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arXiv · 2108.06334

Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles

Joe Davighi·Scott Melville·Tevong You
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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.

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Joe Davighi, Scott Melville, Tevong You. 2021-08-13. Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles. https://doi.org/10.1007/jhep02(2022)167

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