A recursive structure for the \eps-expansion of scalar one-loop integrals

by Paul Mork (Uni Bonn)

Wednesday 10 Jun 2026, 11:00 → 13:00 Europe/Berlin

Scalar one-loop Feynman integrals admit a geometric interpretation at \eps=0 as volumes of simplices in hyperbolic space, which are known in terms of multiple polylogarithms (MPLs). A natural question is how to compute the higher-order coefficients in the \eps-expansion of dimensionally regularised scalar one-loop integrals.

In this talk I discuss two complementary approaches to this problem. I briefly review a direct integration approach yielding MPL representations for triangle, box and pentagon integrals with arbitrary masses and kinematics. Afterwards, I present a recursive relation connecting the Laurent coefficients of an N-point integral to lower-order coefficients of integrals with more external legs.

Seeded by the corresponding integer-dimensional contributions, this recursion can then be iterated to arbitrary order in \eps, implying that every coefficient in the Laurent expansion of a dimensionally regularised scalar one-loop integral can be expressed in terms of MPLs.