Two-loop rational terms in Yang-Mills theories

• Published in: The journal of high energy physics Vol. 2020; no. 10; pp. 1 - 53
• Main Authors: Lang, Jean-Nicolas, Pozzorini, Stefano, Zhang, Hantian, Zoller, Max F.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020; Springer Nature B.V; SpringerOpen
• Subjects: Amplitudes; Classical and Quantum Gravitation; Dependence; Elementary Particles; Fermions; Gauge theory; High energy physics; Perturbative QCD; Physics; Physics and Astronomy; Precision QED; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; String Theory; Scattering Amplitudes; Precision QED; Perturbative QCD
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2020)016

A bstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the ( D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [ 1 ] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the ( D− 4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to n f fermions with arbitrary masses.