On internal mechanical properties of electroweak magnetic monopoles and their effects on stability

By considering properties of the energy-momentum tensor of the electroweak magnetic monopole and its Born-Infeld extension, we attempt to make comments on the stability of these configurations. Specifically, we perform a study of the behaviour of the so-called internal force and pressure of these extended field-theoretic solitonic objects, which are derived from the energy-momentum tensor. Our method is slightly different from the so-called Laue's criterion for stability of nuclear matter, a local form of which had been proposed and applied in the earlier literature to the 't Hooft-Polyakov (HP) magnetic monopole, and found to be violated. By applying our method first to HP monopole, we also observe that, despite its topological stability, the total (finite) internal force (which has only radial components) is directed inwards, towards the centre of the monopole, which would imply instability. Thus this mechanical criterion for stability is arguably violated in the case of the HP monopole, as is the local version of Laue's criterion. The criterion is satisfied for the short-range part of the energy momentum tensor, in which the long-range part, due to the massless photon of the U(1) subgroup, is subtracted. This makes the HP monopole mechanically stable by our criterion, which is also confirmed due to its proven topological stability. Par contrast, the total internal force of the Cho-Maison (CM) electroweak monopole has both radial and angular components, which diverge at the origin, leading to rotational instabilities, violating the short-range Laue's criterion for stability. Finally, by studying extensions of the CM, in which the latter is embedded in theories with non-minimal couplings of the hypercharge and Higgs sectors, as well as higher-derivative electromagnetic interactions of Born-Infeld type, we find that the total force, integrated over space, is finite, but, in the Born-Infeld case it has also angular components. The latter feature is interpreted as indicating that, unlike the rest of the CM extensions, the Born-Infeld-CM monopole might be subject to rotations upon the action of perturbations, but this does not necessarily imply mechanical instabilities of the configuration. For such unstable composite monopoles, one expects a decay after production into charged constituent $W^{\pm }$ bosons, which are in principle detectable at colliders.