Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles

TL;DR

This paper develops new positivity bounds for massive spinning particles' scattering amplitudes, strengthening constraints on effective field theories by relating amplitude derivatives to helicity, thus improving upon previous bounds and aiding in constraining higher-dimensional interactions.

Contribution

It introduces novel positivity bounds based on $t$ derivatives and helicity, providing stronger constraints on EFTs for massive spinning particles compared to prior methods.

Findings

Derived bounds relate $t$ derivatives to helicity, strengthening unitarity constraints.

Established that $t$-derivative of amplitude must be positive for large helicities.

Provided new constraints applicable to dimension-6 interactions with milder UV assumptions.

Abstract

We derive new effective field theory (EFT) positivity bounds on the elastic $2\to2$ scattering amplitudes of massive spinning particles from the standard UV properties of unitarity, causality, locality and Lorentz invariance. By bounding the $t$ derivatives of the amplitude (which can be represented as angular momentum matrix elements) in terms of the total ingoing helicity, we derive stronger unitarity bounds on the $s$- and $u$-channel branch cuts which determine the dispersion relation. In contrast to previous positivity bounds, which relate the $t$-derivative to the forward-limit EFT amplitude with no $t$ derivatives, our bounds establish that the $t$-derivative alone must be strictly positive for sufficiently large helicities. Consequently, they provide stronger constraints beyond the forward limit and can be used to constrain dimension-6 interactions with a milder assumption about the high-energy growth of the UV amplitude.