On internal mechanical properties of Electroweak Magnetic Monopoles and their effects on stability

TL;DR

The paper develops an EMT-based framework to probe the internal mechanical properties and stability of magnetic monopoles in the electroweak context, contrasting the stable ’t Hooft–Polyakov monopole with the Cho–Maison monopole and its finite-energy extensions. By decomposing the EMT into short- and long-range (electromagnetic) parts and analyzing radial and angular pressure components, the authors assess Laue-type local stability and the behavior of internal forces under various model extensions, including non-minimal Higgs–hypercharge couplings and string-inspired Born–Infeld corrections. They find that the HP monopole is mechanically stable in the short-range sector, while the original CM monopole is plagued by divergences and angular instabilities; finite-energy CM variants show more nuanced stability, with BI-type extensions yielding finite angular forces and potential rotational responses rather than outright instability. The results provide a mechanical interpretation of monopole viability and outline criteria and extensions that could render electroweak monopoles physically consistent, with implications for collider phenomenology and cosmological relic considerations.

Abstract

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. 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. Finally, by studying finite-energy extensions of the CM, either with non-minimal Higgs couplings with the hypercharge sector or hypercharge Born-Infeld type models, we find that the total force, integrated over space, is finite, but it has also angular components in the Born-Infeld case. The latter feature is interpreted as indicating that the Born-Infeld-CM monopole might be subject to rotations upon the action of perturbations, but it does not necessarily imply instabilities of the configuration.

Figures (25)

• Figure 1: Solutions of $(\ref{['HooftProfileDiffScalar']})$ and $(\ref{['HooftProfileDiffGauge']})$ for various $\gamma$ values with $\mu=\lambda$ and $M_W =1~{\rm GeV}$ fixed, in the HP magnetic monopole. $f(r)$ solutions approach zero asymptotically and $H(r)/r$ solutions approach asymptotically $H(r)/r \xrightarrow{r \rightarrow \infty} 1$. Orange, green, red, blue and purple lines correspond to $\gamma$$1,0.5,0.1,0.0001$ and $0$ respectively.
• Figure 2: The HP-monopole Hamiltonian density $\mathcal{H}$ according to $(\ref{['Hamiltonian Hooft']})$ for various $\lambda_0$ values, with $\mu=\lambda$ and $M_W=1$$\rm GeV$ fixed. Blue, orange, green, red and purple lines correspond to $\gamma = 1,0.5,0.1,0.0001,0$ respectively.
• Figure 3: Radial and Polar Pressure for various $\gamma$ values with $\mu (\frac{1}{\rm GeV})=\lambda$ and $M_W =1~\rm GeV$ fixed, in the HP magnetic monopole. Blue, orange, green, red and purple lines correspond to $\gamma = 1,0.5,0.1$ and $0.0001$ respectively. At the BPS limit both radial and polar pressure vanish.
• Figure 4: Radial Force $(\ref{['RadialForceHooft']})$ for various $\gamma$ values with $\mu (\frac{1}{\rm GeV})=\lambda$ and $M_W =1~\rm GeV$ fixed, in the HP magnetic monopole. Blue, orange, green and red lines correspond to $\gamma = 1,0.5,0.1$ and $0.0001$ respectively.
• Figure 5: Internal Force Fields for $\gamma =1$ and $\gamma =0.5$, in the HP magnetic monopole.