Scalar one-loop 4-point integrals

TL;DR

This paper provides comprehensive formulas for scalar one-loop 4-point integrals used in quantum field theory calculations, supporting complex internal masses and covering various regularization schemes.

Contribution

It offers new, explicit results for scalar 4-point functions with complex masses, including multiple regularization methods, enhancing computational tools in particle physics.

Findings

Two independent formulas with 72 and 32 dilogarithms for the general case.

Explicit results for soft and collinear singularities in various regularizations.

Support for complex internal masses in the calculations.

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.