The non-planar Feynman diagram with seven massless, scalar propagators and four on-shell legs (the crossed double box) is calculated analytically in dimensional regularization. The non-planar diagram with six propagators is also discussed.
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 ǫ = (4−D)/2, where D is the space-time dimension, up to order O ǫ 0 . 1
A useful connection between two-loop massive vacuum integrals and one-loop offshell triangle diagrams with massless internal particles is established for arbitrary values of the space-time dimension n.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.