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Transverse Spin Physics: Recent Developments

Feng Yuan Lawrence Berkeley National Laboratory

RBRC, Brookhaven National Laboratory

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Transverse spin physics

Goal Quark transversity distributions Orbital motion of quarks and gluons?

Single transverse spin asymmetry Various transverse momentum dependent

physics (additional information on nucleon structure)

Sivers function (PDF) Collins function (FF) …

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Outline

Introduction: single transverse spin phenomena

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

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What’s Single spin asymmetry?

Single Transverse SpinAsymmetry (SSA)

Final state particle isAzimuthal symmetric

Transverse plane

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Motivations: Its strong tied with the quark orbital

angular momentumWe have beautiful dataNontrivial QCD dynamics, and

fundamental test of the factorization, and the universality of PDFs, FFs,…

Single Spin Asymmetry

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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

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,NPB03 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).

Two major contributions

Sivers effect in the distribution

Collins effect in the fragmentation

Other contributions…

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kTST

P

(zk+pT)~pTXsT

(k,sT)

ST (PXkT)

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Semi-Inclusive DIS Transverse Momentum Dependent (TMD)

Parton Distributions and Fragmentations Novel Single Spin Asymmetries

U: unpolarized beamT: transversely polarized target

Universality of the Collins Fragmentation

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Collins effects in e+e-

Reliable place to extract the information on the Collins fragmentation function

Belle Col., PRL 06

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Collins asymmetry in pp collisions

Collins Fragmentation function

Quark transversity distribution

FY, arXiv:0709.3272 [hep-ph]

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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

Extract the quark transversity from e+e- and SIDIS expreiments

[1] Soffer et al. PRD 65 (02)

[2] Korotkov et al. EPJC 18 (01)

[3] Schweitzer et al., PRD 64 (01)

[4] Wakamatsu, PLB 509 (01)

[5] Pasquini et al., PRD 72 (05)

[6] Anselmino et al., PRD 75 (07)

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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Predictions at RHIC

Quark transversity: Martin-Schafer-Stratmann-Vogelsang, 98Collins function: fit to the HERMES data, Vogelsang-Yuan, 05

Collins contribution to SSA in inclusive hadron pp--> Pi X

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•Leading jet fragmentation contribution•Lower cut for the jet (>1GeV), upper cut for the fragmentation (<1GeV)

Add a soft contribution ~Pt

Recent STAR data

May indicate the importance of the soft contribution

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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

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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

A difficulty at next-leading-power (1/Q) Mismatch at low and high transverse

momentum SIDIS at 1/Q Bacchetta-Boer-Diehl-Mulders, 0803.0227

The factorization needs to be carefully examined at this order Earlier works indicates possible problems

Afanasev-Carlson, PRD, 2006 Gamberg-Hwang-Metz-Schlegel, PLB, 2006

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04/18/23 0.1 0.2 0.3 x

0

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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

Heavy quarkonium production (gg channel) ep scattering

No SSA in color-singlet model Final state interaction in color-octet model

pp scattering Only initial state interaction in color-singlet ISI and FSI cancel out in color-octet

Open charm or beauty Different SSAs for charm and anti-charm

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Color-singlet model

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Final state interactions with quark and anti-quark cancel out eachother, no SSA in color-singlet model

Color-octet model

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Final state interactions can be summarized into a gauge link to infinity, nonzero SSA

pp scattering

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•Color-singlet model: only initial state interaction, non-zero SSA•Color-octet model: initial and final state interactions cancel out, no SSA

J/Psi Production at lower energy (JPARC or FAIR) Quark-channel dominates

Color-singlet: only initial state interaction contributes, -1/2Nc relative to Drell-Yan

Color-octet: both initial and final state interactions contribute, -(Nc^2+1)/2Nc relative to DY

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JPARC prediction

Proportional to the sum of u- and d- quark Sivers function: fitted to HERMES data, Vogelsang-Yuan 05

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Final A_N depends on the weight of the quark-channel contribution

Heavy quark SSA

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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

A factor ~4 difference between charm and anticharm

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At JPARC, the quark channel contributes ~60% for charm cross sections

FAIR at GSI

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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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What can we learn from SSA

Quark Orbital Angular Momentum

e.g, Sivers function ~ the wave function amplitude with nonzero orbital angular momentum!

Vanishes if quarks only in s-state!Ji-Ma-Yuan, NPB03Brodsky-Yuan, PRD06

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Take Drell-Yan as an example(with non-zero transverse momentum q?) We need a loop to generate a phase

Twist-three CorrelationsEfremov-Teryaev, 82, 84Qiu-Sterman, 91,98

Kane et al., hard parton model

+++

-+++

-

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Further factorization (q?

<<Q) The collinear gluons dominate

Twist-three CorrelationsEfremov-Teryaev, 82, 84Qiu-Sterman, 91,98

Transverse Momentum Dependent distributions

Sivers, 90, Collins, 93,02Brodsky-Hwang-Schmidt,02Ji-Qiu-Vogelsang-Yuan,06

q?<<Q

4504/18/23 Users Meeting, BNL

New challenge from STAR data (2006)Talks by Ogawa and Nogach in SPIN2006

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Extend to all other TMDs: large Pt power counting kt-even distributions have the same

dependence on kt

kt-odd distributions are suppressed at large kt

Power Counting Rule

kt-even: 1/kt2

kt-odd: 1/kt4

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SIDIS cross sections at large Pt

1/Pt2

1/Pt4

1/Pt3

1/Pt5

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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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