Probing effective field theory approach in the CP violating minimal linear $$\sigma $$ σ model

Abstract

Abstract The Minimal Linear $$\sigma $$ σ 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 $$\texttt {s}$$ s which spontaneously breaks the global SO(5) symmetry and the validity of conclusions based on the Effective Field Theory approach with the field $$\texttt {s}$$ 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 $$\sigma $$ σ 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 $$\texttt {s}$$ s is investigated.