Transcript QCD Factorization for Semi

QCD Factorization for
Semi-inclusive DIS
Feng Yuan
RBRC , Brookhaven National Laboratory
Sep. 22, 2005
APS/JPS Hawaii
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Outline
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Introduction: physics of TMD
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QCD factorization for semi-inclusive
DIS
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Some phenomenological results
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Summary
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Inclusive and
Semi-inclusive DIS
Inclusive DIS:
Partonic Distribution depending on
the longitudinal momentum fraction
Semi-inclusive DIS:
Probe additional information for parto
transverse distribution in nucleon
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APS/JPS Hawaii
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Different P? Region
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Integrate out P?
-- similar to inclusive DIS, probe int. PDF
Large P? (ÀQCD)
-- hard gluon radiation, can be calculated from
perturbative QCD,
Polarized ->q-g-q correlations
Low P? (»QCD)
-- nonperturbative information (TMD): new
factorization formula
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APS/JPS Hawaii
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TMD Physics
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A way to measure Transversity Distribution, the
last unkown leading twist distribution
Collins 1993
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The Novel Single Spin Asymmetries
Connections with GPDs, and Quantum Phase
Space Wigner distributions
Quark Orbital Angular Momentum and
Many others …
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APS/JPS Hawaii
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TMD Distribution: the definition
Gauge Invariance requires the Gauge Link
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Brodsky,Hwang,Schmidt 02’
Collins 02’
Belitsky,Ji,Yuan 02’
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This definition is also
consistent with the
QCD factorization
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One-loop Factorization: virtual
•Vertex corrections (single quark target)
p′
p
k
Four possible regions for the gluon
momentum k:
1) k is collinear to p (parton distribution)
2) k is collinear to p′ (fragmentation)
3) k is soft (Soft factor)
4) k is hard (pQCD correction)
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APS/JPS Hawaii
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One-Loop Factorization: real
 Gluon Radiation (single quark target)
p′
k
p
Three reagions for the gluon momentum k:
1) k is collinear to p (parton distribution)
2) k is collinear to p′ (fragmentation)
3) k is soft (Soft factor)
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APS/JPS Hawaii
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All Orders in Perturbation Theory
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Consider an arbitrary Feynman diagram
Find the singular contributions from different
regions of the momentum integrations
Power counting to determine the leading regions
Factorize the soft (Grammer-Yennie) and
collinear gluons (Ward Identity)
Factorization theorem.
(Collins, Soper, Sterman, Perturbative QCD, Mueller ed.)
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APS/JPS Hawaii
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Factorization
Soft Factor
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Ma, Ji, Yuan, 2004
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SIDIS Cross Section: QCD
Factorization
At leading power of 1/Q
Sivers Asym.
Collins Asym.
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APS/JPS Hawaii
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The Factorization Applies to
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Semi-inclusive DIS (polarized and unpolarized)
Drell-Yan at Low transverse momentum
Di-hadron production in e+e- annihilation
(extract the Collins function)
Di-jet and/or di-hadron correlation at hadron
collider (work in progress)
Many others, …
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APS/JPS Hawaii
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Phenomenology
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Semi-inclusive DIS (Vogelsang, Yuan, 05)
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See also Efremov, et al., 04, 05;
Anselmino, et al., 05
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COMPASS
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At RHIC
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Summary
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The QCD factorization theorem has been
proved for semi-inclusive DIS
Some phenomenological studies showed very
promising results as compared with the old data
and on the predictions for the future
experiments as well
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APS/JPS Hawaii
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