Integrand reduction of one-loop scattering amplitudes through Laurent series expansion

Abstract

We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master integrals are the solutions of a diagonal system of equations, properly corrected by counterterms whose parametric form is konwn a priori. The Laurent expansion of the integrand is implemented through polynomial division. The extension of the integrand-reduction to the case of numerators with rank larger than the number of propagators is discussed as well.

Comments: v2: Published version: references and two appendices added. v3: Eq.(6.11) corrected, Appendix B updated accordingly