Using a 2-loop approximation for β-functions, we have considered the corresponding renormalization group improved effective potential in the Dual Abelian Higgs Model (DAHM) of scalar monopoles and calculated the phase transition (critical) couplings in U(1) and SU(N) regularized gauge theories. In contrast to our previous result α crit ≈ 0.17, obtained in the one-loop approximation with the DAHM effective potential (see Ref.[20]), the critical value of the electric fine structure constant in the 2-loop approximation, calculated in the present paper, is equal to α crit ≈ 0.208 and coincides with the lattice result for compact QED [10]: α lat crit ≈ 0.20±0.015. Following the 't Hooft's idea of the "abelization" of monopole vacuum in the Yang-Mills theories, we have obtained an estimation of the SU(N) triple point couplingThis relation was used for the description of the Planck scale values of the inverse running constants α −1 i (µ) (i=1,2,3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the Multiple Point Model [16].

The present theory is based on the assumption that at the very small (Planck scale) distances our space-time is discrete, and this discreteness influences on the Planck scale physics. Considering our (3+1)-dimensional space-time as a regular hypercubic lattice with a parameter a = λ P , where λ P is the Planck length, we have investigated a role of lattice artifact monopoles which is essential near the Planck scale if the Family replicated gauge group model (FRGGM) is an extension of the Standard Model at high energies. It was shown that monopoles have N times smaller magnetic charge in FRGGM than in SM (N is the number of families in FRGGM). These monopoles can give an additional contribution to beta-functions of the renormalisation group equations for the running fine structure constants α i (µ) (i=1,2,3 correspond to the U(1), SU(2), and SU (3) gauge groups of the Standard Model). We have used the Dirac relation for renormalised electric and magnetic charges. Also we have estimated the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. Different role of monopoles in the vicinity of the Planck scale gives rise or to AntiGUT, or to the new possibility of unification of gauge interactions (including gravity) at the scale µ GUT ≈ 10 18.4 GeV. We discussed the possibility of the [SU(5)] 3 SUSY or [SO(10)] 3 SUSY unifications.

In the present paper the phase transition in the regularized U(1) gauge theory is investigated using the dual Abelian Higgs model of scalar monopoles. The corresponding renormalization group improved effective potential, analogous to the Coleman-Weinberg's one, was considered in the two-loop approximation for β functions, and the phase transition

Considering our (3 + 1)-dimensional space-time as, in some way, discrete or lattice with a parameter a = λ P , where λ P is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to beta-functions of the renormalisation group equations for the running fine structure constants α i (µ) (i=1,2,3 correspond to the U(1), SU(2) and SU (3) gauge groups of the Standard Model) in the Family Replicated Gauge Group Model (FRGGM) which is an extension of the Standard Model at high energies. It was shown that monopoles have N f am times smaller magnetic charge in FRGGM than in SM (N f am is the number of families in FRGGM). We have estimated also the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have shown that, in contrast to the case of AntiGUT when the FRGGM undergoes the breakdown at µ = µ G ∼ 10 18 GeV, we have the possibility of unification if the FRGGM-breakdown occurs at µ G ∼ 10 14 GeV. By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale µ GU T ≈ 10 18.4 GeV. We discussed the possibility of [SU (5)] 3 or [SO(10)] 3 (SUSY or not SUSY) unifications.

Oscillations of the Dirac neutrinos of three generations in vacuum are considered with allowance made for the effect of the CP-violating leptonic phase (analogue of the quark CP phase) in the lepton mixing matrix. The general formulas for the probabilities of neutrino transition from one sort to another in oscillations are obtained as functions of three mixing angles and the CP phase. It is found that the leptonic CP phase can, in principle, be reconstructed by measuring the oscillation-averaged probabilities of neutrino transition from one sort to another. The manifestation of the CP phase as a deviation of the probabilities of direct processes from those of inverse processes is an effect that is practically unobservable as yet. © 2001 MAIK "Nauka/Interperiodica".