ITP South Building 6620

In this talk, I will discuss the generalisation of renormalisation procedure such that the renormalised two-loop amplitudes in D dimensions can be reconstructed by amplitudes with four dimensional numerators in loop integrands, which enables the numerical two-loop amplitudes constructions. Under this generalisation, the two-loop rational terms naturally emerge together with UV counterterms. I will further prove that the two-loop rational terms are local counterterms, and provide a generic method to compute them from massive one-scale tadpole integrals. The analytical results of QED two-loop rational terms will be presented at the end.