Effective theories of universal theories

TL;DR

This paper clarifies the conditions under which oblique parameters apply to universal theories within EFT, characterizes these theories at dimension-6 with 16 parameters, and provides a basis-independent framework for experimental constraints.

Contribution

It explicitly derives restrictions on EFT for universal theories and defines 16 basis-independent parameters for comprehensive phenomenological analysis.

Findings

Universal theories at dimension-6 are characterized by 16 parameters.

Oblique parameters are only applicable under specific EFT restrictions.

A basis-independent parameter set enables consistent experimental constraints.

Abstract

It is well-known but sometimes overlooked that constraints on the oblique parameters (most notably $S$ and $T$ parameters) are generally speaking only applicable to a special class of new physics scenarios known as universal theories. In the effective field theory (EFT) framework, the oblique parameters should not be associated with Wilson coefficients in a particular operator basis, unless restrictions have been imposed on the EFT so that it describes universal theories. We work out these restrictions, and present a detailed EFT analysis of universal theories. We find that at the dimension-6 level, universal theories are completely characterized by 16 parameters. They are conveniently chosen to be: 5 oblique parameters that agree with the commonly-adopted ones, 4 anomalous triple-gauge couplings, 3 rescaling factors for the $h^3$, $hff$, $hVV$ vertices, 3 parameters for $hVV$ vertices absent in the Standard Model, and 1 four-fermion coupling of order $y_f^2$. All these parameters are defined in an unambiguous and basis-independent way, allowing for consistent constraints on the universal theories parameter space from precision electroweak and Higgs data.