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On the integrand-reduction method for two-loop scattering amplitudes. (English) Zbl 1306.81357

Summary: 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 \( \mathcal{N} = 4 \) 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 semi analytic evaluation.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81V22 Unified quantum theories
81T60 Supersymmetric field theories in quantum mechanics
81U05 \(2\)-body potential quantum scattering theory
81T18 Feynman diagrams
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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