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Efficient Computation of One-Loop Feynman Integrals and Fixed-Branch Integrals to High Orders in ε
Rui-Jun Huang, Dong-Shan Jian, Yan-Qing Ma, Dao-Ming Mu, Wen-Hao Wu
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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 ϵ. 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 ϵ 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}.
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