# Massive Higher Spins: Effective Theory and Consistency

## TL;DR

This paper develops an effective field theory for massive higher-spin particles, revealing constraints from positivity bounds that influence the theory's cutoff and highlight the significance of higher-derivative operators, with a detailed analysis of spin-3 particles.

## Contribution

It constructs the effective theory for massive higher-spin particles and uncovers the emergence of an extended Galileon-like symmetry at high energies.

## Key findings

- Positivity bounds limit the cutoff below the naive strong-coupling scale.
- Higher-derivative operators become important at low energies.
- An extended Galileon-like symmetry emerges for spin-3 particles at high energy.

## Abstract

We construct the effective field theory for a single massive higher-spin particle in flat spacetime. Positivity bounds of the S-matrix force the cutoff of the theory to be well below the naive strong-coupling scale, forbid any potential and make therefore higher-derivative operators important even at low energy. As interesting application, we discuss in detail the massive spin-3 theory and show that an extended Galileon-like symmetry of the longitudinal modes, even with spin, emerges at high energy.