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.

http://arxiv.org/icons/sfx.gif