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A. V. Borisov

Publications and source records attributed to A. V. Borisov.

At least 19 recordsLinked to original sources
arXiv2024

Neutrino Mass in Effective Field Theory

In this review, the seesaw mechanism for generating the mass of active light neutrinos (both Majorana and Dirac) is considered on the basis of effective field theory. In particular, we review certain models that extend the Standard Model by introducing heavy sterile neutrinos and discuss the corresponding mechanisms for generating small masses of active neutrinos. Two Appendices briefly describe the properties of Weyl, Dirac, and Majorana spinors in four dimensions and the interrelations between such spinors. The third Appendix provides a simple proof of the theorem on Takagi diagonalization of a mass matrix for Majorana fermions.

hep-ph↗
arXiv2022

Electron angular correlation in neutrinoless double beta decay and new physics

The angular correlation of the electrons in the neutrinoless double beta decay ($0\nu2β$) is calculated taking into account the nucleon recoil, the $S$ and $P$-waves for the electrons and the electron mass using a general Lorentz invariant effective Lagrangian. We show that the angular coefficient is essentially independent of the nuclear matrix element models. We work out the angular coefficient in several scenarios for new physics, in particular, in the left-right symmetric models.

hep-ph↗
arXiv2022

Probing new physics in the Neutrinoless double beta decay using electron angular correlation

The angular correlation of the electrons emitted in the neutrinoless double beta decay ($0\nu2β$) is presented using a general Lorentz invariant effective Lagrangian for the leptonic and hadronic charged weak currents. We show that the coefficient $K$ in the angular correlation $dΓ/d\cos θ\propto (1-K\cos θ)$ is essentially independent of the nuclear matrix element models and present its numerical values for the five nuclei of interest ($^{76}{Ge}$, $^{82}{Se}$, $^{100}{Mo}$, $^{130}{Te}$, and $^{136}{Xe}$), assuming that the $0\nu2β$-decays in these nuclei are induced solely by a light Majorana neutrino, $ν_M$. This coefficient varies between $K=0.81$ (for the $^{76}{Ge}$ nucleus) and $K=0.88$ (for the $^{82}{Se}$ and $^{100}{Mo}$ nuclei), calculated taking into account the effects from the nucleon recoil, the $S$ and $P$-waves for the outgoing electrons and the electron mass. Deviation of $K$ from its values derived here would indicate the presence of New Physics (NP) in addition to a light Majorana neutrino, and we work out the angular coefficients in several $ν_M + {NP}$ scenarios for the $^{76}{Ge}$ nucleus. As an illustration of the correlations among the $0\nu2β$ observables (half-life $T_{1/2}$, the coefficient $K$, and the effective Majorana neutrino mass $|< m>|$) and the parameters of the underlying NP model, we analyze the left-right symmetric models, taking into account current phenomenological bounds on the right-handed $W_R$-boson mass and the left-right mixing parameter $ζ$.

hep-ph↗
arXiv2020

On inhomogeneous nonholonomic Bilimovich system

We consider a simple motivating example of a non-Hamiltonian dynamical system with time-dependent constraints obtained by imposing rheonomic non-integrable Bilimovich's constraint on a freely rotating rigid body. Dynamics of this low-dimensional nonlinear nonautonomous dynamic system involves different kinds of stable and unstable attractors, quasi and strange attractors, compact and noncompact invariant attractive curves, etc. To study this cautionary example we apply the Poincaré map method to disambiguate and discover multiscale temporal dynamics, specifically the coarse-grained dynamics resulting from fast-scale nonlinear control via nonholonomic Bilimovich's constraint.

nlin.CD↗
arXiv2020

On rheonomic nonholonomic deformations of the Euler equations proposed by Bilimovich

In 1913 A.D. Bilimovich observed that rheonomic linear and homogeneous in generalized velocities constraints are ideal. As a typical example, he considered rheonomic nonholonomic deformation of the Euler equations which scleronomic version is equivalent to the nonholonomic Suslov system. For the Bilimovich system equations of motion are reduced to quadrature, which is discussed in rheonomic and scleronomic cases.

nlin.SI↗
arXiv2018

Reduction and relative equilibria for the 2-body problem in spaces of constant curvature

We consider the two-body problem on surfaces of constant non-zero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show there are two relative equilibria where the masses are separated by a distance q. One of these is geometrically of elliptic type and the other of hyperbolic type. The hyperbolic ones are always unstable, while the elliptic ones are stable when sufficiently close, but unstable when far apart. On the sphere of positive curvature, if the masses are different, there is a unique relative equilibrium (RE) for every angular separation except π/2. When the angle is acute, the RE is elliptic, and when it is obtuse the RE can be either elliptic or linearly unstable. We show using a KAM argument that the acute ones are almost always nonlinearly stable. If the masses are equal there are two families of relative equilibria: one where the masses are at equal angles with the axis of rotation (`isosceles RE') and the other when the two masses subtend a right angle at the centre of the sphere. The isosceles RE are elliptic if the angle subtended by the particles is acute and is unstable if it is obtuse. At π/2, the two families meet and a pitchfork bifurcation takes place. Right-angled RE are elliptic away from the bifurcation point. In each of the two geometric settings, we use a global reduction to eliminate the group of symmetries and analyse the resulting reduced equations which live on a 5-dimensional phase space and possess one Casimir function.

math-ph↗
arXiv2011

Lepton-number violating meson decays in theories beyond the Standard Model

After discussion of mechanisms of lepton number violation, we consider meson decays $K^+ \toπ^ - \ell ^ + \ell '^ +$ and $D^ + \to K^ - \ell ^ + \ell '^ +$ ($\ell,\ell ' = e,μ$) with $ΔL= 2$ in the Standard Model extended by massive Majorana neutrinos and in a supersymmetric extension of the Standard Model with explicit breaking of R-parity by trilinear or bilinear Yukawa couplings in the superpotential. We give estimates of the branching ratios for these decays and compare the effectiveness of various decay mechanisms taking into account present experimental bounds on lepton mixing, masses of neutrinos and superparticles, and R-parity violating couplings.

hep-ph↗
arXiv2011

Neutrinoless double beta decay: searching for new physics with comparison of different nuclei

The neutrinoless double beta decay is analyzed using a general Lorentz invariant effective Lagrangian for various decaying nuclei of current experimental interest: $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{136}$Xe. We work out the half-lives and angular correlation coefficients of the outgoing electrons in several scenarios for new physics: the left-right symmetric models, the R-parity-violating SUSY and models with leptoquarks. The theoretical uncertainty in the nuclear matrix elements is discussed.

hep-ph↗
arXiv2011

Neutrino emission from a strongly magnetized degenerate electron gas: the Compton mechanism via a neutrino magnetic moment

We derive relative upper bounds on the effective magnetic moment of Dirac neutrinos from comparison of the standard weak and electromagnetic mechanisms of the neutrino luminosity due to the Compton-like photoproduction of neutrino pairs in a degenerate gas of electrons on the lowest Landau level in a strong magnetic field. These bounds are close to the known astrophysical and laboratory ones.

hep-ph↗
arXiv2008

Bilinear R-parity Violation in Rare Meson Decays

We discuss rare meson decays $K^ + \to π^ - \ell ^ + \ell '^ +$ and $D^ + \to K^ - \ell ^ + \ell '^ +$ ($\ell ,\ell ' = e,μ$) in a supersymmetric extension of the standard model with explicit breaking of R-parity by bilinear Yukawa couplings in the superpotential. Estimates of the branching ratios for these decays are given. We also compare our numerical results with analogous ones previously obtained for two other mechanisms of lepton number violation: exchange by massive Majorana neutrinos and trilinear R-parity violation.

hep-ph↗
arXiv2006

Neutrinoless double beta decay: Electron angular correlation as a probe of new physics

The angular distribution of the final electrons in the so-called long range mechanism of the neutrinoless double beta decay ($0\nu2β$) is derived for the general Lorentz invariant effective Lagrangian. Possible theories beyond the SM are classified from their effects on the angular distribution, which could be used to discriminate among various particle physics models inducing $0\nu2β$ decays. However, additional input on the effective couplings will be required to single out the light Majorana-neutrino mechanism. Alternatively, measurements of the effective neutrino mass and angular distribution in $0\nu2β$ decays can be used to test the correlations among the parameters of the underlying physics models. This is illustrated for the left-right symmetric model, taking into account current phenomenological bounds.

hep-ph↗
arXiv2006

Rare semileptonic meson decays in R-parity violating MSSM

We discuss rare meson decays $K^ + \to π^ - \ell ^ + \ell '^ + $ and $D^ + \to K^ - \ell ^ + \ell '^ +$ ($\ell, \ell'=e, μ$) in a supersymmetric extension of the Standard Model with R-parity violation. Estimates of the branching ratios for these decays are presented.

hep-ph↗
arXiv2005

Effects of heavy Majorana neutrinos at lepton-proton colliders

We discuss the prospects of detecting the processes $e^+p\to\barν_e\ell^+\ell'^+X$ and $ν_ep\to e\ell^+\ell'^+X$ ($\ell,\ell'=e,μ,τ$) under the conditions of the present $ep$ collider HERA and of future colliders. These high-energy processes are assumed to be mediated by the exchange of heavy Majorana neutrinos (HMN). We consider two simple scenarios for the HMN mass spectrum: the effective singlet ($m_1\ll m_2<m_3...$) and the effective doublet ($m_1<m_2\ll m_3...$). For the latter case, the cross section includes information about CP-violating phases.

hep-ph↗
arXiv2005

Majorana Neutrinos and Same-Sign Dilepton Production at LHC and in Rare Meson Decays

We discuss same-sign dilepton production mediated by Majorana neutrinos in high-energy proton-proton collisions $pp\ra \ell^+ \ell^{\prime +}X$ for $\ell,~ \ell^\prime = e,~ μ,~ τ$ at the LHC energy $\sqrt{s}=14$ TeV, and in the rare decays of $K$, $D$, $D_s$, and $B$ mesons of the type $M^{+}\ra M^{\prime -}\ell ^{+}\ell ^{\prime+}$. For the $pp$ reaction, assuming one heavy Majorana neutrino of mass $m_N$, we present discovery limits in the $(m_{N},|U_{\ell N}U_{\ell^\prime N}|)$ plane where $U_{\ell N}$ are the mixing parameters. Taking into account the present limits from low energy experiments, we show that at LHC for the nominal luminosity L=100 fb$^{-1}$ there is no room for observable same-sign dilepton signals. However, increasing the integrated luminosity by a factor 30, one will have sensitivity to heavy Majorana neutrinos up to a mass $m_N\leq 1.5$ TeV only in the dilepton channels $μμ$ and $μτ$, but other dilepton states will not be detectable due to the already existing strong constraints. We work out a large number of rare meson decays, both for the light and heavy Majorana neutrino scenarios, and argue that the present experimental bounds on the branching ratios are too weak to set reasonable limits on the effective Majorana masses.

hep-ph↗
arXiv2005

Hamiltonization of nonholonomic systems

We consider some issues of the representation in the Hamiltonian form of two problems of nonholonomic mechanics, namely, the Chaplygin's ball problem and the Veselova problem. We show that these systems can be written as generalized Chaplygin systems and can be integrated by the method of reducing multiplier. We also indicate the algebraic form of the Poisson brackets of these systems (after the time substitution). Generalizations of the problems are considered and new realizations of nonholonomic constraints are presented. Some nonholonomic systems with an invariant measure and a sufficient number of first integrals are indicated, for which the question of the representation in the Hamiltonian form is still open, even after the time substitution.

nlin.SI↗
arXiv2005

Reduction and chaotic behavior of point vortices on a plane and a sphere

We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied to the vortex dynamics, it requires substantial modification. Reduction of four vortices on a sphere is given in more detail. We also use the Poincare surface-of-section technique to perform the reduction a four-vortex system on a sphere.

nlin.SI↗