Probing Effective Field Theory Approach in the CP Violating Minimal Linear $\sigma$ Model

TL;DR

This paper explores the validity of the Effective Field Theory approach within the CP-violating Minimal Linear Sigma Model, analyzing Higgs properties, the radial mode effects, and the nature of the electroweak phase transition.

Contribution

It investigates the EFT validity and phenomenology of the CP-violating Minimal Linear Sigma Model, including Higgs pseudo-Goldstone behavior and phase transition characteristics.

Findings

EFT approach remains valid after heavy mode decoupling.

CP violation induces pseudoscalar components in Yukawa couplings.

Electroweak phase transition characteristics are affected by the field s.

Abstract

The Minimal Linear $\sigma$ Model is a useful theoretical laboratory. One can investigate in a perturbative renormalisable model the properties of the Higgs boson as a pseudo-Goldstone boson, the phenomenological effects of the radial mode of the field $\mathtt{s}$ which spontaneously breaks the global $SO(5)$ symmetry and the validity of conclusions based on the Effective Field Theory approach with the field $\mathtt{s}$ in the spectrum, after the decoupling of heavy degrees of freedom. In this paper all those issues are discussed in the framework of the Minimal Linear $\sigma$ Model with CP violating phases leading to pseudoscalar components in the effective Standard Model Yukawa couplings. Also the character of the electroweak phase transition in the presence of the field $\mathtt{s}$ is investigated.