Exploring the S-Matrix of Massless Particles

TL;DR

This paper investigates the space of tree-level scattering amplitudes for massless particles in four dimensions using a generalized on-shell approach, revealing known theories and hints of possible high-spin couplings.

Contribution

It extends the on-shell representation framework to systematically explore consistent couplings, including potential high-spin interactions, at tree level.

Findings

Reconstructed all known theories from three-particle amplitudes.

Identified signatures suggesting the existence of high-spin couplings.

Proposed a framework that could be adapted to search for new theories.

Abstract

We use the recently proposed generalised on-shell representation for scattering amplitudes and a consistency test to explore the space of tree-level consistent couplings in four-dimensional Minkowski spacetime. The extension of the constructible notion implied by the generalised on-shell representation, i.e. the possibility to reconstruct at tree level all the scattering amplitudes from the three-particle ones, together with the imposition of the consistency conditions at four-particle level, allow to rediscover all the known theories and their algebra structure, if any. Interestingly, this analysis seems to leave room for high-spin couplings, provided that at least the requirement of locality is weakened. We do not claim to have found tree-level consistent high-spin theories, but rather that our methods show signatures of them and very likely, with a suitable modification, they can be a good framework to perform a systematic search.