Phase transition in the Higgs model of scalar fields with electric and magnetic charges

Using a one-loop renormalization group improvement for the effective potent ial in the Higgs model of electrodynamics with electrically and magneticall y charged scalar fields, we argue for the existence of a triple (critical) point in the phase diagram (lambda (run), g(run)(4)), where lambda (run) is the renormalized running self-interaction constant of the Higgs scalar mon opoles and g(run) is their running magnetic charge. This triple point is a boundary point of three first-order phase transitions in the dual sector of the Higgs scalar electrodynamics: The "Coulomb" and two confinement phases meet together at this critical point. Considering the arguments for the on e-loop approximation validity in the region of parameters around the triple point A we have obtained the following triple point values of the running couplings: (lambda ((A)) ,g((A))(2))) approximate to (-13.4; 18.6), which a re independent of the electric charge influence and two-loop corrections to g(run)(2) with high accuracy of deviations. At the triple point the mass o f monopoles is equal to zero. The corresponding critical value of the elect ric fine structure constant turns out to be alpha (crit) = pi /g((A))(2) ap proximate to 0.17 by the Dirac relation. This value is close to the alpha ( iat)(crit) approximate to 0.20 +/- 0.015, which in a U(1) lattice gauge the ory corresponds to the phase transition between the "Coulomb" and confineme nt phases. In our theory for alpha greater than or equal to alpha (crit) it there are two phases for the confinement of the electrically charged parti cles. The results of the present paper are very encouraging for the antigra nd unification theory which was developed previously as a realistic alterna tive to SUSY GUT's. The paper is also devoted to the discussion of this pro blem.