Is there any Nambu monopolium out there?

TL;DR

This paper explores the theoretical possibility of Nambu-type monopole-antimonopole bound states, called monopolium, analyzing conditions for their existence and estimating their ground state energies across a wide mass and length scale.

Contribution

It introduces a Nambu-type non confining attractive potential for monopole-antimonopole interactions and investigates the formation and properties of monopolium states.

Findings

Conditions for bound state existence are verified.

Ground state energies are estimated for a range of masses and interaction lengths.

Discussion includes non-relativistic and relativistic regimes.

Abstract

Magnetic monopoles have been a subject of study for more than a century since the first ideas by A. Vaschy and P. Curie, circa 1890. In 1974, Y. Nambu proposed a model for magnetic monopoles exploring a parallelism between the broken symmetry Higgs and the superconductivity Ginzburg-Landau theories in order to describe the pions quark-antiquark confinement states. There, Nambu describes an energetic string where its end points behave like two magnetic monopoles with opposite magnetic charges -- quark and antiquark. Consequently, not only the interaction among monopole and antimonopole, mediated by a massive vector boson (Yukawa potential), but also the energetic string (linear potential) contributes to the effective interaction potential. We propose here a monopole-antimonopole non confining attractive interaction of the Nambu-type, and then investigate the formation of bound states, the monopolium. Some necessary conditions for the existence of bound states to be fulfilled by the proposed Nambu-type potential, Kato weakness, Set\^o and Bargmann conditions, are verified. In the following, ground state energies are estimated for a variety of monopolium reduced mass, from $10^2$MeV to $10^2$TeV, and Compton interaction lengths, from $10^{-2}$am to $10^{-1}$pm, where discussion about non relativistic and relativistic limits validation is carried out.