Five fundamental problems - neutrino oscillations, baryogenesis, dark matter, inflation, strong CP problem - are solved at one stroke in SM-A-S-H (Standard Model-Axion-Seesaw-Higgs portal inflation) model by Andreas Ringwald et. al. The Standard Mode
l (SM) particle content was extended by three right-handed SM-singlet neutrinos $N_i$, a vector-like color triplet quark $Q$, a complex SM-singlet scalar field $sigma$ that stabilises the Higgs potential, all of them being charged under a global lepton number (hyper-charge) and Peccei-Quinn (PQ) $U(1)$ symmetry. We found numerically that SMASH model not only solves five fundamental problems but also the sixth problem Vacuum Metastability through the extended scalar sector.
In the present paper, we investigated the gravitational black-hole-hedgehogs 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), w
e 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 $M_{BH}approx 3.65times 10^{18},, {rm{GeV}}$ and radius $delta approx 6cdot 10^{-21} {rm{GeV}}^{-1}.$ We investigated the metric in the vicinity of the black-hole-hedgehog and estimated its horizon radius: $r_happrox 1.14 delta$. We have considered the phase transition from the false vacuum to the true vacuum and confirmed the stability of the EW--vacuum.
We present a new cosmological model of the Universe based on the two discoveries: 1. cosmological constant is very small, and 2. Nature shows a new law in physics called Multiple Point Principle (MPP). The MPP predicts the two degenerate vacua of the
Universe with VEV $v_1approx 246$ Gev and $v_2sim 10^{18}$ GeV, which provide masses of the Higgs boson and top-quark. A new cosmological model assumes the formation of two universal bubbles. The Universe at first stage of its existing is a bubble with a de-Sitter spacetime inside, having black-holes-hedgehogs as topological defects of the vacuum. Such a bubble has a false vacuum with VEV $v_2$, which decays very quickly. Cooling Universe has a new phase transition, transforming the false vacuum to the true (Electroweak) vacuum. Hedgehogs confined, and the universal bubble is transformed into the bubble having spacetime with FLRW-metric and the vacuum with new topological defects of $U(1)_{(el-mag)}$ group: magnetic vortices and Sidharths pointlike defects. The problem of stability/metastability of the EW-vacuum is investigated. Noncommutativity of the vacua spacetime manifold is discussed. The prediction of a new physics is given by the future observations at LHC of the triplet $SU(2)$ Higgs bosons (at energies $Esim 10$ TeV), and/or of the new bound states $6t + 6bar t$ formed by top-antitop quarks (at $Esim 1$ TeV). The problem What comes beyond the Standard Model is discussed at the end of this paper.
We investigate the prospects for determining the octant of $theta_{23}$ in the future long baseline oscillation experiments. We present our results as contour plots on the ($theta_{23}-45^circ$, $delta$)--plane, where $delta$ is the CP phase, showing
the true values of $theta_{23}$ for which the octant can be experimentally determined at 3$,sigma$, 2$,sigma$ and 1$,sigma$ confidence level, in particular, the impact of the non-unitarity of neutrino mixing.
The recent data indicate that the neutrino mixing angle $theta_{23}$ deviates from the maximal-mixing value of 45$^circ$, showing two nearly degenerate solutions, one in the lower octant (LO) ($theta_{23}<45^circ$) and one in the higher octant (HO) (
$theta_{23}>45^circ$). We investigate, using numerical simulations, the prospects for determining the octant of $theta_{23}$ in the future long baseline oscillation experiments. We present our results as contour plots on the ($theta_{23}-45^circ$, $delta$)--plane, where $delta$ is the $CP$ phase, showing the true values of $theta_{23}$ for which the octant can be experimentally determined at 3$,sigma$, 2$,sigma$ and 1$,sigma$ confidence level. In particular, we study the impact of the possible nonunitarity of neutrino mixing on the experimental determination of $theta_{23}$ in those experiments.
We review our speculation, that in the pure Standard Model the exchange of Higgses, including also the ones eaten by $W^{pm}$ and Z, and of gluons together make a bound state of 6 top plus 6 anti top quarks bind so strongly that its mass gets down to
about 1/3 of the mass of the collective mass 12 $m_t$ of the 12 constituent quarks. The true importance of this speculated bound state is that it makes it possible to uphold, even inside the Standard Mode, our proposal for what is really a new law of nature saying that there are several phases of empty space, vacua, all having very small energy densities (of the order of the present energy density in the universe). The reason suggested for believing in this new law called the Multiple (Criticality) Point Principle is, that estimating the mass of the speculated bound state using the Multiple Point Principle leads to two consistent mass-values; and they even agree with a crude bag-model like estimate of the mass of this bound state. Very, unfortunately, the statistical fluctuation so popular last year, when interpreted as the digamma resonance F(750), turned out not to be a real resonance, because our estimated bound state mass is just around the mass of 750 GeV.
In the present paper, assuming the Multiple Point Principle (MPP) as a new law of Nature, we considered the existence of the two degenerate vacua of the Universe: a) the first Electroweak (EW) vacuum at $v_1approx 246$ GeV -- true vacuum, and b) the
second Planck scale false vacuum at $v_2 sim 10^{18}$ GeV. In these vacua we investigated different topological defects. The main aim of this paper is an investigation of the black-hole-hedgehogs configurations as defects of the false vacuum. In the framework of the $f(R)$ gravity, described by the Gravi-Weak unification model, we considered a black-hole solution, which corresponds to a hedgehog -- global monopole, that has been swallowed by the black-hole with mass core $M_{BH}sim 10^{18}$ GeV and radius $deltasim 10^{-21}$ GeV$^{-1}$. Considering the results of the hedgehog lattice theory in the framework of the $SU(2)$ Yang-Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehogs confinement phase ($T_csim 10^{18}$ GeV). This result gave us the possibility to conclude that the SM shows a new physics (with contributions of the $SU(2)$-triplet Higgs bosons) at the scale $sim 10$ TeV. Theory predicts the stability of the EW-vacuum and the accuracy of the MPP.
We study the possibility of determining the octant of the neutrino mixing angle $theta_{23}$, that is, whether $theta_{23}> 45^circ$ or $theta_{23}<45^circ$, in long baseline neutrino experiments. Here we numerically derived the sensitivity limits wi
thin which these experiments can determine, by measuring the probability of the $ u_{mu}to u_{e}$ transitions, the octant of $theta_{23}$ with a $5sigma$ certainty. The interference of the CP violation angle $delta$ with these limits, as well as the effects of the baseline length and the run-time ratio of neutrino and antineutrino modes of the beam have been analyzed.
In this review we present a theory of cosmological constant and Dark Energy (DE), based on the topological structure of the vacuum. The Multiple Point Principle (MPP) is reviewed. It demonstrates the existence of the two vacua into the SM. The Frogga
tt-Nielsens prediction of the top-quark and Higgs masses is given in the assumption that there exist two degenerate vacua in the SM. This prediction was improved by the next order calculations. We also considered B.G. Sidharths theory of cosmological constant based on the non-commutative geometry of the Planck scale space-time, what gives an extremely small DE density providing the accelerating expansion of the Universe. Theory of two degenerate vacua - the Planck scale phase and Electroweak (EW) phase - also is reviewed, topological defects in these vacua are investigated, also the Compton wavelength phase suggested by B.G. Sidharth was discussed. A general theory of the phase transition and the problem of the vacuum stability in the SM is reviewed. Assuming that the recently discovered at the LHC new resonance with mass $m_S simeq 750$ GeV is a new scalar $S$ bound state $6t + 6bar t$, earlier predicted by C.D. Froggatt, H.B. Nielsen and L.V. Laperashvili, we try to provide the vacuum stability in the SM and exact accuracy of the MPP.
In the present paper we argue that the correction to the Higgs mass coming from the bound state of 6 top and 6 anti-top quarks, predicted early by C.D. Froggatt and ourselves, leads to the Standard Model vacuum stability and confirms the accuracy of
the multiple point principle (principle of degenerate vacua) for all experimentally valued parameters (Higgs mass, top-quark mass, etc.). Fitting to get the vacuum degeneracy requires a mass of the bound state, just in the region of the new two photon state in LHC, 750-760 GeV.
