Efficient Computation of One-Loop Feynman Integrals and Fixed-Branch Integrals to High Orders in $\epsilon$

Abstract

We propose a novel method, called the dimension-changing transformation (DCT), to compute one-loop Feynman integrals and recently introduced fixed-branch integrals to arbitrary orders in $\epsilon$. The DCT relates one-loop Feynman integrals or fixed-branch integrals in one spacetime dimension to their corresponding quantities with auxiliary mass in any other dimension, making the expansion to high orders in $\epsilon$ highly efficient. We applied this method to several examples to demonstrate its validity and efficiency. The approach introduced in this work has been implemented in an open-source C++ package, available at \href{https://gitlab.com/multiloop-pku/dct}{https://gitlab.com/multiloop-pku/dct}.