skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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:
 [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
  1. RWTH Aachen Univ., Aachen (Germany)
  2. Illinois Inst. of Technology, Chicago, IL (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
  3. Albert-Ludwigs-Univ., Freiburg (Germany)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
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.
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. doi:10.1007/JHEP06(2019)121.
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. doi:10.1007/JHEP06(2019)121. https://www.osti.gov/servlets/purl/1529333.
@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 = {2019},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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


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

  • Harlander, Robert V.; Neumann, Tobias
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)161

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

  • Nogueira, P.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 559, Issue 1
  • DOI: 10.1016/j.nima.2005.11.151

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

  • Wang, Paul S.
  • Proceedings of the fourth ACM symposium on Symbolic and algebraic computation - SYMSAC '81
  • DOI: 10.1145/800206.806398

Version 3 of RunDec and CRunDec
journal, March 2018


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

  • Fousse, Laurent; Hanrot, Guillaume; Lefèvre, Vincent
  • ACM Transactions on Mathematical Software, Vol. 33, Issue 2
  • DOI: 10.1145/1236463.1236468

Fast Solvers for Dense Linear Systems
journal, October 2008


Scale Setting in Lattice QCD
conference, April 2014

  • Sommer, Rainer
  • Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)
  • DOI: 10.22323/1.187.0015

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

  • Luescher, Martin
  • Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)
  • DOI: 10.22323/1.187.0016

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


Wilson flow and renormalization
conference, May 2015

  • Ramos, Alberto
  • Proceedings of The 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)
  • DOI: 10.22323/1.214.0017

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


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

  • Genz, A. C.; Malik, A. A.
  • SIAM Journal on Numerical Analysis, Vol. 20, Issue 3
  • DOI: 10.1137/0720038

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

  • Borsányi, Szabolcs; Dürr, Stephan; Fodor, Zoltán
  • Journal of High Energy Physics, Vol. 2012, Issue 9
  • DOI: 10.1007/JHEP09(2012)010

Quasi parton distributions and the gradient flow
journal, March 2017

  • Monahan, Christopher; Orginos, Kostas
  • Journal of High Energy Physics, Vol. 2017, Issue 3
  • DOI: 10.1007/JHEP03(2017)116

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

  • Lambrou, Eliana
  • Proceedings of 34th annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)
  • DOI: 10.22323/1.256.0196

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