04/10/23 1

Transversity: Opportunities Now and Future

Feng Yuan Lawrence Berkeley National Laboratory

RBRC, Brookhaven National Laboratory

Transverse spin physics

04/10/23 HALL A Meeting 2007 2

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Outline

Transversity and transverse spin physics

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

In DIS,

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Parton distributions

Quark distribution matrixP,k)

Gauge links

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Leading order quark distribution expands at leading order,

Although a leading-twist distribution, transversity is chiral-odd, and doesn’t contribute to the DIS structure function

Unpolarized

helicity

transversity

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Measuring transversity is difficult

Have to multiply another chiral-odd object (distribution or fragmentation)Drell-Yan and other processes in

hadronic collisionsTwo-hadron production in DISSemi-inclusive single hadron production

in DIS

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Drell-Yan is an ideal place

Combining two transversity distributions in Drell-Yan lepton pair production

+

-

-

+qT

qT

Double Transverse spin asymmetry

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Opportunity at RHIC

Vogelsang, et al, PRD, 1999

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Semi-inclusive DIS Collins fragmentation function is

chiral-odd

Combining with the quark

transversity leads to single transverse-spin asymmetry in SIDIS

Opening a whole window of SSAs in SIDIS

(k,sT)(zk+pT)

~pTXsT

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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

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 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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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:Universality 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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Collins from HERMES Large, positive asymmetries:

no surprise from u-quark dominance

Large, negative asymmetries:first a surprise, now understood by large, negative disfavored Collins function

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Collins from COMPASS

Smaller asymmetries than in proton case

PRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007

First extraction of Collins functions and transversity distributions from fitting HERMES + COMPASS + BELLE data

By Anselmino et al., PRD 75 (07)

Comparison with some models

[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)

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

04/10/23 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

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

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The asymmetry could be related to that in DIS, only at the leading order (one-gluon exchange),

qTDIS--- Sivers function from DIS

qt--- imbalance of the dijet

Hsivers depends on subprocess

Qiu,Vogelsang,Yuan, 07

This simple picture does not hold for two-gluon exchanges

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

Integrated over transverse momentumSimilar calculations can be

Shown for QCD

Failure or Opportunity?

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Collins,Qiu,0705.2141

Future opportunities at JLab

Transverse spin physics with proton and neutron targetsCrucial to extract the quark transversity

Detailed mapping of TMDs at 12 GeV upgrade

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Different PT Region Integrate out PT (w/o weight)

-- normal factorization, similar to inclusive DIS

Large PT (>>QCD)-- hard gluon radiation, can be calculated from perturbative QCD

Low PT (~QCD)-- nonperturbative information: TMD factorization formula

? ! 12GeV

12GeV

12GeV

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PT dependence

Which is valid for all Pt range

SSA is suppressed by 1/Pt at large Pt

Sivers function at low Pt Qiu-Sterman Twist-three

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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

Opportunities at other experiments

RHIC and RHIC II Collins effects, quark transversity Drell-Yan, quark Sivers Heavy flavor, gluon Sivers

JPARC (pp collision at low energy) Drell-Yan, quark Sivers effects

GSI-FAIR (ppbar collision) Drell-Yan, quark transversity Quark Sivers effects

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Summary

We are in the early stages of a very exciting era of transverse spin physics studies, where the future JLAB, RHIC, 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

4604/10/23 Users Meeting, BNL

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

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Some comments

It’s difficult to explain this pattern in the current theoretical approaches Fragmentation (Collins effect) contributions?

One possible reason could be the partial cancellation between the favored and disfavored contribution to Pi^0 production Check with the charged pions?

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Recent theoretical developments(twist-three) Complete formalism for single

inclusive hadron production in pp collision has been derived, including the derivative and non-derivative terms

Qiu, Sterman, 91, 98Kouvaris,Qiu,Vogelsang,Yuan, 06See also Koike, et al., 06,07

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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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Two-hadron interference frag. fun. In DIS

Collins,Heppelmann,Ladinsky, 94Jaffe,Jin,Tang, 97Bacchetta,Radici, 04,06