providing the phase to a nonzero SSA

Ward identity is not easy to apply Non-universality in general Only in special case, we have “Special Universality”

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DIS and Drell-Yan

Initial state vs. final state interactions

“Universality”: fundamental QCD prediction

HERMES

* *

Drell-Yan DIS

04/21/23 0.1 0.2 0.3 x

0

0

Experiment SIDIS vs Drell Yan

HERMES Sivers Results RHIC II Drell Yan Projections

Markus DiefenthalerDIS WorkshopMunich, April 2007

http://spin.riken.bnl.gov/rsc/

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Proposed by Boer-Vogelsang Pheno. studies: Vogelsang-Yuan 05; Bomhof-Mulders-Vogelsang-Yuan 07; Bacchetta, et al, photon-jet correlation, 07

Initial state and/or final state interactions? Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099,

hep-ph/0505268, hep-ph/0601171, hep-ph/0609206 Qiu-Vogelsang-Yuan, arXiv:0704.1153; 0706.1196 Collins-Qiu, arXiv:0705.2141  Voglesang-Yuan, arXiv:0708.4398 Collins, arXiv:0708.4410 Bomhof-Mulders, arXiv:0709.1390

Factorization? Universality?

Non-universality: Dijet-correlation at RHIC

The simple picture does not hold for two-gluon exchanges

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Qiu,Collins, 0705.4121;Vogelang-Yuan, 0708.4398;Collins, 0708.4410

Integrated over transverse momentumBecchetta-Bomhof-Mulders-Pijlman, 04-06

Another example:Heavy flavor production

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ISI: contribute to quark and anti-quark

~1/4Nc

FSI: contribute to anti-quark

~2/4Nc

FSI: contribute to quark

~(Nc^2-2)/4Nc

Kang’s talk

Puzzles Continue

Experiment sidePt-dependence A_N from STARSivers effect: COMPASS vs HERMESSSA for Keons, antiproton

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Future: Theory challenges

Quantitative connection to the OAM QCD corrections Soft gluon resummation at small pt …

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Transverse Spin Wish (to do) ListExperiment

Drell-Yan Photon-jet Tensor charge (h_1) Large P_t SSA (1/P_t) Double spin asymmetry P_t

depdence W and z production

(reconstruction low pt) Flavor separation via He3 at RHIC large-x Sivers/Collins Polarized nucleon-nucleus

experiments (nuclear effects in B-M function)

Theory Relation to OAM Evolution Soft gluon resummation Robust separation of Sivers and

Collins in pp P_t behavior Explore More functional

dependence (kt,x)

What if we don’t see DY=-DIS Can we determine the sign of the transversity function?

PKU-RBRC Workshop on Transverse Spin

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Summary

We are in the early stages of a very exciting era of transverse spin physics studies, where the future RHIC, JLAB, JPARC, FAIR, and EIC experiments will certainly play very important roles

We will learn more about QCD dynamics and nucleon structure from these studies, especially for the quark orbital motion

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Transition from Perturbative region to Nonperturbative region? Compare different region of PT

Nonperturbative TMD Perturbative region

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Twist-3 Fit to data

E704

STAR

Kouvaris,Qiu,Vogelsang,Yuan, 06

RHIC

BRAMHS

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Compare to 2006 data from RHIC

J.H. Lee, SPIN 2006

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