Theory and applications of parton pseudodistributions

Radyushkin, A. V.

doi:10.1142/S0217751X20300021

Title: Theory and applications of parton pseudodistributions

Abstract

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator $M(z,p)$ of the parton fields is a function $M(ν,-z^2)$ of Lorentz invariants $ν=-(zp)$, the Ioffe time, and the invariant interval $z^2$. This observation allows to extract the Ioffe-time distribution $M(ν,-z^2)$ from Euclidean separations z accessible on the lattice. Another basic feature is the use of the ratio $M(ν,-z^2)≡M(ν,-z^2)/M(0,-z^2)$, that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining $z^2$-dependence of the reduced Ioffe-time distribution $M(ν,-z^2)$ corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions $f(x,μ^2)$ using matching relations. The ν-dependence of $M(ν,-z^2)$ governs the x-dependence of parton densities $f(x,μ^2)$. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now inmore » progress.« less

Authors:

^[1]

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

Publication Date:: 2020-02-20

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:: 1604344

Report Number(s):: JLAB-THY-19-3118; DOE/OR-23177-4856; arXiv:1912.04244
Journal ID: ISSN 0217-751X; TRN: US2104226

Grant/Contract Number:: FG02-97ER41028; AC05-06OR23177

Resource Type:: Accepted Manuscript

Journal Name:: International Journal of Modern Physics A

Additional Journal Information:: Journal Volume: 35; Journal Issue: 05; Journal ID: ISSN 0217-751X

Publisher:: World Scientific

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Parton distributions; lattice; quantum chromodynamics

Citation Formats


                    Radyushkin, A. V. Theory and applications of parton pseudodistributions.  United States: N. p., 2020. 
Web.  doi:10.1142/S0217751X20300021.

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                    Radyushkin, A. V. Theory and applications of parton pseudodistributions.  United States.  https://doi.org/10.1142/S0217751X20300021

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                    Radyushkin, A. V. Thu .  
"Theory and applications of parton pseudodistributions".  United States.  https://doi.org/10.1142/S0217751X20300021.  https://www.osti.gov/servlets/purl/1604344.

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@article{osti_1604344,

  title        = {Theory and applications of parton pseudodistributions},

  author       = {Radyushkin, A. V.},

  abstractNote = {We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator $M(z,p)$ of the parton fields is a function $M(ν,-z^2)$ of Lorentz invariants $ν=-(zp)$, the Ioffe time, and the invariant interval $z^2$. This observation allows to extract the Ioffe-time distribution $M(ν,-z^2)$ from Euclidean separations z accessible on the lattice. Another basic feature is the use of the ratio $M(ν,-z^2)≡M(ν,-z^2)/M(0,-z^2)$, that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining $z^2$-dependence of the reduced Ioffe-time distribution $M(ν,-z^2)$ corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions $f(x,μ^2)$ using matching relations. The ν-dependence of $M(ν,-z^2)$ governs the x-dependence of parton densities $f(x,μ^2)$. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.},

  doi          = {10.1142/S0217751X20300021},

  journal      = {International Journal of Modern Physics A},

  number       = 05,

  volume       = 35,

  place        = {United States},

  year         = {2020},

  month        = {2}

}

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Title: Theory and applications of parton pseudodistributions

Abstract

Citation Formats

Exclusive processes in position space and the pion distribution amplitude journal, May 2008

Mass corrections to scaling in deep inelastic processes journal, December 1976

Constraints on large- x parton distributions from new weak boson production and deep-inelastic scattering data journal, June 2016

Moments of Ioffe time parton distribution functions from non-local matrix elements journal, November 2018

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

Structure of parton quasi-distributions and their moments journal, January 2019

Unraveling high-energy hadron structures with lattice QCD journal, December 2018

Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations journal, January 2018

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

Virtuality and transverse momentum dependence of the pion distribution amplitude journal, March 2016

Positivity constraints for anomalous dimensions journal, October 1973

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

Parton distribution functions from Ioffe time pseudo-distributions journal, December 2019

Short-distance and light-cone expansions for products of currents journal, November 1978

Gauge-Invariant Decomposition of Nucleon Spin journal, January 1997

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

Renormalization of loop functions for all loops journal, August 1981

Ioffe-time distributions instead of parton momentum distributions in the description of deep inelastic scattering journal, June 1995

On Gauge Invariance and Vacuum Polarization journal, June 1951

Parton distributions from high-precision collider data: NNPDF Collaboration journal, October 2017

Parton Physics on a Euclidean Lattice journal, June 2013

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

Renormalizability of phase factors in non-abelian gauge theory journal, July 1980

Renormalizability of quasiparton distribution functions journal, November 2017

Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks journal, April 2019

Unravelling higher twists journal, February 1983

Evolution equations for QCD string operators journal, January 1989

One-loop evolution of parton pseudo-distribution functions on the lattice journal, July 2018

Parton distributions in the LHC era: MMHT 2014 PDFs journal, May 2015

Parton distributions from lattice data: the nonsinglet case journal, October 2019

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results journal, June 2019

A Relativistic Equation for Bound-State Problems journal, December 1951

Hard processes, parton model and QCD journal, February 1980

Exclusive processes in perturbative quantum chromodynamics journal, November 1980

Gauge fields as rings of glue journal, January 1980

Freedom at moderate energies: Masses in color dynamics journal, October 1976

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

Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD journal, January 1994

Nonperturbative evolution of parton quasi-distributions journal, April 2017

Pion distribution amplitude and quasidistributions journal, March 2017

Nonforward parton distributions journal, November 1997

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

Deep-inelastic scattering and the operator product expansion in lattice QCD journal, January 2006

Renormalizability of the heavy quark effective theory journal, January 1994

A General Survey of the Theory of the Bethe-Salpeter Equation journal, January 1969

Lattice QCD exploration of parton pseudo-distribution functions journal, November 2017

Quark pseudodistributions at short distances journal, June 2018

Double distributions and evolution equations journal, December 1998

Parton distributions for the LHC journal, July 2009

Generalized parton distributions and pseudodistributions journal, December 2019

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point journal, June 2019

Asymptotic freedom in parton language journal, August 1977

Space-time picture of photon and neutrino scattering and electroproduction cross section asymptotics journal, September 1969

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions journal, August 2017

On spectral properties of parton correlation functions and multiparton wave functions journal, November 1983

Parton distribution functions from reduced Ioffe-time distributions journal, April 2018

Field theory approach to processes with large momentum transfer. III. Gauge theories journal, September 1980

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

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

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

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

Power corrections and renormalons in parton quasidistributions journal, January 2019

Pion valence structure from Ioffe-time parton pseudodistribution functions journal, December 2019

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

On the renormalization and short-distance properties of hadronic operators in QCD journal, July 1981

Updated lattice results for parton distributions journal, July 2017

The renormalization of the string operator in QCD journal, January 1982

Exclusive processes in position space and the pion distribution amplitude
journal, May 2008

Mass corrections to scaling in deep inelastic processes
journal, December 1976

Constraints on large- $x$ parton distributions from new weak boson production and deep-inelastic scattering data
journal, June 2016

Moments of Ioffe time parton distribution functions from non-local matrix elements
journal, November 2018

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

Structure of parton quasi-distributions and their moments
journal, January 2019

Unraveling high-energy hadron structures with lattice QCD
journal, December 2018

Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations
journal, January 2018

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

Virtuality and transverse momentum dependence of the pion distribution amplitude
journal, March 2016

Positivity constraints for anomalous dimensions
journal, October 1973

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

Parton distribution functions from Ioffe time pseudo-distributions
journal, December 2019

Short-distance and light-cone expansions for products of currents
journal, November 1978

Gauge-Invariant Decomposition of Nucleon Spin
journal, January 1997

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

Renormalization of loop functions for all loops
journal, August 1981

Ioffe-time distributions instead of parton momentum distributions in the description of deep inelastic scattering
journal, June 1995

On Gauge Invariance and Vacuum Polarization
journal, June 1951

Parton distributions from high-precision collider data: NNPDF Collaboration
journal, October 2017

Parton Physics on a Euclidean Lattice
journal, June 2013

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

Renormalizability of phase factors in non-abelian gauge theory
journal, July 1980

Renormalizability of quasiparton distribution functions
journal, November 2017

Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks
journal, April 2019

Unravelling higher twists
journal, February 1983

Evolution equations for QCD string operators
journal, January 1989

One-loop evolution of parton pseudo-distribution functions on the lattice
journal, July 2018

Parton distributions in the LHC era: MMHT 2014 PDFs
journal, May 2015

Parton distributions from lattice data: the nonsinglet case
journal, October 2019

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results
journal, June 2019

A Relativistic Equation for Bound-State Problems
journal, December 1951

Hard processes, parton model and QCD
journal, February 1980

Exclusive processes in perturbative quantum chromodynamics
journal, November 1980

Gauge fields as rings of glue
journal, January 1980

Freedom at moderate energies: Masses in color dynamics
journal, October 1976

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

Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD
journal, January 1994

Nonperturbative evolution of parton quasi-distributions
journal, April 2017

Pion distribution amplitude and quasidistributions
journal, March 2017

Nonforward parton distributions
journal, November 1997

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

Deep-inelastic scattering and the operator product expansion in lattice QCD
journal, January 2006

Renormalizability of the heavy quark effective theory
journal, January 1994

A General Survey of the Theory of the Bethe-Salpeter Equation
journal, January 1969

Lattice QCD exploration of parton pseudo-distribution functions
journal, November 2017

Quark pseudodistributions at short distances
journal, June 2018

Double distributions and evolution equations
journal, December 1998

Parton distributions for the LHC
journal, July 2009

Generalized parton distributions and pseudodistributions
journal, December 2019

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
journal, June 2019

Asymptotic freedom in parton language
journal, August 1977

Space-time picture of photon and neutrino scattering and electroproduction cross section asymptotics
journal, September 1969

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions
journal, August 2017

On spectral properties of parton correlation functions and multiparton wave functions
journal, November 1983

Parton distribution functions from reduced Ioffe-time distributions
journal, April 2018

Field theory approach to processes with large momentum transfer. III. Gauge theories
journal, September 1980

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

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

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

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

Power corrections and renormalons in parton quasidistributions
journal, January 2019

Pion valence structure from Ioffe-time parton pseudodistribution functions
journal, December 2019

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

On the renormalization and short-distance properties of hadronic operators in QCD
journal, July 1981

Updated lattice results for parton distributions
journal, July 2017

The renormalization of the string operator in QCD
journal, January 1982