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Semi-inclusive DIS:
factorization
Feng Yuan
Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
7/7/2017
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Outline
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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 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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Different PT Region
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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
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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’
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Belitsky,Ji,Yuan
02’
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
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Collinear divergence : ln(m2)
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Double Logarithms: ln2(2 b2)
--- Collins-Soper equation
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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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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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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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Factorization
Soft Factor
SIR05 JLab
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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, …
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 Except
for dijet-correlation at hadron colliders
because of mixture of ISI and FSI effects
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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
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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
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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
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The two mechanisms at intermediate P
generate the same physics!
Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006
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A difficulty at next-leadingpower (1/Q)
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Mismatch at low and high transverse
momentum SIDIS at 1/Q
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Bacchetta-Boer-Diehl-Mulders, 0803.0227
The factorization needs to be carefully
examined at this order
 Earlier
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works indicates possible problems
Afanasev-Carlson, PRD, 2006
Gamberg-Hwang-Metz-Schlegel, PLB, 2006
7/7/2017
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Transition from Perturbative region
to Nonperturbative region?
Nonperturbative TMD
Perturbative region
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Summary
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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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