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

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 $|⟨\bar{q}q⟩|$ 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 ${\theta }_h\approx \pi$.

Comments: 10 pages