Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
Abstract
We derive new effective field theory (EFT) positivity bounds on the elastic 22 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.