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

TL;DR

The paper introduces the dimension-changing transformation (DCT), a new method that efficiently computes one-loop Feynman integrals and fixed-branch integrals to high orders in epsilon by relating different spacetime dimensions.

Contribution

The novel DCT method relates integrals across dimensions, enabling high-order epsilon expansions efficiently, and is implemented in an open-source C++ package.

Findings

Demonstrated validity and efficiency through multiple examples

Enabled high-order epsilon expansions in one-loop integrals

Provided an open-source implementation for broad use

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}.