Unitarity relation and unitarity bounds for scalars with different sound speeds

TL;DR

This paper derives unitarity relations and bounds for scalar fields with different sound speeds, providing tools to estimate the strong coupling scale in related effective field theories, with explicit calculations in a simple two-scalar model.

Contribution

It introduces unitarity relations for scalars with different sound speeds and derives bounds applicable to their effective field theories, extending previous work limited to unit sound speed.

Findings

Derived explicit unitarity relations for scalars with different sound speeds.

Established unitarity bounds for general and special cases.

Performed explicit calculations in a two-scalar model to illustrate the relations.

Abstract

Motivated by scalar-tensor gravities, we consider a theory which contains massless scalar fields with different sound speeds. We derive unitarity relations for partial wave amplitudes of $2 \to 2$ scattering, with explicit formulas for contributions of two-particle intermediate states. Making use of these relations, we obtain unitarity bounds both in the most general case and in the case considered in literature for unit sound speed. These bounds can be used for estimating the strong coupling scale of a pertinent EFT. We illustrate our unitarity relations by explicit calculation to the first non-trivial order in couplings in a simple model of two scalar fields with different sound speeds.