Results and techniques for higher order calculations within the gradientflow formalism
Abstract
We describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradientflow formalism. This includes a collection of all relevant Feynman rules of the fivedimensional 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 threeloop 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 reevaluate an earlier result for the threeloop gluon condensate, improving on its accuracy.
 Authors:

 RWTH Aachen Univ., Aachen (Germany)
 Illinois Inst. of Technology, Chicago, IL (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 AlbertLudwigsUniv., 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)
 OSTI Identifier:
 1529333
 Report Number(s):
 arXiv:1905.00882; FERMILABPUB19151T; FRPHENO2019003; IITCAPP1902; TTK1915
Journal ID: ISSN 10298479; 1732898
 Grant/Contract Number:
 AC0207CH11359
 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 10298479
 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 gradientflow 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 gradientflow formalism. United States. doi:https://doi.org/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 gradientflow formalism". United States. doi:https://doi.org/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 gradientflow 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 gradientflow formalism. This includes a collection of all relevant Feynman rules of the fivedimensional 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 threeloop 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 reevaluate an earlier result for the threeloop 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}
}
Web of Science
Works referenced in this record:
Chiral symmetry and the YangMills gradient flow
journal, April 2013
 Lüscher, Martin
 Journal of High Energy Physics, Vol. 2013, Issue 4
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
Automatic Feynman Graph Generation
journal, April 1993
 Nogueira, P.
 Journal of Computational Physics, Vol. 105, Issue 2
HypExp 2, Expanding hypergeometric functions about halfinteger parameters
journal, May 2008
 Huber, Tobias; Maître, Daniel
 Computer Physics Communications, Vol. 178, Issue 10
Trivializing Maps, the Wilson Flow and the HMC Algorithm
journal, November 2009
 Lüscher, Martin
 Communications in Mathematical Physics, Vol. 293, Issue 3
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
Finding linear dependencies in integrationbyparts equations: A Monte Carlo approach
journal, May 2014
 Kant, Philipp
 Computer Physics Communications, Vol. 185, Issue 5
A padic algorithm for univariate partial fractions
conference, January 1981
 Wang, Paul S.
 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation  SYMSAC '81
Version 3 of RunDec and CRunDec
journal, March 2018
 Herren, Florian; Steinhauser, Matthias
 Computer Physics Communications, Vol. 224
MPFR: A multipleprecision binary floatingpoint library with correct rounding
journal, June 2007
 Fousse, Laurent; Hanrot, Guillaume; Lefèvre, Vincent
 ACM Transactions on Mathematical Software, Vol. 33, Issue 2
Fast Solvers for Dense Linear Systems
journal, October 2008
 Kauers, Manuel
 Nuclear Physics B  Proceedings Supplements, Vol. 183
Scale Setting in Lattice QCD
conference, April 2014
 Sommer, Rainer
 Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)
Future applications of the YangMills gradient flow in lattice QCD
conference, April 2014
 Luescher, Martin
 Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)
Perturbative analysis of the gradient flow in nonabelian gauge theories
journal, February 2011
 Lüscher, Martin; Weisz, Peter
 Journal of High Energy Physics, Vol. 2011, Issue 2
A theorem on analytical calculability of 4loop renormalization group functions
journal, March 1981
 Tkachov, F. V.
 Physics Letters B, Vol. 100, Issue 1
Multiple polylogarithms, cyclotomy and modular complexes
journal, January 1998
 Goncharov, A. B.
 Mathematical Research Letters, Vol. 5, Issue 4
Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
journal, March 2015
 Panzer, Erik
 Computer Physics Communications, Vol. 188
Wilson flow and renormalization
conference, May 2015
 Ramos, Alberto
 Proceedings of The 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)
Scattering amplitudes over finite fields and multivariate functional reconstruction
journal, December 2016
 Peraro, Tiziano
 Journal of High Energy Physics, Vol. 2016, Issue 12
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
Highprecision scale setting in lattice QCD
journal, September 2012
 Borsányi, Szabolcs; Dürr, Stephan; Fodor, Zoltán
 Journal of High Energy Physics, Vol. 2012, Issue 9
Quasi parton distributions and the gradient flow
journal, March 2017
 Monahan, Christopher; Orginos, Kostas
 Journal of High Energy Physics, Vol. 2017, Issue 3
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)
Ti k ZFeynman: Feynman diagrams with Ti k Z
journal, January 2017
 Ellis, Joshua P.
 Computer Physics Communications, Vol. 210
FIESTA 3: Clusterparallelizable multiloop numerical calculations in physical regions
journal, July 2014
 Smirnov, A. V.
 Computer Physics Communications, Vol. 185, Issue 7
On hyperlogarithms and Feynman integrals with divergences and many scales
journal, March 2014
 Panzer, Erik
 Journal of High Energy Physics, Vol. 2014, Issue 3
Infinite N phase transitions in continuum Wilson loop operators
journal, March 2006
 Narayanan, Rajamani; Neuberger, Herbert
 Journal of High Energy Physics, Vol. 2006, Issue 03
HypExp 2, expanding hypergeometric functions about halfinteger parameters
journal, April 2012
 Huber, Tobias; Maître, Daniel
 Computer Physics Communications, Vol. 183, Issue 4
FORM version 4.0
journal, May 2013
 Kuipers, J.; Ueda, T.; Vermaseren, J. A. M.
 Computer Physics Communications, Vol. 184, Issue 5
Geometries from field theories
journal, October 2015
 Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya
 Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 10
Flow equation for the large N scalar model and induced geometries
journal, August 2016
 Aoki, Sinya; Balog, Janos; Onogi, Tetsuya
 Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 8
The perturbative QCD gradient flow to three loops
text, January 2016
 Harlander, Robert V.; Neumann, Tobias
 RWTH Aachen University