Capping the positivity cone: dimension-8 Higgs operators in the SMEFT

TL;DR

This paper develops new linear UV unitarity bounds for dimension-8 Higgs operators in the SMEFT, improving upon previous positivity bounds by incorporating full crossing symmetry and null constraints, with implications for experimental vector boson scattering.

Contribution

It introduces a set of linear UV unitarity conditions that extend traditional positivity bounds, enabling more precise bounds on dimension-8 SMEFT operators using dispersion relations.

Findings

Derived linear UV unitarity bounds for dimension-8 operators.

Demonstrated bounds using Higgs scattering and crossing symmetry.

Compared new bounds with traditional perturbative unitarity limits.

Abstract

SMEFT Wilson coefficients are subject to various positivity bounds in order to be consistent with the fundamental principles of S-matrix. Previous bounds on dimension-8 SMEFT operators have been obtained using the positivity part of UV partial wave unitarity and form a (projective) convex cone. We derive a set of linear UV unitarity conditions that go beyond positivity and are easy to implement in an optimization scheme with dispersion relations in a multi-field EFT. Using Higgs scattering as an example, we demonstrate how to obtain closed bounds in the space of the three relevant dimension-8 coefficients, making use of the UV unitarity conditions as well as so-called null constraints that arise from full crossing symmetry. Specifically, we show that they are bounded by inequalities schematically going like $C<O\left((4\pi)^2\right)$. We compare the newly obtained upper bounds with the traditional perturbative unitarity bounds from within the EFT, and discuss some phenomenological implications of the two-sided positivity bounds in the context of experimental probes of Vector Boson Scattering.