Determining arbitrary Feynman integrals by vacuum integrals

By introducing an auxiliary parameter, we find a new representation for Feynman integrals, which defines a Feynman integral by analytical continuation of a series containing only vacuum integrals. The new representation therefore conceptually translates the problem of computing Feynman integrals to the problem of performing analytical continuations. As an application of the new representation, we use it to construct a novel reduction method for multiloop Feynman integrals, which is expected to be more efficient than the known integration-by-parts reduction method. Using the new method, we successfully reduced all complicated two-loop integrals in the gg -> HH process and gg -> ggg process.