# Positivity Bounds for Scalar Theories

## TL;DR

This paper derives an infinite set of positivity bounds on scalar field theories assuming a consistent UV completion, constraining low-energy parameters and potentially bounding the mass of new particles.

## Contribution

It introduces a novel set of positivity bounds for scalar theories based on amplitude properties, linking low-energy effective theory coefficients to UV completion constraints.

## Key findings

- Derived infinite positivity bounds on scalar amplitudes.
- Bounded operator coefficients in low-energy theories.
- Placed upper limits on masses of potential new particles.

## Abstract

Assuming the existence of a local, analytic, unitary UV completion in a Poincar\'{e} invariant scalar field theory with a mass gap, we derive an infinite number of positivity requirements using the known properties of the amplitude at and away from the forward scattering limit. These take the form of bounds on combinations of the pole subtracted scattering amplitude and its derivatives. In turn, these positivity requirements act as constraints on the operator coefficients in the low energy effective theory. For certain theories these constraints can be used to place an upper bound on the mass of the next lightest state that must lie beyond the low energy effective theory if such a UV completion is to ever exist.