Results and techniques for higher order calculations within the gradient-flow formalism

Artz, Johannes; Harlander, Robert V.; Lange, Fabian; Neumann, Tobias; Prausa, Mario

doi:10.1007/JHEP06(2019)121

Title: Results and techniques for higher order calculations within the gradient-flow formalism

Abstract

We describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of the five-dimensional field theory and the composite operators considered in this paper. Tools from standard perturbative calculations are used to obtain Green's functions at finite flow time $$t$$ at higher orders in perturbation theory. The three-loop results for the quark condensate at finite $$t$$ and the conversion factor for the "ringed" quark fields to the $$\overline{\mbox{MS}}$$ scheme are presented as applications. We also re-evaluate an earlier result for the three-loop gluon condensate, improving on its accuracy.

Authors:

Artz, Johannes ^[1];

^[1];

^[2];

^[3]

RWTH Aachen Univ., Aachen (Germany)
Illinois Inst. of Technology, Chicago, IL (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Albert-Ludwigs-Univ., Freiburg (Germany)

Publication Date:: Mon Jun 24 00:00:00 EDT 2019

Research Org.:: Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1529333

Report Number(s):: arXiv:1905.00882; FERMILAB-PUB-19-151-T; FR-PHENO-2019-003; IIT-CAPP-19-02; TTK-19-15
Journal ID: ISSN 1029-8479; 1732898

Grant/Contract Number:: AC02-07CH11359

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: 2019; Journal Issue: 6; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Perturbative QCD

Citation Formats


                    Artz, Johannes, Harlander, Robert V., Lange, Fabian, Neumann, Tobias, and Prausa, Mario. Results and techniques for higher order calculations within the gradient-flow formalism.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP06(2019)121.

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                    Artz, Johannes, Harlander, Robert V., Lange, Fabian, Neumann, Tobias, & Prausa, Mario. Results and techniques for higher order calculations within the gradient-flow formalism.  United States.  https://doi.org/10.1007/JHEP06(2019)121

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                    Artz, Johannes, Harlander, Robert V., Lange, Fabian, Neumann, Tobias, and Prausa, Mario. Mon .  
"Results and techniques for higher order calculations within the gradient-flow formalism".  United States.  https://doi.org/10.1007/JHEP06(2019)121.  https://www.osti.gov/servlets/purl/1529333.

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@article{osti_1529333,

  title        = {Results and techniques for higher order calculations within the gradient-flow formalism},

  author       = {Artz, Johannes and Harlander, Robert V. and Lange, Fabian and Neumann, Tobias and Prausa, Mario},

  abstractNote = {We describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of the five-dimensional field theory and the composite operators considered in this paper. Tools from standard perturbative calculations are used to obtain Green's functions at finite flow time $t$ at higher orders in perturbation theory. The three-loop results for the quark condensate at finite $t$ and the conversion factor for the "ringed" quark fields to the $\overline{\mbox{MS}}$ scheme are presented as applications. We also re-evaluate an earlier result for the three-loop gluon condensate, improving on its accuracy.},

  doi          = {10.1007/JHEP06(2019)121},

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

  number       = 6,

  volume       = 2019,

  place        = {United States},

  year         = {Mon Jun 24 00:00:00 EDT 2019},

  month        = {Mon Jun 24 00:00:00 EDT 2019}

}

Copy to clipboard

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Works referenced in this record:

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Title: Results and techniques for higher order calculations within the gradient-flow formalism

Abstract

Citation Formats

Chiral symmetry and the Yang-Mills gradient flow journal, April 2013

The perturbative QCD gradient flow to three loops journal, June 2016

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses dataset, January 2019

HypExp 2, expanding hypergeometric functions about half-integer parameters journal, April 2012

Automatic Feynman Graph Generation journal, April 1993

HypExp 2, Expanding hypergeometric functions about half-integer parameters journal, May 2008

Trivializing Maps, the Wilson Flow and the HMC Algorithm journal, November 2009

Abusing qgraf journal, April 2006

Finding linear dependencies in integration-by-parts equations: A Monte Carlo approach journal, May 2014

A p-adic algorithm for univariate partial fractions conference, January 1981

Version 3 of RunDec and CRunDec journal, March 2018

MPFR: A multiple-precision binary floating-point library with correct rounding journal, June 2007

FORM version 4.0 journal, May 2013

Fast Solvers for Dense Linear Systems journal, October 2008

Scale Setting in Lattice QCD conference, April 2014

Future applications of the Yang-Mills gradient flow in lattice QCD conference, April 2014

Perturbative analysis of the gradient flow in non-abelian gauge theories journal, February 2011

A theorem on analytical calculability of 4-loop renormalization group functions journal, March 1981

Multiple polylogarithms, cyclotomy and modular complexes journal, January 1998

Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals journal, March 2015

The perturbative QCD gradient flow to three loops text, January 2016

Wilson flow and renormalization conference, May 2015

Scattering amplitudes over finite fields and multivariate functional reconstruction journal, December 2016

An Imbedded Family of Fully Symmetric Numerical Integration Rules journal, June 1983

Flow equation for the large N scalar model and induced geometries journal, August 2016

High-precision scale setting in lattice QCD journal, September 2012

Quasi parton distributions and the gradient flow journal, March 2017

Determining $\alpha_s$ by using the gradient flow in the quenched theory conference, March 2017

Geometries from field theories journal, October 2015

Ti k Z-Feynman: Feynman diagrams with Ti k Z journal, January 2017

FIESTA 3: Cluster-parallelizable multiloop numerical calculations in physical regions journal, July 2014

On hyperlogarithms and Feynman integrals with divergences and many scales journal, March 2014

Infinite N phase transitions in continuum Wilson loop operators journal, March 2006

AdS geometry from CFT on a general conformally flat manifold journal, August 2018

Flow equation, conformal symmetry, and anti-de Sitter geometry journal, March 2018

Holographic geometry for nonrelativistic systems emerging from generalized flow equations journal, June 2019

Energy–momentum tensor from the Yang–Mills gradient flow journal, August 2013

Lattice energy-momentum tensor from the Yang-Mills gradient flow--inclusion of fermion fields journal, June 2014

The two-loop energy–momentum tensor within the gradient-flow formalism journal, November 2018

Thermodynamics in quenched QCD: energy–momentum tensor with two-loop order coefficients in the gradient-flow formalism journal, February 2019

Smeared quasidistributions in perturbation theory journal, March 2018

Corrections of to the decay of the Z boson into bottom quarks journal, April 1998

Group Theory Factors for Feynman Diagrams journal, January 1999

Integration by parts: The algorithm to calculate β-functions in 4 loops journal, November 1981

High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations journal, December 2000

Kira—A Feynman integral reduction program journal, September 2018

Numerical evaluation of multi-loop integrals by sector decomposition journal, March 2004

HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters journal, July 2006

Gradient flow and the Wilsonian renormalization group flow journal, May 2018

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses journal, December 2000

Special values of multiple polylogarithms journal, October 2000

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses dataset, January 2019

Perturbative analysis of the gradient flow in non-abelian gauge theories text, January 2011

FORM version 4.0 text, January 2012

Future applications of the Yang-Mills gradient flow in lattice QCD preprint, January 2013

Geometries from field theories text, January 2015

TikZ-Feynman: Feynman diagrams with TikZ text, January 2016

Scattering amplitudes over finite fields and multivariate functional reconstruction text, January 2016

Chiral symmetry and the Yang-Mills gradient flow
journal, April 2013

The perturbative QCD gradient flow to three loops
journal, June 2016

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
dataset, January 2019

HypExp 2, expanding hypergeometric functions about half-integer parameters
journal, April 2012

Automatic Feynman Graph Generation
journal, April 1993

HypExp 2, Expanding hypergeometric functions about half-integer parameters
journal, May 2008

Trivializing Maps, the Wilson Flow and the HMC Algorithm
journal, November 2009

Abusing qgraf
journal, April 2006

Finding linear dependencies in integration-by-parts equations: A Monte Carlo approach
journal, May 2014

A p-adic algorithm for univariate partial fractions
conference, January 1981

Version 3 of RunDec and CRunDec
journal, March 2018

MPFR: A multiple-precision binary floating-point library with correct rounding
journal, June 2007

FORM version 4.0
journal, May 2013

Fast Solvers for Dense Linear Systems
journal, October 2008

Scale Setting in Lattice QCD
conference, April 2014

Future applications of the Yang-Mills gradient flow in lattice QCD
conference, April 2014

Perturbative analysis of the gradient flow in non-abelian gauge theories
journal, February 2011

A theorem on analytical calculability of 4-loop renormalization group functions
journal, March 1981

Multiple polylogarithms, cyclotomy and modular complexes
journal, January 1998

Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
journal, March 2015

The perturbative QCD gradient flow to three loops
text, January 2016

Wilson flow and renormalization
conference, May 2015

Scattering amplitudes over finite fields and multivariate functional reconstruction
journal, December 2016

An Imbedded Family of Fully Symmetric Numerical Integration Rules
journal, June 1983

Flow equation for the large N scalar model and induced geometries
journal, August 2016

High-precision scale setting in lattice QCD
journal, September 2012

Quasi parton distributions and the gradient flow
journal, March 2017

Determining $\alpha_s$ by using the gradient flow in the quenched theory
conference, March 2017

Geometries from field theories
journal, October 2015

Ti k Z-Feynman: Feynman diagrams with Ti k Z
journal, January 2017

FIESTA 3: Cluster-parallelizable multiloop numerical calculations in physical regions
journal, July 2014

On hyperlogarithms and Feynman integrals with divergences and many scales
journal, March 2014

Infinite N phase transitions in continuum Wilson loop operators
journal, March 2006

AdS geometry from CFT on a general conformally flat manifold
journal, August 2018

Flow equation, conformal symmetry, and anti-de Sitter geometry
journal, March 2018

Holographic geometry for nonrelativistic systems emerging from generalized flow equations
journal, June 2019

Energy–momentum tensor from the Yang–Mills gradient flow
journal, August 2013

Lattice energy-momentum tensor from the Yang-Mills gradient flow--inclusion of fermion fields
journal, June 2014

The two-loop energy–momentum tensor within the gradient-flow formalism
journal, November 2018

Thermodynamics in quenched QCD: energy–momentum tensor with two-loop order coefficients in the gradient-flow formalism
journal, February 2019

Smeared quasidistributions in perturbation theory
journal, March 2018

Corrections of to the decay of the Z boson into bottom quarks
journal, April 1998

Group Theory Factors for Feynman Diagrams
journal, January 1999

Integration by parts: The algorithm to calculate β-functions in 4 loops
journal, November 1981

High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations
journal, December 2000

Kira—A Feynman integral reduction program
journal, September 2018

Numerical evaluation of multi-loop integrals by sector decomposition
journal, March 2004

HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
journal, July 2006

Gradient flow and the Wilsonian renormalization group flow
journal, May 2018

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
journal, December 2000

Special values of multiple polylogarithms
journal, October 2000

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
dataset, January 2019

Perturbative analysis of the gradient flow in non-abelian gauge theories
text, January 2011

FORM version 4.0
text, January 2012

Future applications of the Yang-Mills gradient flow in lattice QCD
preprint, January 2013

Geometries from field theories
text, January 2015

TikZ-Feynman: Feynman diagrams with TikZ
text, January 2016

Scattering amplitudes over finite fields and multivariate functional reconstruction
text, January 2016