Abstract
Contrary to the standard model that does not admit topologically nontrivial solitons, two Higgs doublet models admit topologically stable vortex strings and domain walls. We numerically confirm the existence of a topological Z-string confining fractional Z-flux inside. We show that topological strings at sin θW = 0 limit reduce to non-Abelian strings which possess non-Abelian moduli S2 associated with spontaneous breakdown of the SU(2) custodial symmetry. We numerically solve the equations of motion for various parameter choices. It is found that a gauging U(1)Y always lowers the tension of the Z-string while it keeps that of the W-string. On the other hand, a deformation of the Higgs potential is either raising or lowering the tensions of the Z-string and W-string. We numerically obtain an effective potential for the non-Abelian moduli S2 for various parameter deformations under the restriction tan β = 1. It is the first time to show that there exists a certain parameter region where the topological W-string can be the most stable topological excitation, contrary to conventional wisdom of electroweak theories. We also obtain numerical solutions of composites of the string and domain walls in a certain condition.
Highlights
Degree of freedom (charged Higgs bosons (H±), CP-even Higgs bosons (H) and CP-odd Higgs boson (A)), which can be in principle produced at the LHC. (See, e.g., refs. [4,5,6,7]2 and references therein for phenomenological studies of 2HDM.) Two Higgs doublet fields are required when one considers supersymmetric extension of the SM.3
The topological EW string has two distinguishable aspects: it is a global string whose winding partially goes inside the global phase U(1)a, and it is, at the same time, a local string in the sense that the rest of winding is supplemented by an SU(2)W gauge transformation, thereby leading a fractional magnetic flux of a Z-boson confined in the vortex core [40]
We have studied properties of the topological vortex strings and domain walls in the 2HDM in detail
Summary
We further assume that the Higgs fields develop non-zero vacuum expectation values (VEVs) as. This occurs when at least one eigenvalue of the mass matrix is negative, we can set v1 and v2 are simultaneously positive without loss of generality. It should be noted here that, even when the potential has the custodial symmetry, it is explicitly broken by the existence of U(1)Y gauge interaction, which is the subgroup of SU(2)R. Where ha (a = 0, 1, 2, 3) are complex scalar fields Plugging this into Lagrangian, we find the mass spectrum: there are four NG bosons (three of them are eaten by the weak gauge bosons) and four massive modes. This will support the existence of several kinds of topologically stable strings as explained in the followings
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