Simplifying 5-point tensor reduction

Abstract

The 5-point tensors have the property that after insertion of the metric tensor $g^{\mu \nu }$ in terms of external momenta, all $g^{\mu \nu }$-contributions in the tensor decomposition cancel. If furthermore the tensors are contracted with external momenta, the inverse 5-point Gram determinant $({)}_5$ cancels automatically. If the remaining 4-point sub-Gram determinant ${\left(\genfrac{}{}{0ex}{}{s}{s}\right)}_5$ is not small then this approach appears to be particularly efficient in numerical calculations. We also indicate how to deal with small ${\left(\genfrac{}{}{0ex}{}{s}{s}\right)}_5$. Explicit formulae for tensors of degree 2 and 3 are given for large and small (sub-) Gram determinants.

Comments: 8 pages, Talk presented at XXXV International Conference of Theoretical Physics Matter to the Deepest: Recent Developments in Physics of Fundamental Interactions, Ustron'11