False Vacuum Decay in Two-Higgs-Doublet Models Plus a Scalar or Pseudoscalar

Abstract

The Two-Higgs Doublet Model (2HDM) is one of the simplest extensions to the Standard Model of particle physics. Despite its simplicity, the 2HDM has the potential to resolve several outstanding problems in high-energy physics, such as baryogenesis, and the generation of neutrino masses. Additionally, its scalar and pseudoscalar extensions 2HDM+$s/a$ are among the most promising simplified models for dark matter. These extensions are theoretically consistent, sufficiently generic to encompass a broad range of theoretical scenarios, and are rich with new physics. However, as with any quantum field theory, the 2HDM(+$s/a$) models have vast parameter spaces which can only be constrained through observations. In this thesis, I constrain the 2HDM(+$s/a$) parameter spaces with the observation that our universe's vacuum has not decayed in the past $ 10^{10}$ years. The analysis is split into two parts. First, I analyse the behaviour of leading order vacua appearing at field values of $|\phi|<10^{4}$ GeV. I find that in the 2HDM, when the new 2HDM masses $m_H,m_{H^\pm},m_A$ are set to be large ($\gtrsim 800\,$GeV), no second vacuum is generated at either tree-level or one-loop order. Second, I examine radiatively-induced vacua appearing at $|\phi|\gtrsim 10^5\,$GeV. To do this, I extend Fubini's instanton solution to multiple fields, and calculate the leading order contribution to the tunneling rate. I find that when the 2HDM masses are degenerate, a large fraction of the low $\tan\beta\lesssim 3$ region is excluded by false vacuum decay. In addition, as opposed to flavour and electroweak constraints, mass degeneracies generically serve to destabilise the vacuum. Consequently, I expect false vacuum decay constraints to work together with flavour and electroweak constraints to efficiently rule out the 2HDM parameter space. As for the 2HDM+$s/a$ models, I found that in addition to the constraints on the 2HDM, large dark matter Yukawa couplings $y_\chi\gtrsim 0.8$ are excluded by false vacuum decay. Thus, this thesis provides a comprehensive study of constraints on the 2HDM($+s/a$) through false vacuum decay, and lays a foundation for future research on radiatively-induced false vacuum decay in theories with extended scalar sectors.