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On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes · Around

2011

On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes

Mastrolia, Pierpaolo, Ossola, Giovanni

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We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes.

We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop momenta, and that the reduction of the amplitudes in terms of master integrals can be realized through polynomial fitting of the integrand, without any apriori knowledge of the integral basis.
We discuss how the polynomial shapes of the residues determine the basis of master integrals appearing in the final result.
We present a four-dimensional constructive algorithm that we apply to planar and non-planar contributions to the 4- and 5-point MHV amplitudes in N=4 SYM.

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