Renormalization and matching for the Collins-Soper kernel from lattice QCD

Ebert, Markus A.; Stewart, Iain W.; Zhao, Yong

doi:10.1007/JHEP03(2020)099

Title: Renormalization and matching for the Collins-Soper kernel from lattice QCD

Abstract

The Collins-Soper kernel, which governs the energy evolution of transverse- momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI'/MOM) scheme, as well as the conversion factor from the RI'/MOM-renormalized quasi-TMDPDF to the $ \overline{\mathrm{MS}} $ scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.

Authors:

^[1]; Stewart, Iain W. ^[1]; Zhao, Yong ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)

Publication Date:: Tue Mar 17 00:00:00 EDT 2020

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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

OSTI Identifier:: 1614987

Alternate Identifier(s):: OSTI ID: 1635608

Report Number(s):: BNL-213837-2020-JAAM
Journal ID: ISSN 1029-8479; TRN: US2106330

Grant/Contract Number:: SC0012704; SC0011090

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 3; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; lattice field theory simulation; QCD phenomenology; parton; distribution function; quantum chromodynamics; lattice; renormalization; transverse momentum dependence; correlation function; transverse momentum; Drell-Yan process; Wilson loop; Euclidean

Citation Formats


                    Ebert, Markus A., Stewart, Iain W., and Zhao, Yong. Renormalization and matching for the Collins-Soper kernel from lattice QCD.  United States: N. p., 2020. 
Web.  doi:10.1007/JHEP03(2020)099.

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                    Ebert, Markus A., Stewart, Iain W., & Zhao, Yong. Renormalization and matching for the Collins-Soper kernel from lattice QCD.  United States.  https://doi.org/10.1007/JHEP03(2020)099

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                    Ebert, Markus A., Stewart, Iain W., and Zhao, Yong. Tue .  
"Renormalization and matching for the Collins-Soper kernel from lattice QCD".  United States.  https://doi.org/10.1007/JHEP03(2020)099.  https://www.osti.gov/servlets/purl/1614987.

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@article{osti_1614987,

  title        = {Renormalization and matching for the Collins-Soper kernel from lattice QCD},

  author       = {Ebert, Markus A. and Stewart, Iain W. and Zhao, Yong},

  abstractNote = {The Collins-Soper kernel, which governs the energy evolution of transverse- momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI'/MOM) scheme, as well as the conversion factor from the RI'/MOM-renormalized quasi-TMDPDF to the \( \overline{\mathrm{MS}} \) scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.},

  doi          = {10.1007/JHEP03(2020)099},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 3,

  volume       = 2020,

  place        = {United States},

  year         = {Tue Mar 17 00:00:00 EDT 2020},

  month        = {Tue Mar 17 00:00:00 EDT 2020}

}

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Similar Records

Title: Renormalization and matching for the Collins-Soper kernel from lattice QCD

Abstract

Citation Formats

The three-loop splitting functions in QCD: the singlet case journal, July 2004

Lattice QCD calculations of nucleon transverse momentum-dependent parton distributions using clover and domain wall fermions conference, July 2016

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

Renormalization of quasiparton distribution journal, August 2015

The three-loop splitting functions in QCD: the non-singlet case journal, June 2004

Leading and next-to-leading large-$n_f$ terms in the cusp anomalous dimension and quark-antiquark potential conference, October 2016

Parton Physics on a Euclidean Lattice journal, June 2013

Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all journal, September 2016

One-loop matching for parton distributions: Nonsinglet case journal, July 2014

Lattice perturbation theory journal, July 2003

Erratum to: Higgs boson production at hadron colliders: hard-collinear coefficients at the NNLO journal, August 2012

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

Calculation of the transverse parton distribution functions at next-to-next-to-leading order journal, June 2014

Rapidity renormalized TMD soft and beam functions at two loops journal, March 2016

Universal transverse momentum dependent soft function at NNLO journal, March 2016

Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order journal, September 2016

Transverse parton distribution and fragmentation functions at NNLO: the quark case journal, October 2019

Transverse parton distribution and fragmentation functions at NNLO: the gluon case journal, January 2020

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

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

Non-perturbative QCD effects in q T spectra of Drell-Yan and Z-boson production journal, November 2014

Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production journal, June 2017

Analysis of vector boson production within TMD factorization journal, January 2018

Exploring quark transverse momentum distributions with lattice QCD journal, May 2011

Sivers and Boer-Mulders observables from lattice QCD journal, May 2012

Lattice QCD study of the Boer-Mulders effect in a pion journal, March 2016

Nucleon transverse momentum-dependent parton distributions in lattice QCD: Renormalization patterns and discretization effects journal, November 2017

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

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

Renormalization of the Wilson loops beyond the leading order journal, January 1987

Non-leading corrections to the Drell-Yan cross section at small transverse momentum journal, October 1984

Drell-Yan cross sections at small transverse momentum journal, January 1985

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

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

Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation journal, January 2017

Correspondence between Soft and Rapidity Anomalous Dimensions journal, February 2017

Four-loop non-singlet splitting functions in the planar limit and beyond journal, October 2017

On quartic colour factors in splitting functions and the gluon cusp anomalous dimension journal, July 2018

A planar four-loop form factor and cusp anomalous dimension in QCD journal, May 2016

Large- n f contributions to the four-loop splitting functions in QCD journal, February 2017

Four-loop photon quark form factor and cusp anomalous dimension in the large-N c limit of QCD journal, March 2017

Four-loop cusp anomalous dimension in QED journal, June 2018

Four-loop quark form factor with quartic fundamental colour factor journal, February 2019

Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles journal, May 2019

Power corrections and renormalons in Transverse Momentum Distributions journal, March 2017

Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production journal, June 2019

Pion-induced Drell-Yan processes within TMD factorization journal, October 2019

Parton physics from large-momentum effective field theory journal, May 2014

Extracting parton distribution functions from lattice QCD calculations journal, October 2018

QCD Factorization and PDFs from Lattice QCD Calculation journal, January 2015

One-loop matching for generalized parton distributions journal, July 2015

One-loop matching for transversity generalized parton distribution journal, September 2015

Nondipolar Wilson links for quasiparton distribution functions journal, October 2016

Improved quasi parton distribution through Wilson line renormalization journal, February 2017

Lattice corrections to the quark quasidistribution at one loop journal, May 2017

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements journal, July 2017

Perturbative renormalization of quasi-parton distribution functions journal, September 2017

Note on lattice regularization and equal-time correlators for parton distribution functions journal, July 2017

More on large-momentum effective theory approach to parton physics journal, November 2017

Renormalization in Large Momentum Effective Theory of Parton Physics journal, March 2018

Renormalizability of quasiparton distribution functions journal, November 2017

Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field journal, July 2018

Gluon quasidistribution function at one loop journal, February 2018

Symmetry properties of nonlocal quark bilinear operators on a Lattice (LP 3 Collaboration) journal, September 2019

Matching the quasiparton distribution in a momentum subtraction scheme journal, March 2018

On the power divergence in quasi gluon distribution function journal, May 2018

Renormalization of Wilson-line operators in the presence of nonzero quark masses journal, July 2018

Factorization theorem relating Euclidean and light-cone parton distributions journal, September 2018

Light-cone distribution amplitudes of vector meson in a large momentum effective theory journal, June 2018

Euclidean versus Minkowski short distance journal, September 2018

Accessing Gluon Parton Distributions in Large Momentum Effective Theory journal, April 2019

Multiplicative Renormalizability of Operators defining Quasiparton Distributions journal, February 2019

Matching the meson quasidistribution amplitude in the RI/MOM scheme journal, May 2019

Nucleon helicity and transversity parton distributions from lattice QCD journal, October 2016

Target mass effects in parton quasi-distributions journal, July 2017

Power corrections and renormalons in parton quasidistributions journal, January 2019

The three-loop splitting functions in QCD: the singlet case
journal, July 2004

Lattice QCD calculations of nucleon transverse momentum-dependent parton distributions using clover and domain wall fermions
conference, July 2016

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

Renormalization of quasiparton distribution
journal, August 2015

The three-loop splitting functions in QCD: the non-singlet case
journal, June 2004

Leading and next-to-leading large-$n_f$ terms in the cusp anomalous dimension and quark-antiquark potential
conference, October 2016

Parton Physics on a Euclidean Lattice
journal, June 2013

Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all
journal, September 2016

One-loop matching for parton distributions: Nonsinglet case
journal, July 2014

Lattice perturbation theory
journal, July 2003

Erratum to: Higgs boson production at hadron colliders: hard-collinear coefficients at the NNLO
journal, August 2012

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

Calculation of the transverse parton distribution functions at next-to-next-to-leading order
journal, June 2014

Rapidity renormalized TMD soft and beam functions at two loops
journal, March 2016

Universal transverse momentum dependent soft function at NNLO
journal, March 2016

Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order
journal, September 2016

Transverse parton distribution and fragmentation functions at NNLO: the quark case
journal, October 2019

Transverse parton distribution and fragmentation functions at NNLO: the gluon case
journal, January 2020

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

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

Non-perturbative QCD effects in q T spectra of Drell-Yan and Z-boson production
journal, November 2014

Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production
journal, June 2017

Analysis of vector boson production within TMD factorization
journal, January 2018

Exploring quark transverse momentum distributions with lattice QCD
journal, May 2011

Sivers and Boer-Mulders observables from lattice QCD
journal, May 2012

Lattice QCD study of the Boer-Mulders effect in a pion
journal, March 2016

Nucleon transverse momentum-dependent parton distributions in lattice QCD: Renormalization patterns and discretization effects
journal, November 2017

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

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

Renormalization of the Wilson loops beyond the leading order
journal, January 1987

Non-leading corrections to the Drell-Yan cross section at small transverse momentum
journal, October 1984

Drell-Yan cross sections at small transverse momentum
journal, January 1985

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

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

Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation
journal, January 2017

Correspondence between Soft and Rapidity Anomalous Dimensions
journal, February 2017

Four-loop non-singlet splitting functions in the planar limit and beyond
journal, October 2017

On quartic colour factors in splitting functions and the gluon cusp anomalous dimension
journal, July 2018

A planar four-loop form factor and cusp anomalous dimension in QCD
journal, May 2016

Large- n f contributions to the four-loop splitting functions in QCD
journal, February 2017

Four-loop photon quark form factor and cusp anomalous dimension in the large-N c limit of QCD
journal, March 2017

Four-loop cusp anomalous dimension in QED
journal, June 2018

Four-loop quark form factor with quartic fundamental colour factor
journal, February 2019

Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
journal, May 2019

Power corrections and renormalons in Transverse Momentum Distributions
journal, March 2017

Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
journal, June 2019

Pion-induced Drell-Yan processes within TMD factorization
journal, October 2019

Parton physics from large-momentum effective field theory
journal, May 2014

Extracting parton distribution functions from lattice QCD calculations
journal, October 2018

QCD Factorization and PDFs from Lattice QCD Calculation
journal, January 2015

One-loop matching for generalized parton distributions
journal, July 2015

One-loop matching for transversity generalized parton distribution
journal, September 2015

Nondipolar Wilson links for quasiparton distribution functions
journal, October 2016

Improved quasi parton distribution through Wilson line renormalization
journal, February 2017

Lattice corrections to the quark quasidistribution at one loop
journal, May 2017

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements
journal, July 2017

Perturbative renormalization of quasi-parton distribution functions
journal, September 2017

Note on lattice regularization and equal-time correlators for parton distribution functions
journal, July 2017

More on large-momentum effective theory approach to parton physics
journal, November 2017

Renormalization in Large Momentum Effective Theory of Parton Physics
journal, March 2018

Renormalizability of quasiparton distribution functions
journal, November 2017

Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field
journal, July 2018

Gluon quasidistribution function at one loop
journal, February 2018

Symmetry properties of nonlocal quark bilinear operators on a Lattice (LP ³ Collaboration)
journal, September 2019

Matching the quasiparton distribution in a momentum subtraction scheme
journal, March 2018

On the power divergence in quasi gluon distribution function
journal, May 2018

Renormalization of Wilson-line operators in the presence of nonzero quark masses
journal, July 2018

Factorization theorem relating Euclidean and light-cone parton distributions
journal, September 2018

Light-cone distribution amplitudes of vector meson in a large momentum effective theory
journal, June 2018

Euclidean versus Minkowski short distance
journal, September 2018

Accessing Gluon Parton Distributions in Large Momentum Effective Theory
journal, April 2019

Multiplicative Renormalizability of Operators defining Quasiparton Distributions
journal, February 2019

Matching the meson quasidistribution amplitude in the RI/MOM scheme
journal, May 2019

Nucleon helicity and transversity parton distributions from lattice QCD
journal, October 2016

Target mass effects in parton quasi-distributions
journal, July 2017

Power corrections and renormalons in parton quasidistributions
journal, January 2019

Flavor structure of the nucleon sea from lattice QCD
journal, March 2015

Lattice calculation of parton distributions
journal, July 2015

Updated lattice results for parton distributions
journal, July 2017