Rational terms of UV origin to all loop orders

Numerical approaches to computations typically reconstruct the numerators of Feynman diagrams in four dimensions. In doing so, certain rational terms arising from the (D − 4)-dimensional part of the numerator multiplying ultraviolet (UV) poles in dimensional regularisation are not captured and need to be obtained by other means. At one-loop these rational terms of UV origin can be computed from a set of process-independent Feynman rules. Recently, it was shown that this approach can be extended to two loops. In this paper, we show that to all loop orders it is possible to compute rational terms of UV origin through process-independent vertices that are polynomial in masses and momenta.