qcd factorization for semi-inclusive dis

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Sep. 22, 2005 APS/JPS Hawaii 1 QCD QCD Factorization Factorization for Semi- for Semi- inclusive DIS inclusive DIS Feng Yuan RBRC , , Brookhaven National Laboratory

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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 Presentation

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Page 1: QCD Factorization for Semi-inclusive DIS

Sep. 22, 2005 APS/JPS Hawaii 1

QCD QCD Factorization for Factorization for Semi-inclusive Semi-inclusive

DISDISFeng Yuan RBRC , , Brookhaven National

Laboratory

Page 2: QCD Factorization for Semi-inclusive DIS

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

Page 3: QCD Factorization for Semi-inclusive DIS

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

Page 4: QCD Factorization for Semi-inclusive DIS

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

Page 5: QCD Factorization for Semi-inclusive DIS

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 …

Page 6: QCD Factorization for Semi-inclusive DIS

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’

Page 7: QCD Factorization for Semi-inclusive DIS

Sep. 22, 2005 APS/JPS Hawaii 7

This definition is This definition is also consistent also consistent

with the with the QCD factorizationQCD factorization

Page 8: QCD Factorization for Semi-inclusive DIS

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)

Page 9: QCD Factorization for Semi-inclusive DIS

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

Page 10: QCD Factorization for Semi-inclusive DIS

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.)

Page 11: QCD Factorization for Semi-inclusive DIS

Sep. 22, 2005 11APS/JPS Hawaii

FactorizationFactorization

Soft Factor

Ma, Ji, Yuan, 2004

Page 12: QCD Factorization for Semi-inclusive DIS

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.

Page 13: QCD Factorization for Semi-inclusive DIS

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, …

Page 14: QCD Factorization for Semi-inclusive DIS

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

Page 15: QCD Factorization for Semi-inclusive DIS

Sep. 22, 2005 15APS/JPS Hawaii

COMPASSCOMPASS

Page 16: QCD Factorization for Semi-inclusive DIS

Sep. 22, 2005 16APS/JPS Hawaii

At RHICAt RHIC

Page 17: QCD Factorization for Semi-inclusive DIS

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