Causality bounds on scalar-tensor EFTs

TL;DR

This paper derives bounds on scalar-tensor effective field theories' Wilson coefficients using dispersion relations and crossing symmetry, providing constraints relevant for phenomenology and theoretical consistency.

Contribution

It introduces a method to compute causality and positivity bounds on scalar-tensor EFTs, including the scalar-Gauss-Bonnet couplings, by analyzing IR and UV scattering data.

Findings

Sharp bounds on scalar-Gauss-Bonnet couplings.

Wilson coefficients can be estimated from dispersion relations.

Bounds vary with the $( ext{partial}\phi)^4$ coefficient and have phenomenological implications.

Abstract

We compute the causality/positivity bounds on the Wilson coefficients of scalar-tensor effective field theories. Two-sided bounds are obtained by extracting IR information from UV physics via dispersion relations of scattering amplitudes, making use of the full crossing symmetry. The graviton $t$-channel pole is carefully treated in the numerical optimization, taking into account the constraints with fixed impact parameters. It is shown that the typical sizes of the Wilson coefficients can be estimated by simply inspecting the dispersion relations. We carve out sharp bounds on the leading coefficients, particularly, the scalar-Gauss-Bonnet couplings, and discuss how some bounds vary with the leading $(\partial\phi)^4$ coefficient and as well as phenomenological implications of the causality bounds.