Status Report (theory): Unveil the Mysterious of Single Spin Asymmetry

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Status Report (theory) Unveil the Mysterious of
Single Spin Asymmetry

• Feng Yuan
• Lawrence Berkeley National Laboratory
• RBRC, Brookhaven National Laboratory

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Outline

• Introduction
• Two approaches Transverse Momentum Dependent and
  Twist-three Collinear
• Highlights (bias) of recent developments
• Unifying the two approach
• QCD dynamics Universality and Factorization
• Phenomenology
• First attempt to extract transversity,
• Challenges and Puzzles

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Whats Single spin asymmetry?
Transverse plane
Final state particle is Azimuthal symmetric
Single Transverse Spin Asymmetry (SSA)
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Single Spin Asymmetry

• Motivations
• It is hard to understand it in QCD
• Its strong tied with the quark orbital angular
  momentum
• We have beautiful data
• Nontrivial QCD dynamics, and fundamental test of
  the factorization, and the universality of Parton
  Distribution Functions, Fragmentation Functions,

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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 aSmq/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

.
Sivers function ST (PXkT)
P
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Two contributions, e.g., in DIS

• Fragmentation
• Collins Function

• Distribution
• Sivers Function

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Transverse momentum dependence

• QCD Dynamics

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Transition from Perturbative region to
Nonperturbative region

• Compare different region of PT

Nonperturbative TMD
Perturbative region
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Perturbative tail is calculable

• Transverse momentum dependence

Power counting, Brodsky-Farrar, 1973
Integrated Parton Distributions Twist-three
functions
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A unified picture (leading pt/Q)
Transverse momentum dependent
Collinear/ longitudinal
PT
?QCD
Q
PT
ltlt
ltlt
Ji-Qiu-Vogelsang-Yuan,2006 Yuan-Zhou, 2009
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Universality of the Collins Fragmentation
HERMES, COMPASS, JLab
BELLE (KEK), BESIII(?)
Yuan PRL08
ep--gt e Pi X
pp--gt jet(-gtPi) X
ee--gt Pi Pi X
Metz 02, Collins-Metz 02, Yuan 07, Gamberg-Mukherj
ee-Mulders 08
Under investigate by STAR experiments at RHIC
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Model calculations
Metz 02, Collins-Metz 02 Gamberg-Mukherjee-Mulder
s, 08 Universality of the Collins function!!
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Similar arguments for pp collisions
Yuan, PRL08,PRD08
Conjecture the Collins function will be the same
as ee- and SIDIS
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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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Testable prediction at RHIC

• Initial state vs. final state interactions
• Universality QCD prediction

?
?
DIS
Drell-Yan
HERMES
Brodsky-Hwang-Schmidt 02 Collins 02
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Experiment SIDIS vs Drell Yan
HERMES Sivers Results
RHIC II Drell Yan Projections
0
Markus Diefenthaler DIS Workshop Munich, April
2007
0
0.1 0.2 0.3 x
http//spin.riken.bnl.gov/rsc/
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NLO corrections to SSA
Vogelsang-Yuan, arXiv0904.0410 

• SSA in Drell-Yan as an example,
• Collinear factorization

Collinear functions, evolution Kang-Qiu, 08

Zhou-Yuan-Liang, 08
Braun et al., 0909.3410
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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
RHIC
STAR
E704
BRAMHS
Kouvaris,Qiu,Vogelsang,Yuan, 06
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(No Transcript)
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New challenge from STAR data (2006)

• Anselmino et al.,
• Kouvaris et al.,

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Summary and Outlook

• Based on recent developments, we have shown that
  the TMD and collinear factorization approaches
  are consistent in the intermediate transverse
  momentum region
• Next-to-leading order QCD corrections to the
  Drell-Yan SSA have been calculated for the first
  time
• There are still puzzles!!