arXiv subjects

D. A. Ryzhikh

Publications and source records attributed to D. A. Ryzhikh.

11 recordsLinked to original sources

arXiv2003

Monopoles and Family Replicated Unification

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 $a=λ_\text{P}$, where $λ_\text{P}$ 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 $α_\text{i}(μ)$ (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 $μ_\text{GUT}\approx 10^{18.4}$ GeV. We discussed the possibility of the [SU(5)]$^3$ SUSY or [SO(10)]$^3$ SUSY unifications.

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arXiv2003

Proceedings to the workshops 'What comes beyond the Standard model', 2000, 2001, 2002, Volume 2: Proceedings (Part II)

Contents (Part 2): 8.Renormalization of Coupling Constants in the Minimal SUSY Models (R. B. Nevzorov, K. A. Ter-Martirosyan and M. A. Trusov) 9.Multiple Point Model and Phase Transition Couplings ...(L.V. Laperashvili, D.A. Ryzhikh and H.B. Nielsen) 10.Family Replicated Fit of All Quark and Lepton Masses and Mixings (H. B. Nielsen and Y. Takanishi) 11.Family Replicated Calculation of Baryogenesis (H. B. Nielsen and Y. Takanishi) 12. Neutrino Oscillations in Vacuum on the Large Distance (D.A. Ryzhikh and K.A. Ter-Martirosyan) 13. Possibility of an Additional Source of Time Reversal Violation for Neutrinos (R. Erdem) 14.Quark-Lepton Masses and the Neutrino Puzzle in the AGUT Model (C.D. Froggatt) 15.Neutrinos in the Family Replicated Gauge Group Model (C.D. Froggatt) (Contents of Part 1 [hep-ph/0301029]: 1.Derivation of Lorentz Invariance and Three Space Dimensions in Generic Field Theory (C D. Froggatt and H. B. Nielsen) 2.Unitary Representations, Noncompact Groups SO(q; d - q)...(N. Mankoc Borstnik, H. B. Nielsen and D. Lukman) 3.Weyl Spinor of SO(1; 13), Families of Spinors ...(A. Borstnik Bracic and N. Mankoc Borstnik) 4.A Tight Packing Problem (A. Kleppe) 5.Why so Few Particle Species? ... (D.L. Bennett and A. Kleppe) 6.About Number of Families (D. Lukman, A. Kleppe and N.S. Mankoc Borstnik) 7.Coupling Constant Unification in Spin-Charge Unifying Model ....(N. Mankoc Borstnik and H. B. Nielsen))

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arXiv2002

Proceedings to the Workshops ''What comes beyond the Standard model'' 2000,2001, VOLUME 1: Festschrift dedicated to the 60th birthday of Holger Bech Nielsen

The present volume is the collection of contributions by friends of Holger Bech Nielsen for his 60th birthday. Contents: 1.Unified internal space of spins and charges (N. Mankoc Borstnik) 2.Semitopological Q-Rings (M. Axenides) 3.Non-local axial anomalies in the Standard model (D. Melikhov, B. Stech) 4.Could there be a fourth generation? (C.D. Froggatt) 5.Another complex Bateman equation (D.B. Fairlie) 6.Non-associative loops for Holger Bech Nielsen (P.H. Frampton) 7.Particles, fluids and vortices (J.W. van Holten) 8.Results on 2D current algebras (J.L. Petersen) 9.Phase transition in gauge theories and the Planck scale physics (L.V. Laperashvili and D.A. Ryzhikh) 10.Some remarks on the 'classical' large N limit (P. Olesen) 11.String theory and the size of hadrons (L. Susskind) 12.Relativity and $c/sqrt3$ (S.I. Blinnikov, L.B. Okun and M.I. Vysotsky) 13.Vortices (Jeff Greensite)

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arXiv2002

Monopoles near the Planck Scale and Unification

Considering our (3+1)-dimensional space-time as, in some way, discrete or l attice 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 $N_{fam}$ times smaller magnetic charge in FRGGM than in SM ($N_{fam}$ is the number of families in FRGGM). We have estimated al so 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 $μ=μ_G\sim 10^{18}$ GeV, we have the possibility of unification if the FRGGM-breakdown occurs at $μ_G\sim 10^{14}$ GeV. By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale $μ_{GUT}\approx 10^{18.4}$ GeV. We discussed the possibility of $[SU(5)]^3$ or $[SO(10)]^3$ (SUSY or not SUSY) unifications.

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arXiv2001

Multiple Point Model and Phase Transition Couplings in the Two-Loop Approximation of Dual Scalar Electrodynamics

The phase transition "Coulomb-confinement" in the U(1) regularized gauge theory is considered in the framework of dual Abelian Higgs model of scalar monopoles (shortly: Higgs monopole model). The effective potential analogous to the Coleman-Weinberg's one, improved by the renormalization group equation, is constructed, using beta-functions in the two-loop approximation. The value of QED critical fine structure constant was calculated: $α_{crit}\approx 0.208$, in correspondence with lattice result: $α_{crit}^{lat}\approx 0.20\pm 0.015$.

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arXiv2001

[SU(5)]^3 SUSY unification

In the present paper we demonstrate the possibility of the [SUSY(5)]^3 SUSY unification at the energy scale $μ_{GUT}\approx 10^{18.3} GeV$ with the value of GUT inverse finestructure constant $α_{GUT}^{-1}\approx 34.4$, which is very close to its critical value $α_{5, crit}^{-1}\approx 34.0$, existing at the Planck scale.

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arXiv2001

Neutrino Mixing and Leptonic CP Phase in Neutrino Oscillations

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.

hep-ph↗

arXiv2001

Phase Transition in Gauge Theories and Multiple Point Model

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 (critical) dual and non-dual couplings were calculated in the U(1) gauge theory. It was shown that the critical value of the renormalized electric fine structure constant $α_{\text{crit}}\approx 0.208$ obtained in this paper coincides with the lattice result for compact QED: $α_{\text{crit}}^{\text{lat}}\approx 0.20\pm 0.015$. This result and the behavior of $α$ in the vicinity of the phase transition point were compared with the Multiple Point Model prediction for the values of $α$ near the Planck scale. Such a comparison is very encouraging for the Multiple Point Model assuming the existence of the multiple critical point at the Planck scale.

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arXiv2001

Phase Transition in Gauge Theories and the Planck Scale Physics

The present paper is based on the modified part of the review "Random Dynamics and Multiple Point Model" by L.V.Laperashvili, H.B.Nielsen, D.A.Ryzhikh and N.Stillits, in preparation for publication in Russian, which contains the results of our joint activity with H.B.Nielsen concerning the investigations of phase transitions in gauge theories. In this review we have presented the main ideas of the Nielsen's Random Dynamics (RD) and his achievements (with co-authors) in the Anti-Grand Unification Theory (AGUT) and Multiple Point Model (MPM). We have considered also the theory of Scale Relativity (SR) by L.Nottale, which has a lot in common with RD: both theories lead to the discreteness of our space-time, giving rise to the new description of physics at very small distances. In this paper we have demonstrated the possibility of [SU(5)]$^3$ SUSY unification with superparticles of masses $M\approx 10^{18.3}$ GeV and calculated its critical point -- critical value of the inverse finestucture constant -- at $α_{5,crit}^{-1} = α_5^{-1}(μ_{Pl})\approx 34.0$ (close to $α_{GUT}^{-1}\approx 34.4$) with a hope that such an unified theory approaches the (multi)critical point at the Planck scale.

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arXiv2001

Phase Transition Couplings in U(1) and SU(N) Regularized Gauge Theories

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 $α_{crit} \approx 0.17$, 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 $α_{crit}\approx 0.208$ and coincides with the lattice result for compact QED [10]: $α_{crit}^{lat} \approx 0.20\pm 0.015$. 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 coupling constants, which is $α_{N,crit}^{-1}=\frac{N}{2}\sqrt{\frac{N+1}{N-1}} α_{U(1),crit}^{-1}$. This relation was used for the description of the Planck scale values of the inverse running constants $α_i^{-1}(μ)$ (i=1,2,3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the Multiple Point Model [16].

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arXiv1999

Mass and CKM Matrices of Quarks and Leptons, the Leptonic CP-phase in neutrino oscillations

A general approach for construction of quark and lepton mass matrices is formulated. The hierarchy of quarks and charged leptons ("electrons") is large, it leads using the experimental values of mixing angles to the hierarchical mass matrix slightly deviating from one's suggested earlier by Stech and including naturally the CP-phase. The same method based on the rotation of generation numbers in the diagonal mass matrix is used in the electron-neutrino sector of theory, where neutrino mass matrix is determined by the Majorano see-saw approach. The hierarchy of neutrino masses, much smaller than for quarks, was used including all existing (even preliminary) experimental data on neutrinos mixing. The leptonic mass matrix found in this way includes not known value of the leptonic CP-phase. It leads to a large $ν_μν_τ$ oscillations and suppresses the $ν_eν_τ$ and also $ν_e ν_μ$ oscillations. The explicit expressions for the probabilities of neutrino oscillation were obtained in order to specify the role of leptonic CP-phase. The value of time reversal effect (proportional to $\sinδ'$) was found to be small $\sim 1%$. However, a dependence of the values of $ν_e ν_μ, ν_e ν_τ$ transition probabilities, averaged over oscillations, on the leptonic CP-phase has found to be not small - of order of tens percent.

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