A simple method for multi-leg loop calculations

Abstract

In this paper, I present a technique to simplify the tensorial reduction of one-loop integrals with arbitrary internal masses, but at least two massless external legs. By applying the method to rank l tensor integrals, one ends up with at most rank 1 tensor functions with the initial number of denominators, plus tensor integrals with less denominators and rank < l. To illustrate the algorithm, I explicitly compute diagrams contributing to processes of physical interest and show how the usual numerical instabilities due to the appearance of Gram determinants can be controlled.

22 pages, latex file, uses axodraw.sty. The paper has been reorganized and the method extended in n dimensions

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• Connection between Feynman integrals having different values of the space-time dimension
• Final state QCD corrections to off-shell single top production in hadron collisions
• CC10 at $\mathcal{O}({\alpha }_s)$: QCD corrections to $e^{+}{e}^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }u\bar{d}$ at LEP2 and the Next Linear Collider

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