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Numerical approaches to computations typically reconstruct the numerators ofFeynman diagrams in four dimensions. In doing so, certain rational termsarising from the (D-4)-dimensional part of the numerator multiplyingultraviolet (UV) poles in dimensional regularisation are not captured and needto be obtained by other means. At one-loop these rational terms of UV origincan be computed from a set of process-independent Feynman rules. Recently, itwas shown that this approach can be extended to two loops. In this paper, weshow that to all loop orders it is possible to compute rational terms of UVorigin through process-independent vertices that are polynomial in masses andmomenta.

Rational terms of UV origin to all loop orders