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arXiv · 2104.03286

Is there any Nambu monopolium out there?

D. O. R. Azevedo·M. L. Bispo·O. M. Del Cima·D. H. T. Franco·A. R. Pereira
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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.

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D. O. R. Azevedo, M. L. Bispo, O. M. Del Cima, D. H. T. Franco, A. R. Pereira. 2021-04-07. Is there any Nambu monopolium out there?. https://doi.org/10.1209/0295-5075%2Fac1fa0

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