Vacuum angle theta in a strongly interacting hidden sector and its effect

TL;DR

This paper explores how a vacuum angle in a hidden strongly interacting sector influences electroweak symmetry breaking, Higgs properties, and dark matter candidates within a scale-invariant extension of the Standard Model.

Contribution

It introduces the effects of a vacuum angle in a hidden sector on Higgs vacuum expectation value and dark matter particle mass differences, a novel aspect in such models.

Findings

Higgs vacuum expectation value depends on the hidden sector vacuum angle.

Higgs mass condition remains unaffected by the vacuum angle.

Mass difference between hidden-sector pions is significant near .

Abstract

Introducing a vacuum angle $\theta_h$ in a strongly interacting hidden sector like QCD, we study how $\theta_h$ affects physical quantities in a scale invariant extension of the standard model with that hidden sector. In this model the dynamical chiral symmetry breaking occurs in the hidden sector and generates a scale $ \vert \langle {\bar q} q \rangle \vert $ which triggers electroweak symmetry breaking. We find that the expression for a vacuum expectation value of the Higgs field depends on $\theta_h$, while the condition which determines the Higgs particle mass does not. This model contains the hidden-sector pions $\pi^0$ and $\pi^{\pm}$ which are candidates for cold dark matter, and we find the mass difference between the hidden-sector $\pi^0$ and $\pi^{\pm}$ will not be negligible for $\theta_h \approx \pi$.