Abstract
We derive new effective field theory (EFT) positivity bounds on the elastic 2 → 2 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 can provide stronger constraints beyond the forward limit which can be used to constrain dimension-6 interactions with a milder assumption about the high-energy growth of the UV amplitude.
Highlights
By bounding the t derivatives of the amplitude 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 effective field theory (EFT) amplitude with no t derivatives, our bounds establish that the t-derivative alone must be strictly positive for sufficiently large helicities
By detecting deviations from SM predictions. If such deviations are due to heavy new physics, they are efficiently encoded as higher-dimensional operators in the Standard Model Effective Field Theory (SMEFT) framework, and positivity bounds provide a direct connection between these operator coefficients and general properties of the UV
Summary
Our main result is the improved positivity bound (1.5), which follows from new, stronger t-derivative unitarity conditions for spinning particles in the helicity basis. As with other positivity bounds in the literature, the bound (1.5) only applies if the high-energy growth of the amplitude in the UV theory is assumed to be sufficiently bounded This is ensured by the Froissart bound, lim|s|→∞ |A(s, t)| < s2, which follows from unitarity and causality in any local quantum theory with a mass gap. One interesting distinction between (1.5) and previous positivity bounds is that when α ≤ 0 (i.e. for sufficiently large |hu| + |hs|min) the first t-derivative is constrained independently of the forward-limit amplitude without any t-derivatives As a result, this α ≤ 0 bound applies given weaker assumptions about the UV growth.
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