Is there any Nambu monopolium out there?

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 described 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) contribute 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, Setô and Bargmann conditions, are verified. In the following, ground-state energies are estimated for a variety of monopolium reduced mass, from 102 MeV to 102 TeV, and Compton interaction lengths, from am to pm, where discussion about non-relativistic and relativistic limits validation is carried out. Dedicated to the memory of Dr. César Augusto Parga Rodrigues (1939–2021).