Efficient computation of one-loop Feynman integrals and fixed-branch integrals to high orders in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ε</mml:mi></mml:math>

We propose a novel method, called the dimension-changing transformation (), to compute one-loop Feynman integrals and recently introduced fixed-branch integrals to arbitrary orders in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ε</a:mi></a:math>. The relates one-loop Feynman integrals or fixed-branch integrals in a desired spacetime dimension to their corresponding quantities with auxiliary mass in any other dimension, making the expansion to high orders in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>ε</c:mi></c:math> 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 ++ package, along with several examples to demonstrate its efficiency.