Scalar one-loop four-point Feynman integrals with complex internal masses

Abstract Based on Kreimer’s method [Z. Phys. C 54, 667 (1992) and Int. J. Mod. Phys. A 8, 1797 (1993)], we present analytic results for scalar one-loop four-point Feynman integrals with complex internal masses. The results are not only valid for complex internal masses, but also for real internal mass cases. Unlike the traditional approach proposed by ’t Hooft and Veltman [Nucl. Phys. B 153, 365 (1979)], this method can be extended to evaluate tensor integrals directly. Therefore, it may provide a new approach to solve the inverse Gram determinant problem analytically. We then implement the results into a computer package, ONELOOP4PT.CPP. In numerical checks, we compare the program to LoopTools version $2.12$ in both real and complex mass cases. We find a perfect agreement between the results generated from this work and LoopTools.