Journal
NUCLEAR PHYSICS B
Volume 580, Issue 1-2, Pages 577-601Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/S0550-3213(00)00251-0
Keywords
master integrals; tensor reduction; two-loop integrals; crossed box; crossed triangle; dimensional regularization
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The class of the two-loop massless crossed boxes, with light-like external legs, is the final unresolved issue in the program of computing the scattering amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order. In this paper, we describe an algorithm for the tensor reduction of such diagrams. After connecting tensor integrals to scalar ones with arbitrary powers of propagators in higher dimensions, we derive recurrence relations from integration-by-parts and Lorentz-invariance identities, that allow us to write the scalar integrals as a combination of two master crossed boxes plus simpler-topology diagrams. We derive the system of differential equations that the two master integrals satisfy using two different methods, and we use one of these equations to express the second master integral as a function of the first one, already known in the literature. We then give the analytic expansion of the second master integral as a function of epsilon = (4 - D)/2, where D is the space-time dimension, up to order O(epsilon(0)). (C) 2000 Elsevier Science B.V. All rights reserved.
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