Two-loop rational terms in Yang-Mills theories

Journal of High Energy Physics

Max F. Zoller¹  Stefano Pozzorini²  Hantian Zhang²  Jean-Nicolas Lang² 

[1] Paul Scherrer Institut, Forschungsstrasse 111, CH-5232, Villigen PSI, Switzerland;Physik-Institut, Universität Zürich, CH-8057, Zürich, Switzerland;

关键词: Perturbative QCD;    Precision QED;    Scattering Amplitudes;   

DOI  :  10.1007/JHEP10(2020)016

来源: Springer

【 摘 要 】

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 nf fermions with arbitrary masses.

【 授权许可】

CC BY