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

TL;DR

This paper introduces new on-shell recursion relations for tree-level scattering amplitudes of massless particles, enabling their reconstruction from poles, zeroes, and three-particle amplitudes, applicable to any non-trivial massless theory.

Contribution

It develops a generalized recursion framework incorporating boundary terms via zeroes, extending BCFW relations to broader theories of massless particles.

Findings

Recursion relations valid for any non-trivial massless particle theory.

Amplitudes reconstructed from poles, zeroes, and three-particle amplitudes.

Boundary terms expressed as sums over products of lower-point amplitudes.

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.