Monopole solutions in SU(2) Yang-Mills theory which interact with massive nonlinear spinor fields described by the nonlinear Dirac equation are obtained. These solutions describe a magnetic monopole created by a spherical lump of nonlinear spinor fields.

It is shown that the monopole solutions obtained differs in principle from the ’t Hooft-Polyakov monopole so that its: (а) topologically trivial; (b) the radial magnetic field of which decreases as r^-3 ; (c) for its existence no need the Higgs field.

It is demonstrated that the energy spectrum of such a system possesses a global minimum, the appearance of which is due exclusively to the nonlinearity of the Dirac spinor fields. This global minimum can be considered as a mass gap, i.e. the energy difference between a vacuum and the next lowest energy state. A similar minimum was found for the energy spectrum of regular solutions to the nonlinear Dirac equation and this minimun called as “the lightest stable particle”.

References

1. Dzhunushaliev, V. Folomeev, and A. Makhmudov, “Non-Abelian Proca-Dirac-Higgs theory: Particlelike solutions and their energy spectrum,” Phys. Rev. D 99, 076009 (2019).
2. Kojo and N. Su, “The quark mass gap in a magnetic field,” Phys. Lett. B 720, 192 (2013).
3. V. Dzhunushaliev, V. Folomeev and A. Serikbolova, “Monopole solutions in SU(2) Yang-Mills-plus-massive-nonlinear-spinor-field theory” Physics Letters B Volume 806, 135480 (2020).