Abstract
We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero- through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals, and show how discrete symmetries of these varieties largely determine the constraints.
Highlights
Last year’s discovery [1,2] by the ATLAS and CMS Collaborations of a Higgs-like boson completes the particle content of the Standard Model
In this paper we have extended the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs
We have constructed generalized discontinuity operators which isolate each of the four master integrals, annihilating all others
Summary
Last year’s discovery [1,2] by the ATLAS and CMS Collaborations of a Higgs-like boson completes the particle content of the Standard Model. We will use a more intensive form or “maximal” form of generalized unitarity In this approach, one cuts as many propagators as possible and further seeks to fully localize integrands onto global poles to the extent possible. One cuts as many propagators as possible and further seeks to fully localize integrands onto global poles to the extent possible In principle, this allows one to isolate individual integrals on the right-hand side of the higher-loop analog of Eq (1.1). In previous papers [79,80], we showed how to extract the coefficients of double-box master integrals using multidimensional contours around global poles.
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