On the Tree-Level Structure of Scattering Amplitudes of Massless Particles

Abstract

We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their poles and zeroes. The latter determine the boundary term arising in the BCFW-representation when the amplitudes do not vanish as some momenta are taken to infinity along some complex direction. Specifically, such a boundary term can be expressed as a sum of products of two on-shell amplitudes with fewer external states and a factor dependent on the location of the relevant zeroes and poles. This allows us to recast the amplitudes to have the standard BCFW-structure, weighted by a simple factor dependent on a subset of zeroes and poles of the amplitudes. We further comment on the physical interpretation of the zeroes as a particular kinematic limit in the complexified momentum space. The main implication of the existence of such recursion relations is that the tree-level approximation of any consistent theory of massless particles can be fully determined just by the knowledge of the corresponding three-particle amplitudes.

31 pages, 5 figures

References in corpus (7)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Amplitudes and Spinor-Helicity in Six Dimensions
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Taming Tree Amplitudes In General Relativity
• Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• On BCFW shifts of integrands and integrals

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