New positivity bounds from full crossing symmetry

TL;DR

This paper derives new nonlinear positivity bounds for scalar effective field theories by leveraging full crossing symmetry, providing stronger constraints on Wilson coefficients and excluding certain theories from UV completion.

Contribution

It introduces several sets of nonlinear positivity bounds using full crossing symmetry, improving constraints on effective field theories beyond previous linear bounds.

Findings

Stronger bounds on Wilson coefficients than previous methods.

Excludes weakly broken Galileon theories from UV completion.

Provides tighter constraints on chiral perturbation theory coefficients.

Abstract

Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: We refer to these as the $PQ$, $D^{\rm su}$, $D^{\rm stu}$ and $\bar{D}^{\rm stu}$ bounds. While the $PQ$ bounds and $D^{\rm su}$ bounds only make use of the $s\leftrightarrow u$ dispersion relation, the $D^{\rm stu}$ and $\bar{D}^{\rm stu}$ bounds are obtained by further imposing the $s\leftrightarrow t$ crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.