qcd factorization for semi-inclusive dis
DESCRIPTION
QCD Factorization for Semi-inclusive DIS. Feng Yuan RBRC , Brookhaven National Laboratory. Outline. Introduction: physics of TMD QCD factorization for semi-inclusive DIS Some phenomenological results Summary. Inclusive and Semi-inclusive DIS. Inclusive DIS: - PowerPoint PPT PresentationTRANSCRIPT
Sep. 22, 2005 APS/JPS Hawaii 1
QCD QCD Factorization for Factorization for Semi-inclusive Semi-inclusive
DISDISFeng Yuan RBRC , , Brookhaven National
Laboratory
Sep. 22, 2005 2APS/JPS Hawaii
OutlineOutline Introduction: physics of TMD Introduction: physics of TMD QCD factorization for semi-QCD factorization for semi-
inclusive DISinclusive DIS Some phenomenological Some phenomenological
resultsresults SummarySummary
Sep. 22, 2005 3APS/JPS Hawaii
Inclusive and Inclusive and Semi-inclusive DISSemi-inclusive DIS
Inclusive DIS:Partonic Distribution depending on the longitudinal momentum fraction
Semi-inclusive DIS:Probe additional information for partons’transverse distribution in nucleon
Sep. 22, 2005 4APS/JPS Hawaii
Different Different PP?? Region Region
Integrate out P?
-- similar to inclusive DIS, probe int. PDF Large P? (ÀQCD)
-- hard gluon radiation, can be calculated from perturbative QCD,
Polarized ->q-g-q correlations Low P? (»QCD)
-- nonperturbative information (TMD): new factorization formula
Sep. 22, 2005 5APS/JPS Hawaii
TMD PhysicsTMD Physics
A way to measure Transversity A way to measure Transversity Distribution, the last Distribution, the last unkownunkown leading leading twisttwist distribution distribution
Collins 1993Collins 1993 The Novel Single Spin AsymmetriesThe Novel Single Spin Asymmetries Connections with GPDs, and Quantum Connections with GPDs, and Quantum
Phase Space Wigner distributionsPhase Space Wigner distributions Quark Orbital Angular Momentum andQuark Orbital Angular Momentum and
Many others …Many others …
Sep. 22, 2005 6APS/JPS Hawaii
TMD Distribution: the TMD Distribution: the definitiondefinition
Gauge Invariance requires the Gauge Link
Brodsky,Hwang,Schmidt 02’Collins 02’Belitsky,Ji,Yuan 02’
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This definition is This definition is also consistent also consistent
with the with the QCD factorizationQCD factorization
Sep. 22, 2005 8APS/JPS Hawaii
One-loop Factorization: One-loop Factorization: virtualvirtual
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)
p
p′
k
•Vertex corrections (single quark target)Vertex corrections (single quark target)
Sep. 22, 2005 9APS/JPS Hawaii
One-Loop Factorization: One-Loop Factorization: realreal
Gluon Radiation (single quark target)Gluon Radiation (single quark target)
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)
p
p′
k
Sep. 22, 2005 10APS/JPS Hawaii
All Orders in All Orders in Perturbation TheoryPerturbation Theory
Consider an arbitrary Feynman diagramConsider an arbitrary Feynman diagram Find the singular contributions from Find the singular contributions from
different regions of the momentum different regions of the momentum integrationsintegrations
Power counting to determine the leading Power counting to determine the leading regionsregions
Factorize the soft (Grammer-Yennie) and Factorize the soft (Grammer-Yennie) and collinear gluons (Ward Identity)collinear gluons (Ward Identity)
Factorization theorem.Factorization theorem.(Collins, Soper, Sterman, (Collins, Soper, Sterman, Perturbative QCDPerturbative QCD, Mueller ed.), Mueller ed.)
Sep. 22, 2005 11APS/JPS Hawaii
FactorizationFactorization
Soft Factor
Ma, Ji, Yuan, 2004
Sep. 22, 2005 12APS/JPS Hawaii
SIDIS Cross Section: QCD SIDIS Cross Section: QCD FactorizationFactorization
At leading power of 1/Q
Sivers Asym.
Collins Asym.
Sep. 22, 2005 13APS/JPS Hawaii
The Factorization Applies The Factorization Applies toto
Semi-inclusive DIS (polarized and Semi-inclusive DIS (polarized and unpolarized)unpolarized)
Drell-Yan at Low transverse momentumDrell-Yan at Low transverse momentum Di-hadron production in e+e- Di-hadron production in e+e-
annihilation (extract the Collins annihilation (extract the Collins function)function)
Di-jet and/or di-hadron correlation at Di-jet and/or di-hadron correlation at hadron collider (work in progress)hadron collider (work in progress)
Many others, …Many others, …
Sep. 22, 2005 14APS/JPS Hawaii
PhenomenologyPhenomenology Semi-inclusive DIS (Vogelsang, Yuan, Semi-inclusive DIS (Vogelsang, Yuan,
05)05)
See also Efremov, et al., 04, 05; See also Efremov, et al., 04, 05; Anselmino, et al., 05 Anselmino, et al., 05
Sep. 22, 2005 15APS/JPS Hawaii
COMPASSCOMPASS
Sep. 22, 2005 16APS/JPS Hawaii
At RHICAt RHIC
Sep. 22, 2005 17APS/JPS Hawaii
SummarySummary
The QCD factorization theorem has The QCD factorization theorem has been proved for semi-inclusive DISbeen proved for semi-inclusive DIS
Some phenomenological studies Some phenomenological studies showed very promising results as showed very promising results as compared with the old data and on compared with the old data and on the predictions for the future the predictions for the future experiments as wellexperiments as well