O n l i n e T a l k : 20-May-2021
Two-Loop Rational Terms
Efficient numerical algorithms for the construction of one-loop amplitudes have played a crucial role in the automation of NLO calculations, and similar algorithms at two-loop level are highly desirable in order to achieve the precision of theoretical predictions required for the LHC.
Numerical tools construct the numerator of loop integrals in four dimensions, while the missing contributions stemming from the interplay of (D-4)-dimensional numerator parts with 1/(D-4) poles have to bereconstructed separately. At one-loop level a well-established method is to restore these contributions through process-independent rational counterterms.
In this talk we extend the concept of rational terms of UV origin to two loops. We present a master formula for the computation of D-dimensional two-loop scattering amplitudes from amplitudes with four-dimensional numerators and a finite set of universal rational counterterms. A generic method to compute such rational terms from simple tadpole integrals will be discussed, as well as the renormalisation scheme dependence of rational terms. Finally, we present the complete set of two-loop rational terms in SU(N) and U(1) gauge theories in a generic renormalisation scheme.