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Title of Journal: J High Energ Phys

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Abbravation: Journal of High Energy Physics

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Springer Berlin Heidelberg

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DOI

10.1016/0021-9673(71)80019-5

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1029-8479

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Local integrals for planar scattering amplitudes

Authors: N ArkaniHamed J Bourjaily F Cachazo J Trnka
Publish Date: 2012/06/22
Volume: 2012, Issue: 6, Pages: 125-
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Abstract

Recently an explicit recursive formula for the allloop integrand of planar scattering amplitudes in mathcalN = 4 SYM has been described generalizing the BCFW formula for tree amplitudes and making manifest the Yangian symmetry of the theory This has made it possible to easily study the structure of multiloop amplitudes in the theory In this paper we describe a remarkable fact revealed by these investigations the integrand can be expressed in an amazingly simple and manifestly local form when represented in momentumtwistor space using a set of chiral integrals with unit leading singularities As examples we present veryconcise expressions for all 2 and 3loop MHV integrands as well as all 2loop NMHV integrands We also describe a natural set of manifestly IRfinite integrals that can be used to express IRsafe objects such as the ratio function Along the way we give a pedagogical introduction to the foundations of the subject The new local forms of the integrand are closely connected to leading singularities — matching only a small subset of all leading singularities remarkably suffices to determine the full integrand These results strongly suggest the existence of a theory for the integrand directly yielding these local expressions allowing for a more direct understanding of the emergence of local spacetime physics

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