Generalized elastic positivity bounds on interacting massive spin-2 theories

TL;DR

This paper develops generalized elastic positivity bounds involving inelastic scattering to constrain parameter spaces of multi-field spin-2 theories, excluding certain operators and bounding Wilson coefficients in various models.

Contribution

It introduces generalized bounds that incorporate inelastic amplitudes with different masses, providing new constraints on spin-2 effective field theories beyond traditional elastic bounds.

Findings

Excluded previously unconstrained operators in pseudo-linear theory.

Bounded parameter space in cycle and line spin-2 theories.

Provided visualizations of the finite allowed regions for Wilson coefficients.

Abstract

We use generalized elastic positivity bounds to constrain the parameter space of multi-field spin-2 effective field theories. These generalized bounds involve inelastic scattering amplitudes between particles with different masses, which contain kinematic singularities even in the $t=0$ limit. We apply these bounds to the pseudo-linear spin-2 theory, the cycle spin-2 theory and the line spin-2 theory respectively. For the pseudo-linear theory, we exclude the remaining operators that are unconstrained by the usual elastic positivity bounds, thus excluding all the leading (or highest cutoff) interacting operators in the theory. For the cycle and line theory, our approach also provides new bounds on the Wilson coefficients previously unconstrained, bounding the parameter space in both theories to be a finite region ({\it i.e.}, every Wilson coefficient being constrained from both sides). To help visualize these finite regions, we sample various cross sections of them and estimate the total volumes.