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Semi-inclusive DIS: factorization

Feng Yuan Lawrence Berkeley National Laboratory

RBRC, Brookhaven National Laboratory

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Outline Introduction Low PT region: TMD parton

distributions and QCD factorization High PT region: quark-gluon-quark

correlation (ETQS mechanism) Summary

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Inclusive andSemi-inclusive DIS

Inclusive DIS:Partonic Distribution depending on the longitudinal momentum fraction

Semi-inclusive DIS:Probe additional information for partons’transverse distribution in nucleon

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Different PT Region Integrate out PT

-- similar to inclusive DIS, probe int. PDF Large PT (~QCD)

-- hard gluon radiation, can be calculated from perturbative QCD,

Polarized ->q-g-q correlations Low PT (~QCD)

-- nonperturbative information (TMD): new factorization formula

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TMD Physics A way to measure Transversity

Distribution, the last unkown leading twist distribution

Collins 1993 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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TMD Distribution: the definition

Gauge Invariance requires the Gauge Link

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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Illustrate the Factorization(one-loop order)

Take an on-shell quark target Calculate the TMD Dis. and F.F. Separate the cross section into different

pieces Show the soft divergence is cancelled out

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TMD Dis. At One-loop

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No soft divergence

Collinear divergence : ln(m2)

Double Logarithms: ln2(2 b2) --- Collins-Soper equation

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One-loop Factorization: virtual

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)

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One-Loop Factorization: real 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

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All Orders in Perturbation Theory 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.)

14SIR05 JLab

Factorization

Soft Factor

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The Factorization Applies to Semi-inclusive DIS (polarized and

unpolarized) Drell-Yan at Low transverse momentum Di-hadron production in e+e-

annihilation (extract the Collins function)

Many others, … Except for dijet-correlation at hadron colliders

because of mixture of ISI and FSI effects Collins-Qiu, 07; Vogelsang-Yuan, 07; Mulders et al, 04-07 Heavy quarkonium production in pp collision, Yuan, 08

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Power Counting at Large PT

kt-even distributions have the same dependence on kt

kt-odd distributions are suppressed at large kt

Power Counting Rule

kt-even: 1/kt2

kt-odd: 1/kt3

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SIDIS: at Large PT

Large PT SIDIS can be calculated from perturbative QCD (same for TMDs)

Polarized scattering depends on the quark-gluon correlations in the nucleon

Single Spin Asymmetry (Sivers and Collins) at large PT is not suppressed by 1/Q, but by 1/PT

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A unified picture for SSA In DIS and Drell-Yan processes, SSA depends on

Q and transverse-momentum P

At large P, SSA is dominated by twist-3 correlation effects

At moderate P, SSA is dominated by the transverse-momentum-dependent parton distribution/fragmentation functions

The two mechanisms at intermediate P generate the same physics! Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006

A difficulty at next-leading-power (1/Q) Mismatch at low and high transverse

momentum SIDIS at 1/Q Bacchetta-Boer-Diehl-Mulders, 0803.0227

The factorization needs to be carefully examined at this order Earlier works indicates possible problems

Afanasev-Carlson, PRD, 2006 Gamberg-Hwang-Metz-Schlegel, PLB, 2006

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Transition from Perturbative region to Nonperturbative region?

Nonperturbative TMD Perturbative region

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Summary Semi-inclusive DIS provides important

information on nucleon structure and opportunity to study the associated QCD dynamics

QCD factorization and universality of the parton distributions are important aspects in these studies

The PT dependence will provide us information for the perturbative to nonperturbative transition of QCD