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Transverse Spin Overview: Theory Perspective

Feng Yuan Lawrence Berkeley National Laboratory

RBRC, Brookhaven National Laboratory

Feynman Parton Model Inclusive cross sections

probe the momentum (longitudinal) distributions of partons inside nucleon

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Hadronic reactions

Extension to transverse direction…

Momentum Space: Semi-inclusive measurementsTransverse momentum dependent (TMD)

parton distributions Coordinate Space: Deeply Virtual

Compton Scattering and Exclusive processesGeneralized parton distributions (GPD)

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Transverse momentum dependent parton distribution Straightforward extension

Spin average, helicity, and transversity distributions

Transverse momentum-spin correlationsNontrivial distributions, STXPT In quark model, depends on S- and P-

wave interference, or p-p

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Nucleon Structure, spin correlation, orbital motion of quarks and gluon

Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,…Single spin asymmetry phenomena

Motivations…

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What’s Single spin asymmetry?

Single Transverse SpinAsymmetry (SSA)

Final state particle isAzimuthal symmetric

Transverse plane

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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 Colllins 93 Brodsky-Hwang-Schmidt, 02

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

P

kTST

Sivers function ~ ST (PXkT).

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Two contributions, e.g., in DIS

Fragmentation: Collins Function

STXkT

ST

sT

pTXsT

Distribution: Sivers Function

Universality Property

Collins fragmentation function is universalDIS, e+e-, and hadron in jet in pp

Sivers distribution functions are notChange sign between DIS and Drell-YanMore complicated structure for the dijet

correlation pp collisions

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A unified picture between TMD and twist-three (leading pt/Q)

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QQCD PT

Collinear/longitudinal

<<<<

Transverse momentum dependent

Ji-Qiu-Vogelsang-Yuan,2006Yuan-Zhou, 2009

PT

NLO corrections to SSA

SSA in Drell-Yan as an example,

Collinear factorization

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Vogelsang-Yuan, arXiv:0904.0410 

Collinear functions, evolution: Kang-Qiu, 08; Zhou-Yuan-Liang, 08 Braun et al., 0909.3410

Universality of the Collins Fragmentation

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ep--> e Pi X e+e--> Pi Pi X pp--> jet(->Pi) X

Metz 02, Collins-Metz 02,Yuan 07,Gamberg-Mukherjee-Mulders 08Meissner-Metz 0812.3783Yuan-Zhou, 0903.4680

HERMES, COMPASS, JLabJLab BELLE (KEK), BARBAR, , BESIII(?)(?)

The reason is 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”

Brodsky,Hwang,Schmidt 02Collins, 02;Ji,Yuan,02;Belitsky,Ji,Yuan,02

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DIS and Drell-Yan

Initial state vs. final state interactions

“Universality”: 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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Initial state and/or final state interactions

Non-universality: Dijet-correlation at RHIC

Boer-Vogelsang 03Jet 1

Jet 2

P,ST

Standard Factorization breaks, no universality!Bacchetta-Bomhof-Mulders-Pijlman, 04-06Collins-Qiu 08Vogelsang-Yuan 08

Indication from the experimental measurement?

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STAR,0705.4629

Theory calculations use one-gluon exchange formalismFuture photon-jet correlation measurement shall be able to help us to understand this issue

Highlights from recent measurements Pt dependence for single inclusive

hadron SSA Eta SSA much larger than Pi0 Consistency between HERMES and

COMPASS on Sivers in DIS SSA for heavy mesons consistent

with zero

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Theory challenge!!

Exp. Issue

Transverse spin is still in the exploration stage (my opinion) No confirmation from pp collisions for

whatever observed in DIS and e+e- There is no decisive answer for the

underlying mechanism for SSA of ppPi+XCollins or SiversPt dependence (in general)

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Theory wish list (personal bias) Test the non-universality for the Sivers

mechanismDrell-Yan, ideal placephoto-jet could be used as well

Separate Sivers and Collins contributionsHadron in jetDi-hadron correlation

TransversityTwo hadron fragmentation

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Azimuthal distribution of hadrons inside a jet (large PT)

Collins Fragmentation function

Quark transversity distribution

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Extend the Collins measurement in e+e- to pp collisions?

Dilution factor to select the quark-antiquark jets

Looking for dihadrons’ cos2phi correlation

Belle Coll., PRL 06

p

p

Isolate Sivers effects Drell-Yan/W Direct photon production

Initial state interaction Jet production

Initial/final state interactions Dijet/photon-jet correlation

Both initial/final state interactions, factorization breaks down

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TMD

TMD?

Twist-3

Twist-3

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Summary and Outlook

There has been great progress on both theory and experiment sides for (single) transverse spin phenomena Next-to-leading order QCD corrections

and scale evolutions have been carried out

There are still challenges and puzzles!!

theory

theory

[by Naomi Makins]

looking forward to new projects: Jlab12, EIC, JPARC, PAX@FAIR

Global effort in Transverse Spin Physics: Intense Interactions between different collaborationsand Theoreticians

28SPIN Workshop, JLab

New challenge from STAR data (2006)

Anselmino et al., Kouvaris et al.,

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Predictions at RHIC

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

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

Nonperturbative TMD Perturbative region

Perturbative tail is calculable Transverse momentum dependence

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Power counting,Brodsky-Farrar, 1973

Integrated Parton DistributionsTwist-three functions

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Model calculations

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.

Yuan, PRL08,PRD08

Collinear factorization verified at one-loop order Soft-collinear divergence cancelled

out between virtual and real diagrams

Collinear divergence identified as the splitting functions for the antiquark and twist-three correlation functions

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Finite terms

+...

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Threshold limits

Large-z,

The asymmetry should not change dramatically with energy in the forward region

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Twist-3 Fit (LO) to data:

E704

STAR

Kouvaris,Qiu,Vogelsang,Yuan, 06

RHIC

BRAMHS

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