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

Journal Article · 23 June 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP06(2019)121 · OSTI ID:1529333

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)

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.

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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: AC02-07CH11359

OSTI ID:: 1529333

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

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 6 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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