# Determining arbitrary Feynman integrals by vacuum integrals

Liu, Xiao (School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China) ; Ma, Yan-Qing (School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China) (Center for High Energy Physics, Peking University, Beijing 100871, China) (Collaborative Innovation Center of Quantum Matter, Beijing 100871, China)

12 April 2019

Abstract: 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 $gg\to HH$ process and $gg\to ggg$ process.

Published in: Physical Review D 99 (2019)