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04/21/23 1
Semi-inclusive DIS: factorization
Feng Yuan Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
2
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
04/21/23 19
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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
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