T. Riemann

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.

Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N⩾6. A general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N−1)-point Feynman integrals of rank (R−1) (for N⩾6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization.