Stable magnetic monopole in two Higgs doublet models

We show that a stable magnetic monopole with a finite mass can exist in two Higgs doublet models, contrary to the standard model. The monopole is attached by two topological $Z$ strings ($Z$ flux tubes) from both sides.Despite of a trivial second homotopy group, a discrete symmetry $\mathbb{Z}_2$ exchanging the two doublets, which is contact for $\tan \beta = 1$, together with a non-trivial $\pi_1$ for $Z$ strings topologically ensures the stability, where $\tan \beta$ is a ratio of vacuum expectation values of the two Higgs doublets. After analytically constructing an asymptotic form of such a configuration, we explicitly construct a solution of the equation of motion based on a 3D numerical simulation in which magnetic fluxes spherically emanating from the monopole at large distances are deformed in the vicinity of the monopole.