Complete reduction of one-loop tensor 5- and 6-point integrals

Abstract

We perform a complete analytical reduction of general one-loop Feynman integrals with five and six external legs for tensors up to rank $R=3$ and 4, respectively. An elegant formalism with extensive use of signed minors is developed for the cancellation of inverse Gram determinants. The 6-point tensor functions of rank $R$ are expressed in terms of 5-point tensor functions of rank $R\ensuremath{-}1$, and the latter are reduced to scalar four-, three-, and two-point functions. The resulting compact formulas allow both for a study of analytical properties and for efficient numerical programming. They are implemented in Fortran and Mathematica.