Twisted semilocal strings in the MSSM

TL;DR

This paper explores twisted semilocal string solutions in an extended electroweak model with two Higgs doublets, revealing new bifurcations, solution types, and energy properties through analytical and numerical methods.

Contribution

It introduces and analyzes the existence of twisted semilocal strings with different phase factors in a two-Higgs-doublet extension of the electroweak model, including doubly-twisted solutions.

Findings

Existence of regular, finite-energy twisted semilocal strings.

Identification of bifurcations leading to new solution branches.

Discovery of doubly-twisted solutions with lower energy than embedded solutions.

Abstract

The standard electroweak model is extended by means of a second Brout-Englert-Higgs-doublet. The symmetry breaking potential is chosen is such a way that (i) the Lagrangian possesses a custodial symmetry, (ii) a stationary, axially symmetric ansatz of the bosonic fields consistently reduces the Euler-Lagrange equations to a set of differential equations. The potential involves, in particular, a direct interaction between the two doublets. Stationary, axially-symmetric solutions of the classical equations are constructed. Some of them can be assimilated to embedded Nielsen-Olesen strings. From these solutions there are bifurcations and new solutions appear which exhibit the characteristics of the recently constructed twisted semilocal strings. A special emphasis is set on "doubly-twisted" solutions for which the two doublets present different time-dependent phase factors. They are regular and have a finite energy which can be lower than the energy of the embedded twisted solution. Electric-type solutions, such that the fields oscillate asymptotically far from the symmetry-axis, are also reported.