The Boostless Bootstrap and BCFW Momentum Shifts

TL;DR

This paper demonstrates how BCFW momentum shifts can independently verify boostless bootstrap results, providing a consistency check for three-particle interactions that lack Lorentz boost invariance, and clarifies the role of constructibility in this context.

Contribution

It introduces an alternative verification method using BCFW shifts for boostless bootstrap results, challenging the necessity of the constructibility criterion.

Findings

BCFW shifts can verify boostless bootstrap constraints

Constructibility is not essential for deriving non-trivial constraints

Provides a new consistency check for non-Lorentz-invariant interactions

Abstract

In a recent paper [1], three-particle interactions without invariance under Lorentz boosts were constrained by demanding that they yield tree-level four-particle scattering amplitudes with singularities as dictated by unitarity and locality. In this brief note, we show how to obtain an independent verification and consistency check of these boostless bootstrap results using BCFW momentum shifts. We point out that the constructibility criterion, related to the behaviour of the deformed amplitude at infinite BCFW parameter z, is not strictly necessary to obtain non-trivial constraints for the three-particle interactions.