Is there any Nambu monopolium out there?. (arXiv:2104.03286v1 [hep-th])

Is there any Nambu monopolium out there?. (arXiv:2104.03286v1 [hep-th])
<a href="http://arxiv.org/find/hep-th/1/au:+Azevedo_D/0/1/0/all/0/1">D.O.R. Azevedo</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Bispo_M/0/1/0/all/0/1">M.L. Bispo</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Cima_O/0/1/0/all/0/1">O.M. Del Cima</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Franco_D/0/1/0/all/0/1">D.H.T. Franco</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Pereira_A/0/1/0/all/0/1">A.R. Pereira</a>

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.

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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