A new approach to the momentum expansion of multiloop Feynman diagrams

Abstract

We present a new method for the momentum expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function for the coefficients of the small momentum expansion of an arbitrary diagram. The method is applicable for the expansion w.r.t. all or a subset of external momenta. The coefficients of the expansion are obtained by applying a differential operator to a given integral with shifted value of the space-time dimension $d$ and the expansion momenta set equal to zero. Integrals with changed $d$ are evaluated by using the generalized recurrence relations proposed in \cite{OVT1}. We show how the method works for one- and two-loop integrals. It is also illustrated that our method is simpler and more efficient than others.