Scalar one-loop 4-point integrals

Abstract

We provide a complete set of results for the scalar 4-point function appearing in one-loop calculations in QCD, QED, the electroweak Standard Model and popular extensions thereof. Complex internal masses, which are needed for calculations involving unstable particles, are supported throughout, whereas complex momenta are not supported. In particular, for the most general, regular case we present two independent results in terms of 72 and 32 dilogarithms. In addition we list explicit results for all soft- and/or collinear-singular cases in dimensional regularization, mass regularization, and in regularizations of mixed type. The exceptional case with a vanishing modified Cayley determinant, which hardly appears in applications, is not considered.