Mixed signals in the IR: Positivity bounds with indefinite species

TL;DR

This paper derives new positivity bounds for inelastic scattering amplitudes involving multiple particle species, explicitly accounting for mass differences and IR effects, with implications for EFTs like pions and the Standard Model.

Contribution

It introduces novel bounds that incorporate mass differences and IR effects in superposition states, extending previous positivity bounds to more general inelastic processes.

Findings

Derived bounds depend explicitly on mass differences.

Identified non-analyticities from IR mass differences.

Discussed potential applications to EFTs of the Standard Model.

Abstract

In theories with multiple particle species standard fixed-t positivity bounds do not directly apply to 2-to-2 definite species scattering amplitudes when the initial and final state are not the same (inelastic processes). These inelastic amplitudes are nevertheless constrained by positivity bounds indirectly, by considering scattering states which are arbitrary superpositions of definite species two-particle states. While these `superposition bounds' have been studied and utilised extensively in the past, earlier analyses typically consider cases insensitive to relative particle masses and IR branch cuts. Here we derive new families of bounds that take account and depend explicitly on mass differences between species making no assumption of weak-coupling. We emphasise unusual non-analyticities induced by the IR mass difference within the superposition amplitude and use fixed (backwards) angle dispersion relations to prove our bounds. We then discuss extensions of our results to `improved bounds', with implications worth exploring for pions and other EFTs of the Standard Model and Beyond, particularly where IR branch cuts are non-negligible.