Single-Transverse Spin Asymmetries in Hadronic Scattering

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Single-Transverse Spin Asymmetries in Hadronic
Scattering

• Werner Vogelsang ( Feng Yuan)
• BNL Nuclear Theory
• ECT, 06/13/2007

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Mostly based on
X. Ji, J.W. Qiu, WV, F. Yuan,
Phys. Rev. Lett. 97, 082002 (2006)
Phys. Rev. D73, 094017 (2006)
Phys. Lett. B638, 178 (2006)
C. Kouvaris, J.W. Qiu, WV, F. Yuan,
Phys. Rev. D74, 114013 (2006)
( C. Bomhof, P. Mulders, WV, F. Yuan,
Phys. Rev. D75, 074019 (2007) )
J.W. Qiu, WV, F. Yuan,
arXiv0704.1153 hep-ph (Phys. Lett. B, to
appear)
arXiv0706.1196 hep-ph
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Outline
Introduction
Single-spin asymmetries in pp ? hX
How are mechanisms for Single-spin
asymmetries related ?
Conclusions
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I. Introduction
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SSA for single-inclusive process
? example pp ? ?X
? a single large scale (pT)
? power-suppressed
? collinear factorization (Efremov,Teryaev /
Qiu,Sterman TF)
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II. Asymmetry in pp?hX
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collinear factorization
Brahms
y2.95
STAR
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STAR
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typically, hard-scattering calculations based
on LO/NLO fail badly in describing the cross
section
vs23.3GeV
Apanasevich et al.
Bourrely and Soffer
? Resummation of important higher-order
corrections beyond NLO de Florian, WV
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de Florian, WV

• higher-order corrections beyond NLO ?

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Leading logarithms

• expect large enhancement !

de Florian, WV
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de Florian, WV
E706
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WA70
Effects start to become visible at ?S62 GeV
Rapidity dependence ? Spin dependence ?
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lesson from this AN in pp?h X is
power-suppressed !
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power-suppressed effects in QCD much richer
than just mass terms
(Efremov,Teryaev Qiu,Sterman

Kanazawa, Koike)
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ingredients
Collinear factorization.
x1
x2
x2-x1
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full structure
Qiu,Sterman
Transversity
Kanazawa,Koike
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derivative terms
plus, non-derivative terms !
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Assumptions in Qiu Sterman
derivative terms only
valence TF only,
neglect gluon?pion fragmentation
In view of new data, would like to relax some of
these. Kouvaris, Qiu, Yuan, WV
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Remarkably simple answer
Recently proof by Koike Tanaka
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? Ansatz
usual pdf
? Fit to E704, STAR, BRAHMS
? for RHIC, use data with pTgt1 GeV

• for E704, choose pT1.2 GeV
• allow normalization of theory to float (0.5)

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Fit I two-flavor / valence
Fit II allow sea as well
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solid Fit I, dashed Fit II
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Our TF functions
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pT dependence
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Dependence on RHIC c.m.s. energy
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III. How are the mechanisms for single-spin
asymmetries related ?
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have two mechanisms
tied to factorization theorem that applies
Q In what way are mechanisms connected ?
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consider Drell-Yan process at measured qT and
Q
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Step 1 calculate SSA for DY at qT Q
use Qiu/Sterman formalism
Because of Q2 ? 0, there are also hard
poles Propagator (H) has pole at xg?0 No
derivative terms in hard-pole contributions.
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soft-pole
hard-pole
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Step 2 expand this for qT ltlt Q
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Step 3 calculate various factors in TMD
factorized formula
Collins, Soper, Sterman
Ji, Ma, Yuan
At ?QCD ltlt qT can calculate each factor from
one-gluon emission
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Unpolarized pdf
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Sivers function
soft-pole
hard-pole
w/ correct direction of gauge link
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soft-pole, deriv.
hard-pole
hard-pole
soft-pole, non-deriv.
Precisely whats needed to make factorization
work and match on to the Qiu/Sterman result at
small q?!
So
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Take a closer look if one works directly in
small q? limit
?
?
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The interesting question now What happens in
more general QCD hard-scattering ?
Consider pp?jet jet X
jet pair transv. mom.
Underlying this all QCD 2?2 scattering processes
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Example qq ? qq
for Qiu/Sterman calculation subset of diagrams
IS
FS1
FS2
(these are soft-pole)
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Simplify
assume q? ltlt P? from the beginning
more precisely, assume k nearly parallel to
hadron A or B and pick up leading behavior
in q? / P?
reproduces above Drell-Yan results
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k parallel to pol. hadron
(partly even on individual diagram level, as in
Drell-Yan)
Likewise for hard-pole contributions
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What this means
When k nearly parallel to pol. hadron, structure
at this order can be organized as
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Some remarks
highly non-trivial. Relies on a number of
miracles color structure no derivative
terms when k parallel to hadron B
Calculation seems to know how to organize itself
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Some further remarks
the obtained Sivers partonic hard parts are
identical to the ones obtained by Amsterdam
group
the obtained unpolarized partonic hard parts
are identical to the standard 2?2 ones
complete calculation can be redone in context
of Brodsky-Hwang-Schmidt model
identical results as from collinear-factorization
approach
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IV. Conclusions
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Single-inclusive case use Qiu/Sterman
formalism Non-derivative terms have simple
form Not all aspects of data understood
Important input for phenomenology (Note
Sudakov logs)