On the integrand-reduction method for two-loop scattering amplitudes

• Published in: The journal of high energy physics Vol. 2011; no. 11
• Main Authors: Mastrolia, Pierpaolo, Ossola, Giovanni
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.11.2011; Springer Nature B.V
• Subjects: Algorithms; Amplitudes; Classical and Quantum Gravitation; Elementary Particles; Gauge theory; High energy physics; Integrals; Physics; Physics and Astronomy; Polynomials; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Reduction; Relativity Theory; Residues; Scattering; String Theory; NLO Computations; Standard Model; QCD
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2011)014

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 SYM. The technique hereby discussed extends the well-established analogous method holding for one-loop amplitudes, and can be considered a preliminary study towards the systematic reduction at the integrand-level of two-loop amplitudes in any gauge theory, suitable for their automated semianalytic evaluation.