Positivity Bounds for Massive Spin-1 and Spin-2 Fields

TL;DR

This paper applies positivity bounds to low-energy effective theories of massive spin-1 and spin-2 particles, revealing constraints that recover special tunings and structures in massive gravity models.

Contribution

It extends positivity bounds to non-forward scattering for massive spin-1 and spin-2 theories, uncovering new constraints and connections between different massive gravity models.

Findings

Positivity bounds impose special tunings in $ ext{Lambda}_5$ massive gravity.

The $ ext{Lambda}_3$ massive gravity theories are stable under further positivity bounds.

Positivity bounds recover the ghost-free structure of $ ext{Lambda}_3$ theories.

Abstract

We apply the recently developed positivity bounds for particles with spin, applied away from the forward limit, to the low energy effective theories of massive spin-1 and spin-2 theories. For spin-1 theories, we consider the generic Proca EFT which arises at low energies from a heavy Higgs mechanism, and the special case of a charged Galileon for which the EFT is reorganized by the Galileon symmetry. For spin-2, we consider generic $\Lambda_5$ massive gravity theories and the special `ghost-free' $\Lambda_3$ theories. Remarkably we find that at the level of 2-2 scattering, the positivity bounds applied to $\Lambda_5$ massive gravity theories impose the special tunings which generate the $\Lambda_3$ structure. For $\Lambda_3$ massive gravity theories, the island of positivity derived in the forward limit appears relatively stable against further bounds.