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

• Published in: The journal of high energy physics Vol. 2024; no. 3; pp. 180 - 47
• Main Authors: Chen, Qing, Mimasu, Ken, Wu, Tong Arthur, Zhang, Guo-Dong, Zhou, Shuang-Yong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 29.03.2024; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Effective Field Theories; Elementary Particles; Operators; Physics; Physics and Astronomy; Principles; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; S matrix theory; SMEFT; Specific BSM Phenomenology; String Theory; Upper bounds; Effective Field Theories; SMEFT; Specific BSM Phenomenology
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2024)180

A bstract 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 ((4 π ) 2 ). 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.