Transcript QCD Factorization for Semi

Status Report (theory):
Unveil the Mysterious of
Single Spin Asymmetry
Feng Yuan
Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
7/17/2015
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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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What’s 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 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
S
k
Sivers function ~ ST. (PXkT)
 Sivers 90
T
 Colllins
93
 Brodsky-Hwang-Schmidt, 02

T
P
Twist-3 quark-gluon correlations (coll.)
 Efremov-Teryaev,
82, 84
 Qiu-Sterman, 91,98
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Two contributions, e.g., in DIS
pTXsT
Fragmentation:
Collins Function
sT
STXkT
Distribution:
Sivers Function
ST
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QCD Dynamics
TRANSVERSE MOMENTUM
DEPENDENCE
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
QCD
PT
<<
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PT
<<
Q
Ji-Qiu-Vogelsang-Yuan,2006
Yuan-Zhou, 2009
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Universality of the Collins
Fragmentation
HERMES, COMPASS, JLab
BELLE (KEK), BESIII(?)
ep--> e Pi X
e+e--> Pi Pi X
Metz 02, Collins-Metz 02,
Yuan 07,
Gamberg-Mukherjee-Mulders 08
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Yuan PRL08
pp--> jet(->Pi) X
Under investigate by
STAR experiments at RHIC
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Model calculations
Metz 02, Collins-Metz 02:
Gamberg-Mukherjee-Mulders, 08
Universality of the Collins function!!
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Similar arguments for pp collisions
Yuan, PRL08,PRD08
By using the Ward
Identity:
same Collins fun.
Conjecture: the Collins function will be the same as e^+e^- 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
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Initial state vs. final state interactions
*
*
DIS
Drell-Yan
HERMES
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“Universality”: QCD prediction
Brodsky-Hwang-Schmidt 02
17 02
Collins
Experiment SIDIS vs Drell Yan
HERMES Sivers Results
RHIC II Drell Yan Projections
0
0
Markus Diefenthaler
DIS Workshop
Munich, April 2007
0.1
0.2
0.3 x
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http://spin.riken.bnl.gov/rsc/
NLO corrections to SSA
Vogelsang-Yuan, arXiv:0904.0410
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SSA in Drell-Yan as an example,
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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

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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
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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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New challenge from STAR data (2006)
Anselmino et al.,
Kouvaris et al.,
SPIN Workshop, JLab
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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!!

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