Charged and CP-violating Kink Solutions in the Two Higgs Doublet Model

Abstract

Minimal extensions of the Standard Model (SM), such as the so-called Two Higgs Doublet Model (2HDM), can possess several accidental discrete symmetries whose spontaneous breakdown in the early universe usually lead to the formation of domain walls. We extend an earlier work [arXiv:2006.13273] on this topic by studying in more detail the analytic properties of electrically charged and CP-violating kink solutions in the $Z_2$-symmetric 2HDM. We derive the complete set of equations of motion that describe the 1D spatial profile of both the 2HDM vacuum parameters and the would-be Goldstone bosons $G^{1,2,3}$ of the SM. These equations are then solved numerically using the gradient flow technique, and the results of our analysis are presented in different parametrizations of the Higgs doublets. In particular, we show analytically how an electrically charged profile should arise in 1D kink solutions when asymmetric boundary conditions are imposed on the Goldstone mode $G^2$ at spatial infinities, i.e. as $x\to \pm \infty$. If asymmetric boundary conditions are selected at $x\to \pm \infty$ for the Goldstone mode $G^3$ or the longitudinal mode $\theta$ corresponding to a would-be massive photon, the derived kink solutions are then shown to exhibit CP violation. Possible cosmological implications of the electrically charged and CP-violating domain walls in the 2HDM are discussed.

23 pages, 4 figures, references added, to appear in Physical Review D

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• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• Observation of $CP$ violation in charm decays
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• Generalized CP symmetries and special regions of parameter space in the two-Higgs-doublet model
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Cited by in corpus (5)

• Stable $Z$-strings with topological polarization in two Higgs doublet model
• Percolation of Domain Walls in the Two-Higgs Doublet Model
• Complete Classification of Domain Wall Solutions in the ${\mathbb{Z}}_2$-symmetric 2HDM
• Chiral non-Abelian domain walls in the Ginzburg-Landau theory
• Gravitational Wave Mountains: current-carrying domain walls