Multi-spin soft bootstrap and scalar-vector Galileon

TL;DR

This paper employs the soft bootstrap method to classify and discover new effective field theories involving massless vectors and scalars, including a novel scalar-vector Galileon, by analyzing their soft limits and deriving soft theorems.

Contribution

It introduces a generalized soft bootstrap approach for scalar-vector EFTs, leading to the unification of Galileon theories and the discovery of a new scalar-vector Galileon.

Findings

No-go theorems for higher-derivative vector theories.

Unified description of existing Galileon theories.

Discovery of the special scalar-vector Galileon.

Abstract

We use the amplitude soft bootstrap method to explore the space of effective field theories (EFT) of massless vectors and scalars. It is known that demanding vanishing soft limits fixes uniquely a special class of EFTs: non-linear sigma model, scalar Galileon and Born-Infeld theories. Based on the amplitudes analysis, we conjecture no-go theorems for higher-derivative vector theories and theories with coupled vectors and scalars. We then allow for more general soft theorems where the non-trivial part of the soft limit of the (n+1)-pt amplitude is equal to a linear combination of n-pt amplitudes. We derive the form of these soft theorems for general power-counting and spins of particles and use it as an input into the soft bootstrap method in the case of Galileon power-counting and coupled scalar-vector theories. We show that this unifies the description of existing Galileon theories and leads us to the discovery of a new exceptional theory: Special scalar-vector Galileon.