An overview of transverse momentum dependent factorization and evolution

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:: 2016-06-17

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

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

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.  doi: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.  doi: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         = {2016},

  month        = {6}

}

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DOI: 10.1140/epja/i2016-16153-7

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On the breaking of collinear factorization in QCD
journal, November 2012

Forshaw, Jeffrey R.; Seymour, Michael H.; Siódmok, Andrzej
Journal of High Energy Physics, Vol. 2012, Issue 11
DOI: 10.1007/JHEP11(2012)066

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

Rogers, Ted C.
Physical Review D, Vol. 88, Issue 1
DOI: 10.1103/PhysRevD.88.014002

Gaining analytic control of parton showers
journal, December 2007

Bauer, Christian W.; Tackmann, Frank J.
Physical Review D, Vol. 76, Issue 11
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Fully unintegrated parton correlation functions and factorization in lowest-order hard scattering
journal, April 2008

Collins, J. C.; Rogers, T. C.; Staśto, A. M.
Physical Review D, Vol. 77, Issue 8
DOI: 10.1103/PhysRevD.77.085009

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

Rogers, Ted C.
Physical Review D, Vol. 78, Issue 7
DOI: 10.1103/PhysRevD.78.074018

Fully-unintegrated parton distribution and fragmentation functions at perturbative k⊥
journal, April 2012

Jain, Ambar; Procura, Massimiliano; Waalewijn, Wouter J.
Journal of High Energy Physics, Vol. 2012, Issue 4
DOI: 10.1007/JHEP04(2012)132

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In this paper, we study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in e⁺e^- annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins- Soper-Sterman (CSS) formalism, we extract transversity distributions for u and d quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in e⁺e^- annihilations measured by BELLE and BABAR Collaborations and SIDIS datamore »« less
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Title: An overview of transverse momentum dependent factorization and evolution

Abstract

Citation Formats

Parton distribution and decay functions journal, January 1982

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

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

Factorization for one-loop corrections in the Drell-Yan process journal, August 1983

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

Quantum-chromodynamic approach for the large-transverse-momentum production of particles and jets journal, November 1978

Observation of High-Mass Dilepton Pairs in Hadron Collisions at 400 GeV journal, May 1976

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

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

Observation of Structure in the ϒ Region journal, November 1977

Transverse momentum distribution of partons in QCD journal, November 1977

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

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

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

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

Asymmetries in inclusive proton-nucleon scattering at 11.75 GeV/ c journal, December 1978

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

Observation of significant spin effects in hard collisions at 40 GeV/c journal, July 1990

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

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

Analyzing power in inclusive π+ and π− production at high xF with a 200 GeV polarized proton beam journal, August 1991

The spin structure of the nucleon journal, April 2013

Qcd Evolution and Tmd/Spin Experiments journal, January 2012

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

Intrinsic transverse momentum and the polarized Drell-Yan process journal, April 1995

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

Time-reversal odd distribution functions in leptoproduction journal, May 1998

Phenomenology of single spin asymmetries in p ↑ p → π X journal, August 1999

Azimuthal asymmetry in lepton-proton scattering at high energies journal, January 1992

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

Hard processes in quantum chromodynamics journal, February 1980

Hard semi-inclusive processes in QCD journal, September 1978

Small transverse momentum distributions in hard processes journal, August 1979

Partons and Their Transverse Momenta in Quantum Chromodynamics journal, December 1979

Intrinsic transverse momentum: Nongauge theories journal, May 1980

Sudakov suppression in azimuthal spin asymmetries journal, June 2001

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

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

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

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

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

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

Phenomenology of multiple parton radiation in semi-inclusive deep-inelastic scattering journal, November 2001

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

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

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

Production of dimuons from high-energy polarized proton-proton collisions journal, May 1979

Initial-State Interactions and the Drell-Yan Process journal, December 1981

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

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

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

Factorization is not violated journal, October 1998

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

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

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

Soft gluon effects on lepton pairs at hadron colliders journal, November 1997

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

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

Full transverse-momentum spectra of low-mass Drell–Yan pairs at LHC energies journal, August 2003

Fermilab Tevatron run-1 Z boson data and the Collins-Soper-Sterman resummation formalism journal, April 2003

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

Theory of W and Z boson production conference, January 2005

Nonperturbative contributions to a resummed leptonic angular distribution in inclusive neutral vector boson production journal, July 2014

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering journal, March 2002

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

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

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

Universality of non-leading logarithmic contributions in transverse-momentum distributions journal, February 2001

Vector Boson Production at Hadron Colliders: A Fully Exclusive QCD Calculation at Next-to-Next-to-Leading Order journal, August 2009

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

Production of Drell–Yan lepton pairs in hadron collisions: Transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy journal, January 2011

Universality of transverse-momentum resummation and hard factors at the NNLO journal, April 2014

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

Final state interactions and gauge invariant parton distributions journal, April 2003

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

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

The construction of gauge-links in arbitrary hard processes journal, May 2006

Parton distribution and decay functions
journal, January 1982

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

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

Factorization for one-loop corrections in the Drell-Yan process
journal, August 1983

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

Quantum-chromodynamic approach for the large-transverse-momentum production of particles and jets
journal, November 1978

Observation of High-Mass Dilepton Pairs in Hadron Collisions at 400 GeV
journal, May 1976

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

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

Observation of Structure in the $ϒ$ Region
journal, November 1977

Transverse momentum distribution of partons in QCD
journal, November 1977

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

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

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

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

Asymmetries in inclusive proton-nucleon scattering at 11.75 GeV/ c
journal, December 1978

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

Observation of significant spin effects in hard collisions at 40 GeV/c
journal, July 1990

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

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

Analyzing power in inclusive π+ and π− production at high xF with a 200 GeV polarized proton beam
journal, August 1991

The spin structure of the nucleon
journal, April 2013

Qcd Evolution and Tmd/Spin Experiments
journal, January 2012

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

Intrinsic transverse momentum and the polarized Drell-Yan process
journal, April 1995

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

Time-reversal odd distribution functions in leptoproduction
journal, May 1998

Phenomenology of single spin asymmetries in $p^{↑} \vec{p} π X$
journal, August 1999

Azimuthal asymmetry in lepton-proton scattering at high energies
journal, January 1992

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

Hard processes in quantum chromodynamics
journal, February 1980

Hard semi-inclusive processes in QCD
journal, September 1978

Small transverse momentum distributions in hard processes
journal, August 1979

Partons and Their Transverse Momenta in Quantum Chromodynamics
journal, December 1979

Intrinsic transverse momentum: Nongauge theories
journal, May 1980

Sudakov suppression in azimuthal spin asymmetries
journal, June 2001

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

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

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

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

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

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

Phenomenology of multiple parton radiation in semi-inclusive deep-inelastic scattering
journal, November 2001

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

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

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

Production of dimuons from high-energy polarized proton-proton collisions
journal, May 1979

Initial-State Interactions and the Drell-Yan Process
journal, December 1981

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

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

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

Factorization is not violated
journal, October 1998

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

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

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

Soft gluon effects on lepton pairs at hadron colliders
journal, November 1997

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

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

Full transverse-momentum spectra of low-mass Drell–Yan pairs at LHC energies
journal, August 2003

Fermilab Tevatron run-1 Z boson data and the Collins-Soper-Sterman resummation formalism
journal, April 2003

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

Theory of W and Z boson production
conference, January 2005

Nonperturbative contributions to a resummed leptonic angular distribution in inclusive neutral vector boson production
journal, July 2014

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering
journal, March 2002

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

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

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

Universality of non-leading logarithmic contributions in transverse-momentum distributions
journal, February 2001

Vector Boson Production at Hadron Colliders: A Fully Exclusive QCD Calculation at Next-to-Next-to-Leading Order
journal, August 2009

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

Production of Drell–Yan lepton pairs in hadron collisions: Transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy
journal, January 2011

Universality of transverse-momentum resummation and hard factors at the NNLO
journal, April 2014

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

Final state interactions and gauge invariant parton distributions
journal, April 2003

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

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

The construction of gauge-links in arbitrary hard processes
journal, May 2006

Renormalization, Wilson lines, and transverse-momentum-dependent parton-distribution functions
journal, May 2008

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

Endpoint singularities in unintegrated parton distributions
journal, October 2007