Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism

Collins, J.; Gamberg, L.; Prokudin, A.; Rogers, T. C.; Sato, N.; Wang, B.

doi:10.1103/PhysRevD.94.034014

Title: Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism

Abstract

We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W+Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and Q dependence of the cross sections at lower Q are largely governed by the matching to the Y term.

Authors:

Collins, J. ^[1]; Gamberg, L. ^[2]; Prokudin, A. ^[3]; Rogers, T. C. ^[4]; Sato, N. ^[5]; Wang, B. ^[4]

Pennsylvania State Univ., University Park, PA (United States)
Pennsylvania State Univ. Berks, Reading, PA (United States)
Pennsylvania State Univ. Berks, Reading, PA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Mon Aug 08 00:00:00 EDT 2016

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Pennsylvania State Univ. Berks, Reading, PA (United States)

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

OSTI Identifier:: 1294279

Alternate Identifier(s):: OSTI ID: 1286313; OSTI ID: 1905876

Report Number(s):: JLAB-THY-16-2245; DOE/OR/23177-3791; arXiv:1605.00671
Journal ID: ISSN 2470-0010; PRVDAQ; TRN: US1700136

Grant/Contract Number:: AC05-06OR23177; PHY-1623454; FG02-07ER41460; SC0008745

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Volume: 94; Journal Issue: 3; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Factorization, Perturbation theory, Quantum Chromodynamics

Citation Formats


                    Collins, J., Gamberg, L., Prokudin, A., Rogers, T. C., Sato, N., and Wang, B. Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevD.94.034014.

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                    Collins, J., Gamberg, L., Prokudin, A., Rogers, T. C., Sato, N., & Wang, B. Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism.  United States.  https://doi.org/10.1103/PhysRevD.94.034014

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                    Collins, J., Gamberg, L., Prokudin, A., Rogers, T. C., Sato, N., and Wang, B. Mon .  
"Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism".  United States.  https://doi.org/10.1103/PhysRevD.94.034014.  https://www.osti.gov/servlets/purl/1294279.

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@article{osti_1294279,

  title        = {Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism},

  author       = {Collins, J. and Gamberg, L. and Prokudin, A. and Rogers, T. C. and Sato, N. and Wang, B.},

  abstractNote = {We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W+Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and Q dependence of the cross sections at lower Q are largely governed by the matching to the Y term.},

  doi          = {10.1103/PhysRevD.94.034014},

  journal      = {Physical Review. D.},

  number       = 3,

  volume       = 94,

  place        = {United States},

  year         = {Mon Aug 08 00:00:00 EDT 2016},

  month        = {Mon Aug 08 00:00:00 EDT 2016}

}

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Works referenced in this record:

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Title: Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism

Abstract

Citation Formats

An overview of transverse-momentum-dependent factorization and evolution journal, June 2016

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

Small transverse momentum distributions in hard processes journal, August 1979

Parton distributions for high energy collisions journal, March 1992

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel text, January 2014

Soft-gluon resummation for high- p T inclusive-hadron production at COMPASS journal, July 2013

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

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

Model independent evolution of transverse momentum dependent distribution functions (TMDs) at NNLL journal, November 2013

Testing the universality of fragmentation functions journal, March 2001

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

Bessel-weighted asymmetries in semi-inclusive deep inelastic scattering journal, October 2011

Semi-Inclusive Deep Inelastic Scattering processes from small to large PT journal, March 2007

Phenomenology of TMDs journal, January 2015

TMD evolution and the Higgs transverse momentum distribution journal, September 2014

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

Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering text, January 2011

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

Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC journal, March 2006

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

Limits on transverse momentum dependent evolution from semi-inclusive deep inelastic scattering at moderate Q journal, May 2014

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

Unpolarised transverse momentum dependent distribution and fragmentation functions from SIDIS multiplicities journal, April 2014

Semi-Inclusive Deep Inelastic Scattering processes from small to large P_T text, January 2006

Drell–Yan production at small q T , transverse parton distributions and the collinear anomaly journal, June 2011

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes text, January 2014

Foundations of Perturbative QCD book, May 2011

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

Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering text, January 2007

W and Z production at next-to-leading order: From large qT to small journal, February 1991

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

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

Azimuthal asymmetry in lepton-proton scattering at high energies journal, October 1991

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel journal, April 2015

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

Testing the Universality of Fragmentation Functions text, January 2000

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

O ( α s 2 ) QCD corrections to the electroproduction of hadrons with high transverse momentum journal, February 2005

Soft gluon effects on lepton pairs at hadron colliders text, January 1997

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

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

Parton distribution and decay functions journal, January 1982

Intrinsic transverse momentum and parton correlations from dynamical chiral symmetry breaking text, January 2012

Intrinsic transverse momentum and parton correlations from dynamical chiral symmetry breaking journal, January 2013

Investigations into the flavor dependence of partonic transverse momentum journal, November 2013

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC journal, February 2020

Linearly polarized gluons in charmonium and bottomonium production in the color octet model journal, February 2017

Nonperturbative Uncertainties on the Transverse Momentum Distribution of Electroweak Bosons and on the Determination of the W Boson Mass at the LHC journal, March 2019

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC text, January 2019

Suppression of maximal linear gluon polarization in angular asymmetries text, January 2017

First Monte Carlo global analysis of nucleon transversity with lattice QCD constraints text, January 2017

A Short Review on Recent Developments in TMD Factorization and Implementation journal, May 2019

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

A short review on recent developments in TMD factorization and implementation preprint, January 2019

π - N Drell-Yan Process in TMD Factorization journal, January 2019

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

Sivers asymmetry in the pion induced Drell-Yan process at COMPASS within transverse momentum dependent factorization journal, March 2018

Drell–Yan production with the CCFM-K evolution journal, May 2020

On the connection between quark propagation and hadronization journal, September 2020

π - N Drell-Yan Process in TMD Factorization journal, January 2019

Studying the gluon TMDs with J/ψ- and Upsilon- pair production at the LHC conference, September 2019

Combining TMD factorization and collinear factorization preprint, January 2017

Transverse parton momenta in single inclusive hadron production in ${e^ + }{e^ - }$ annihilation processes text, January 2017

Non-perturbative uncertainties on the transverse momentum distribution of electroweak bosons and on the determination of the $W$ boson mass at the LHC preprint, January 2019

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC text, January 2019

Transverse-momentum-dependent parton distributions up to N$^3$LL from Drell-Yan data text, January 2019

Predictive power of transverse-momentum-dependent distributions text, January 2020

Jet-based measurements of Sivers and Collins asymmetries at the future Electron-Ion Collider text, January 2020

Calculation of transverse momentum dependent distributions beyond the leading power preprint, January 2020

Semi-inclusive deep-inelastic scattering in Wandzura-Wilczek-type approximation text, January 2019

An overview of transverse-momentum-dependent factorization and evolution
journal, June 2016

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

Small transverse momentum distributions in hard processes
journal, August 1979

Parton distributions for high energy collisions
journal, March 1992

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
text, January 2014

Soft-gluon resummation for high- $p_{T}$ inclusive-hadron production at COMPASS
journal, July 2013

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

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

Model independent evolution of transverse momentum dependent distribution functions (TMDs) at NNLL
journal, November 2013

Testing the universality of fragmentation functions
journal, March 2001

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

Bessel-weighted asymmetries in semi-inclusive deep inelastic scattering
journal, October 2011

Semi-Inclusive Deep Inelastic Scattering processes from small to large PT
journal, March 2007

Phenomenology of TMDs
journal, January 2015

TMD evolution and the Higgs transverse momentum distribution
journal, September 2014

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

Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering
text, January 2011

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

Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC
journal, March 2006

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

Limits on transverse momentum dependent evolution from semi-inclusive deep inelastic scattering at moderate $Q$
journal, May 2014

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

Unpolarised transverse momentum dependent distribution and fragmentation functions from SIDIS multiplicities
journal, April 2014

Semi-Inclusive Deep Inelastic Scattering processes from small to large P_T
text, January 2006

Drell–Yan production at small q T , transverse parton distributions and the collinear anomaly
journal, June 2011

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes
text, January 2014

Foundations of Perturbative QCD
book, May 2011

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

Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering
text, January 2007

W and Z production at next-to-leading order: From large qT to small
journal, February 1991

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

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

Azimuthal asymmetry in lepton-proton scattering at high energies
journal, October 1991

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
journal, April 2015

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

Testing the Universality of Fragmentation Functions
text, January 2000

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

$O (α_{s}^{2})$ QCD corrections to the electroproduction of hadrons with high transverse momentum
journal, February 2005

Soft gluon effects on lepton pairs at hadron colliders
text, January 1997

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

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

Parton distribution and decay functions
journal, January 1982

Intrinsic transverse momentum and parton correlations from dynamical chiral symmetry breaking
text, January 2012

Intrinsic transverse momentum and parton correlations from dynamical chiral symmetry breaking
journal, January 2013

Investigations into the flavor dependence of partonic transverse momentum
journal, November 2013

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC
journal, February 2020

Linearly polarized gluons in charmonium and bottomonium production in the color octet model
journal, February 2017

Nonperturbative Uncertainties on the Transverse Momentum Distribution of Electroweak Bosons and on the Determination of the $W$ Boson Mass at the LHC
journal, March 2019

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC
text, January 2019

Suppression of maximal linear gluon polarization in angular asymmetries
text, January 2017

First Monte Carlo global analysis of nucleon transversity with lattice QCD constraints
text, January 2017

A Short Review on Recent Developments in TMD Factorization and Implementation
journal, May 2019

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

A short review on recent developments in TMD factorization and implementation
preprint, January 2019

$π - N$ Drell-Yan Process in TMD Factorization
journal, January 2019

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

Sivers asymmetry in the pion induced Drell-Yan process at COMPASS within transverse momentum dependent factorization
journal, March 2018

Drell–Yan production with the CCFM-K evolution
journal, May 2020

On the connection between quark propagation and hadronization
journal, September 2020

$π - N$ Drell-Yan Process in TMD Factorization
journal, January 2019

Studying the gluon TMDs with J/ψ- and Upsilon- pair production at the LHC
conference, September 2019

Combining TMD factorization and collinear factorization
preprint, January 2017

Transverse parton momenta in single inclusive hadron production in ${e^ + }{e^ - }$ annihilation processes
text, January 2017

Non-perturbative uncertainties on the transverse momentum distribution of electroweak bosons and on the determination of the $W$ boson mass at the LHC
preprint, January 2019

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC
text, January 2019

Transverse-momentum-dependent parton distributions up to N$^3$LL from Drell-Yan data
text, January 2019

Predictive power of transverse-momentum-dependent distributions
text, January 2020

Jet-based measurements of Sivers and Collins asymmetries at the future Electron-Ion Collider
text, January 2020

Calculation of transverse momentum dependent distributions beyond the leading power
preprint, January 2020

Semi-inclusive deep-inelastic scattering in Wandzura-Wilczek-type approximation
text, January 2019