Phase Transition Couplings in the Higgsed Monopole Model

Using a one-loop approximation for the effective potential in the Higgs model of electrodynamics for a charged scalar field, we argue for the existence of a triple point for the renormalized (running) values of the selfinteraction $\lambda$ and the "charge" g given by $(\lambda_{run}, g^2) = (-{10/9} \pi^2,{4/3}\sqrt{{5/3}}{\pi^2}) \approx(-11, 17)$. Considering the beta-function as a typical quantity we estimate that the one-loop approximation is valid with accuracy of deviations not more than 30% in the region of the parameters: $0.2 \stackrel{<}{\sim}{\large \alpha, \tilde{\alpha}} \stackrel{<}{\sim}1.35.$ The phase diagram given in the present paper corresponds to the above-mentioned region of $\alpha, \tilde \alpha$. Under the point of view that the Higgs particle is a monopole with a magnetic charge g, the obtained electric fine structure constant turns out to be $\alpha_{crit}\approx{0.18_5}$ by the Dirac relation. This value is very close to the $\alpha_{crit}^{lat}\approx{0.20}$ which in a U(1) lattice gauge theory corresponds to the phase transition between the "Coulomb" and confinement phases. Such a result is very encouraging for the idea of an approximate "universality" (regularization independence) of gauge couplings at the phase transition point. This idea was suggested by the authors in their earlier papers.Comment: 27 pages, 3 figure

Standard Model and Graviweak Unification with (Super)Renormalizable Gravity. Part I: Visible and Invisible Sectors of the Universe

We develop a self-consistent $Spin(4,4)$-invariant model of the unification of gravity with weak $SU(2)$ gauge and Higgs fields in the visible and invisible sectors of our Universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.Comment: 27 page

Generalized dual symmetry of nonabelian theories, monopoles and dyons

In the present talk we present an investigation of nonabelian SU(N) gauge theories, describing a system of fields with non--dual g and dual \tilde g charges and revealing the generalized dual symmetry. The Zwanziger type action is suggested. The renormalization group equations for pure nonabelian theories, in particular for pure SU(3)\times\widetilde{SU(3)} gauge theory (as an example) are analysed. We consider not only monopoles, but also dyons. The behaviour of the QCD total beta--function is investigated. It was shown that this beta--function is antisymmetric under the interchange \alpha\leftrightarrow\frac 1\alpha (here \alpha\equiv\alpha_s), and has zero ("fixed point") at \alpha = 1. Monopoles, or dyons, are responsible for the phase transition. Considering critical points at \alpha_1\approx 0.4 and \alpha_2\approx 2.5, we give an explanation of the freezing of \alpha_s.Comment: 15 pages, 5 figures, Presented at the 12th Lomonosov Conference on Elementary Particle Physics, Moscow State University, Moscow, 25-31 August, 200

The Fundamental-Weak Scale Hierarchy in the Standard Model

The multiple point principle, according to which several vacuum states with the same energy density exist, is put forward as a fine-tuning mechanism predicting the ratio between the fundamental and electroweak scales in the Standard Model (SM). It is shown that this ratio is exponentially huge: $\sim e^{40}$. Using renormalisation group equations for the SM, we obtain the effective potential in the 2-loop approximation and investigate the existence of its postulated second minimum at the fundamental scale. The investigation of the evolution of the top quark Yukawa coupling constant in the 2-loop approximation shows that, with initial values of the top Yukawa coupling in the interval $h(M_t)=0.95\pm 0.03$ (here $M_t$ is the top quark pole mass), a second minimum of the SM effective potential can exist in the region $\phi_{min2}\approx 10^{16}-10^{22}$ GeV. A prediction is made of the existence of a new bound state of 6 top quarks and 6 anti-top quarks, formed due to Higgs boson exchanges between pairs of quarks/anti-quarks. This bound state is supposed to condense in a new phase of the SM vacuum. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The existence of three vacuum states (new, electroweak and fundamental) solves the hierarchy problem in the SM.Comment: 30 pages, 7 figures; to be published in Phys. Atom. Nuc

Gravi-Weak Unification and the Black-Hole-Hedgehog's Solution with Magnetic Field Contribution

In the present paper, we investigated the gravitational black-hole-hedgehog's solution with magnetic field contribution in the framework of the f(R)--gravity described by the Gravi-Weak unification model. Assuming the Multiple Point Principle (MPP), we considered the existence of the two degenerate vacua of the Universe: the first Electroweak (EW) vacuum with $v_1 \approx 246$ GeV ("true vacuum"), and the second Planck scale ("false vacuum") with $v_2 \sim 10^{18}$ GeV. In these vacua, we investigated different topological defects. The main aim of this paper is an investigation of the black-hole-hedgehog configurations as defects of the "false vacuum". We have obtained the solution which corresponds to a global monopole, that has been "swallowed" by the black-hole with core mass $M_{BH}\approx 3.65\times 10^{18}\,\, {\rm{GeV}}$ and radius $\delta \approx 6\cdot 10^{-21} {\rm{GeV}}^{-1}.$ We investigated the metric in the vicinity of the black-hole-hedgehog and estimated its horizon radius: $r_h\approx 1.14 \delta$. We have considered the phase transition from the "false vacuum" to the "true vacuum" and confirmed the stability of the EW--vacuum.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1703.05594, arXiv:1801.06979, arXiv:1605.01169; text overlap with arXiv:1002.4275 by other author