An overview of transverse momentum dependent factorization and evolution

Rogers, Ted C.

doi:10.1140/epja/i2016-16153-7

Title: An overview of transverse momentum dependent factorization and evolution

Abstract

I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. Furthermore, I summarize basic results while attempting to trace their development over that past several decades.

Authors:

Rogers, Ted C. ^[1]

Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Fri Jun 17 00:00:00 EDT 2016

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1273415

Report Number(s):: JLAB-THY-15-2133; DOE/OR/23177-3522; arXiv:1509.04766
Journal ID: ISSN 1434-6001; PII: 521

Grant/Contract Number:: AC05-06OR23177

Resource Type:: Accepted Manuscript

Journal Name:: European Physical Journal. A

Additional Journal Information:: Journal Volume: 52; Journal Issue: 6; Journal ID: ISSN 1434-6001

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Rogers, Ted C. An overview of transverse momentum dependent factorization and evolution.  United States: N. p., 2016. 
Web.  doi:10.1140/epja/i2016-16153-7.

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                    Rogers, Ted C. An overview of transverse momentum dependent factorization and evolution.  United States.  https://doi.org/10.1140/epja/i2016-16153-7

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                    Rogers, Ted C. Fri .  
"An overview of transverse momentum dependent factorization and evolution".  United States.  https://doi.org/10.1140/epja/i2016-16153-7.  https://www.osti.gov/servlets/purl/1273415.

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@article{osti_1273415,

  title        = {An overview of transverse momentum dependent factorization and evolution},

  author       = {Rogers, Ted C.},

  abstractNote = {I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. Furthermore, I summarize basic results while attempting to trace their development over that past several decades.},

  doi          = {10.1140/epja/i2016-16153-7},

  journal      = {European Physical Journal. A},

  number       = 6,

  volume       = 52,

  place        = {United States},

  year         = {Fri Jun 17 00:00:00 EDT 2016},

  month        = {Fri Jun 17 00:00:00 EDT 2016}

}

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Works referencing / citing this record:

Predicting the light-front holographic TMDs of the pion
journal, September 2019

Ahmady, Mohammad; Mondal, Chandan; Sandapen, Ruben
Physical Review D, Vol. 100, Issue 5
DOI: 10.1103/physrevd.100.054005

Transversity parton distribution functions from lattice QCD
text, January 2018

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-05620

Relating Transverse Momentum Dependent and Collinear Factorization Theorems in a Generalized Formalism
text, January 2016

Collins, J.; Gamberg, L.; Prokudin, A.
arXiv
DOI: 10.48550/arxiv.1605.00671

Predicting the light-front holographic TMDs of the pion
text, January 2019

Ahmady, Mohammad; Mondal, Chandan; Sandapen, Ruben
arXiv
DOI: 10.48550/arxiv.1907.06561

Transverse spin observables in hard-scattering hadronic processes within collinear factorization
journal, November 2016

Pitonyak, Daniel
International Journal of Modern Physics A, Vol. 31, Issue 32
DOI: 10.1142/s0217751x16300490

Double hard scattering without double counting
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Diehl, Markus; Gaunt, Jonathan R.; Schoenwald, Kay
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2017-05986

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Ebert, Markus A.; Tackmann, Frank J.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2017-01138

Introduction to GPDs and TMDs
journal, June 2016

Diehl, Markus
The European Physical Journal A, Vol. 52, Issue 6
DOI: 10.1140/epja/i2016-16149-3

Introduction to GPDs and TMDs
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Diehl, Markus
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2016-02423

Transversity parton distribution functions from lattice QCD
text, January 2018

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
arXiv
DOI: 10.48550/arxiv.1807.00232

Double hard scattering without double counting
text, January 2017

Diehl, Markus; Gaunt, Jonathan R.; Schönwald, Kay
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2017-01234

Intrinsic Transverse Motion of the Pion's Valence Quarks
text, January 2018

Shi, Chao; Cloët, Ian C.
arXiv
DOI: 10.48550/arxiv.1806.04799

Where do we stand with a 3-D picture of the proton?
journal, June 2016

Bacchetta, Alessandro
The European Physical Journal A, Vol. 52, Issue 6
DOI: 10.1140/epja/i2016-16163-5

Resummation of Transverse Momentum Distributions in Distribution Space
text, January 2016

Ebert, Markus; Tackmann, Frank J.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2016-05827

Collinear Factorization in Wide-Angle Hadron Pair Production in $e^+e^-$ Annihilation
text, January 2019

Moffat, E.; Rogers, T. C.; Sato, N.
arXiv
DOI: 10.48550/arxiv.1909.02951

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Title: An overview of transverse momentum dependent factorization and evolution

Abstract

Citation Formats

Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory journal, May 2010

Fragmentation of transversely polarized quarks probed in transverse momentum distributions journal, May 1993

Sudakov suppression in azimuthal spin asymmetries journal, June 2001

Three-dimensional imaging of the nucleon and semi-inclusive high-energy reactions journal, December 2015

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction journal, February 1996

Measurement of Asymmetries of Inclusive Pion Production in Proton-Proton Interactions at 6 and 11.8 GeV/ c journal, April 1976

Angular dependences in inclusive two-hadron production at BELLE journal, January 2009

Intrinsic transverse momentum: Nongauge theories journal, May 1980

Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering journal, May 2002

Space-like (vs. time-like) collinear limits in QCD: is factorization violated? journal, July 2012

Effects of QCD resummation on distributions of leptons from the decay of electroweak vector bosons journal, August 1995

QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum journal, February 2005

Resummation for polarized semi-inclusive deep-inelastic scattering at small transverse momentum journal, June 2006

Full transverse-momentum spectra of low-mass Drell-Yan pairs at LHC energies text, January 2003

Wilson lines and transverse-momentum dependent parton distribution functions: A renormalization-group analysis journal, October 2008

Single spin asymmetry in inclusive pion production, Collins effect and the string model preprint, January 1994

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes journal, February 2015

QCD evolution of the Sivers function journal, February 2012

Gauge link structure in quark–quark correlators in hard processes journal, August 2004

Algorithm to compute corrections to the Sudakov form factor journal, September 1980

The parton orbital angular momentum: Status and prospects journal, June 2016

New fits for the non-perturbative parameters in the CSS resummation formalism journal, December 2000

Semi-inclusive deeply inelastic scattering at small q T journal, August 1996

Transverse momentum distributions in the nonperturbative region journal, July 2011

Theory of W and Z boson production text, January 2004

Universality of Soft and Collinear Factors in Hard-Scattering Factorization journal, December 2004

k T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions journal, June 2007

QCD evolution in the fully unintegrated form text, January 2009

QCD factorization for spin-dependent cross sections in DIS and Drell–Yan processes at low transverse momentum journal, September 2004

Single-spin production asymmetries from the hard scattering of pointlike constituents journal, January 1990

Hard processes in quantum chromodynamics journal, February 1980

Leptoproduction of heavy quarks. II. A unified QCD formulation of charged and neutral current processes from fixed-target to collider energies journal, September 1994

Does the Drell-Yan cross section factorize? journal, March 1982

Back-to-back jets in QCD journal, December 1981

Evolution of the helicity and transversity. Transverse-momentum-dependent parton distributions journal, October 2013

Infrared divergences and non-lightlike eikonal lines in Sudakov processes journal, January 2000

Extra spin asymmetries from the breakdown of transverse-momentum-dependent factorization in hadron-hadron collisions journal, July 2013

The structure of large logarithmic corrections at small transverse momentum in hadronic collisions journal, November 2001

Factorization theorem for Drell-Yan at low q T and transverse-momentum distributions on-the-light-cone journal, July 2012

Spin dependence of the inclusive reaction p + p (polarized) → π0 + X at 24 GeV/c for high-pT π0 produced in the central region journal, August 1980

On the cancellation of long-distance, non-factorizing contributions to the Drell-Yan cross section journal, April 1983

Single spin asymmetry in inclusive pion production, Collins effect and the string model journal, February 1997

Transverse momentum distribution of partons in QCD journal, November 1977

Intrinsic transverse momentum and the polarized Drell-Yan process text, January 1994

Foundations of Perturbative QCD book, May 2011

Comparison of spin asymmetries and cross sections in π0 production by 200 GeV polarized antiprotons and protons journal, May 1991

Factorization for short distance hadron-hadron scattering journal, January 1985

Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution journal, June 2011

Back-to-back jets: Fourier transform from b to kT journal, April 1982

Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum text, January 2008

Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-Nucleus Collisions journal, August 1977

No generalized transverse momentum dependent factorization in the hadroproduction of high transverse momentum hadrons journal, May 2010

Single-spin asymmetry in inclusive reactions p ↑ +p→ π + +X, π − +X, and p+X at 13.3 and 18.5 GeV/ c journal, February 1990

Time-reversal odd distribution functions in leptoproduction text, January 1997

Transverse momentum distribution in Drell-Yan pair and W and Z boson production journal, January 1985

Universality of T-odd effects in single spin and azimuthal asymmetries journal, September 2003

Nonperturbative regime in QCD resummation for gauge boson production at hadron colliders journal, October 1994

Production of High-Mass Muon Pairs in Proton-Nucleus Collisions at 400 GeV journal, November 1976

Vector-boson production at hadron colliders: hard-collinear coefficients at the NNLO journal, November 2012

Effects of QCD resummation on distributions of leptons from the decay of electroweak vector bosons journal, August 1995

Next-to-leading order hard scattering using fully unintegrated parton distribution functions journal, October 2008

Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production text, January 2005

Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum journal, August 2008

Semi-inclusive hadron production at DESY HERA: The effect of QCD gluon resummation journal, November 1999

Role of the nonperturbative input in QCD resummed Drell-Yan Q T distributions journal, April 2001

Parton distribution and decay functions journal, January 1982

Theory of W and Z boson production conference, January 2005

The Nonperturbative Regime in QCD Resummation for Gauge Boson Production at Hadron Colliders text, January 1993

Fully unintegrated parton correlation functions and factorization in lowest-order hard scattering journal, April 2008

Universality of the Collins–Soper–Sterman nonperturbative function in vector boson production journal, February 2006

Next-to-Next-to-Leading-Order Logarithmic Corrections at Small Transverse Momentum in Hadronic Collisions journal, November 2000

Measurements of the $W$ Boson Mass with the D0 Detector dissertation, August 2013

Endpoint singularities in unintegrated parton distributions journal, October 2007

Azimuthal dependence in leptoproduction: A simple parton model calculation journal, September 1978

Small transverse momentum distributions in hard processes journal, August 1979

Angular dependences in inclusive two-hadron production at BELLE journal, January 2009

Semi-inclusive deeply inelastic scattering at electron-proton colliders journal, March 1992

Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory
journal, May 2010

Fragmentation of transversely polarized quarks probed in transverse momentum distributions
journal, May 1993

Sudakov suppression in azimuthal spin asymmetries
journal, June 2001

Three-dimensional imaging of the nucleon and semi-inclusive high-energy reactions
journal, December 2015

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, February 1996

Measurement of Asymmetries of Inclusive Pion Production in Proton-Proton Interactions at 6 and 11.8 GeV/ c
journal, April 1976

Angular dependences in inclusive two-hadron production at BELLE
journal, January 2009

Intrinsic transverse momentum: Nongauge theories
journal, May 1980

Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering
journal, May 2002

Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
journal, July 2012

Effects of QCD resummation on distributions of leptons from the decay of electroweak vector bosons
journal, August 1995

QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum
journal, February 2005

Resummation for polarized semi-inclusive deep-inelastic scattering at small transverse momentum
journal, June 2006

Full transverse-momentum spectra of low-mass Drell-Yan pairs at LHC energies
text, January 2003

Wilson lines and transverse-momentum dependent parton distribution functions: A renormalization-group analysis
journal, October 2008

Single spin asymmetry in inclusive pion production, Collins effect and the string model
preprint, January 1994

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes
journal, February 2015

QCD evolution of the Sivers function
journal, February 2012

Gauge link structure in quark–quark correlators in hard processes
journal, August 2004

Algorithm to compute corrections to the Sudakov form factor
journal, September 1980

The parton orbital angular momentum: Status and prospects
journal, June 2016

New fits for the non-perturbative parameters in the CSS resummation formalism
journal, December 2000

Semi-inclusive deeply inelastic scattering at small $q_{T}$
journal, August 1996

Transverse momentum distributions in the nonperturbative region
journal, July 2011

Theory of W and Z boson production
text, January 2004

Universality of Soft and Collinear Factors in Hard-Scattering Factorization
journal, December 2004

$k_{T}$ factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions
journal, June 2007

QCD evolution in the fully unintegrated form
text, January 2009

QCD factorization for spin-dependent cross sections in DIS and Drell–Yan processes at low transverse momentum
journal, September 2004

Single-spin production asymmetries from the hard scattering of pointlike constituents
journal, January 1990

Hard processes in quantum chromodynamics
journal, February 1980

Leptoproduction of heavy quarks. II. A unified QCD formulation of charged and neutral current processes from fixed-target to collider energies
journal, September 1994

Does the Drell-Yan cross section factorize?
journal, March 1982

Back-to-back jets in QCD
journal, December 1981

Evolution of the helicity and transversity. Transverse-momentum-dependent parton distributions
journal, October 2013

Infrared divergences and non-lightlike eikonal lines in Sudakov processes
journal, January 2000

Extra spin asymmetries from the breakdown of transverse-momentum-dependent factorization in hadron-hadron collisions
journal, July 2013

The structure of large logarithmic corrections at small transverse momentum in hadronic collisions
journal, November 2001

Factorization theorem for Drell-Yan at low q T and transverse-momentum distributions on-the-light-cone
journal, July 2012

Spin dependence of the inclusive reaction p + p (polarized) → π0 + X at 24 GeV/c for high-pT π0 produced in the central region
journal, August 1980

On the cancellation of long-distance, non-factorizing contributions to the Drell-Yan cross section
journal, April 1983

Single spin asymmetry in inclusive pion production, Collins effect and the string model
journal, February 1997

Transverse momentum distribution of partons in QCD
journal, November 1977

Intrinsic transverse momentum and the polarized Drell-Yan process
text, January 1994

Foundations of Perturbative QCD
book, May 2011

Comparison of spin asymmetries and cross sections in π0 production by 200 GeV polarized antiprotons and protons
journal, May 1991

Factorization for short distance hadron-hadron scattering
journal, January 1985

Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution
journal, June 2011

Back-to-back jets: Fourier transform from b to kT
journal, April 1982

Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum
text, January 2008

Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-Nucleus Collisions
journal, August 1977

No generalized transverse momentum dependent factorization in the hadroproduction of high transverse momentum hadrons
journal, May 2010

Single-spin asymmetry in inclusive reactions $p_{↑}$ +p→ $π^{+}$ +X, $π^{-}$ +X, and p+X at 13.3 and 18.5 GeV/ c
journal, February 1990

Time-reversal odd distribution functions in leptoproduction
text, January 1997

Transverse momentum distribution in Drell-Yan pair and W and Z boson production
journal, January 1985

Universality of T-odd effects in single spin and azimuthal asymmetries
journal, September 2003

Nonperturbative regime in QCD resummation for gauge boson production at hadron colliders
journal, October 1994

Production of High-Mass Muon Pairs in Proton-Nucleus Collisions at 400 GeV
journal, November 1976

Vector-boson production at hadron colliders: hard-collinear coefficients at the NNLO
journal, November 2012

Effects of QCD resummation on distributions of leptons from the decay of electroweak vector bosons
journal, August 1995

Next-to-leading order hard scattering using fully unintegrated parton distribution functions
journal, October 2008

Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production
text, January 2005

Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum
journal, August 2008

Semi-inclusive hadron production at DESY HERA: The effect of QCD gluon resummation
journal, November 1999

Role of the nonperturbative input in QCD resummed Drell-Yan $Q_{T}$ distributions
journal, April 2001

Parton distribution and decay functions
journal, January 1982

Theory of W and Z boson production
conference, January 2005

The Nonperturbative Regime in QCD Resummation for Gauge Boson Production at Hadron Colliders
text, January 1993

Fully unintegrated parton correlation functions and factorization in lowest-order hard scattering
journal, April 2008

Universality of the Collins–Soper–Sterman nonperturbative function in vector boson production
journal, February 2006

Next-to-Next-to-Leading-Order Logarithmic Corrections at Small Transverse Momentum in Hadronic Collisions
journal, November 2000

Measurements of the $W$ Boson Mass with the D0 Detector
dissertation, August 2013

Endpoint singularities in unintegrated parton distributions
journal, October 2007

Azimuthal dependence in leptoproduction: A simple parton model calculation
journal, September 1978

Small transverse momentum distributions in hard processes
journal, August 1979

Angular dependences in inclusive two-hadron production at BELLE
journal, January 2009

Semi-inclusive deeply inelastic scattering at electron-proton colliders
journal, March 1992

Drell-Yan model at measured QT: Asymptotic smallness of one-loop corrections
journal, January 1980

"Table 13" of "Single Spin Asymmetry in Inclusive Reactions Polarized $P$, $P$ Goes to $\pi^+$, $\pi^-$, and $P$ at High $P$(t) at 13.3-{GeV}/$c$ and 18.5-{GeV}/$c$"
dataset, January 1990

Factorization of the Drell-Yan cross section in perturbation theory
journal, May 1985