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We study neutrino oscillations in background matter within the quantum field theory formalism where neutrino mass eigenstates are virtual particles. In this case, neutrino mass eigenstates are mixed owing to the interaction with matter. Assuming that neutrinos are Majorana particles, we find the exact propagators for massive neutrinos accounting for the interaction with matter by solving the analog of the Dyson equation. These propagators are used to calculate the transition probability which coincides with the prediction of the Mikheyev--Smirnov--Wolfenstein effect. Finally, we analyze the approximations made in our analysis., Comment: 17 pages in pdflatex, 5 pdf figures

We study interacting classical magnetic and pseudoscalar fields in frames of the axion electrodynamics. A large scale pseudoscalar field can be the coherent superposition of axions or axion like particles. We consider the evolution of these fields in a thin spherical layer. Decomposing the magnetic field into the poloidal and toroidal components, we take into account their symmetry properties. The dependence of the pseudoscalar field on the latitude is accounted for the induction equation. Then, we derive the dynamo equations in the low mode approximation. The nonlinear evolution equations for the harmonics of the magnetic and pseudoscalar fields are solved numerically. As an application, we consider a dense axion star embedded in solar plasma. The behavior of the harmonics and their typical oscillations frequencies are obtained. We suggest that such small objects consisting of axions and confined magnetic fields can cause the recently observed flashes in solar corona contributing to its heating., Comment: 11 pages in LaTeX2e, 12 eps figures

We construct a new Yang-Mills 3D-solution on the space of negative scalar curvarure. We discuss a problem of non-abelian gauge symmetry is broken with the assumption that a scalar curvature of the domain is a negative small parameter. In this case we use the following fact: a geometrical scale related with Vassiliev's discriminant of magnetic lines coincids with a physical Kolmogorov scale. This gives an estimation of $\alpha$-effect by the dispersion of the asymptotic ergodic Hopf invariant in the limite with a negative scalar curvature parameter.

We study neutrino spin oscillations while the particles scatter off a rotating black hole surrounded by a thick magnetized accretion disk. Neutrino spin precession is caused by the interaction of the neutrino magnetic moment with the magnetic field in the disk which has both toroidal and poloidal components. Our calculation of the observed neutrino fluxes, accounting for spin oscillations, are based on numerical simulations of the propagation of a great number of incoming test particles using High Performance Parallel Computing. The obtained results significantly improve our previous findings. We briefly discuss the applications for the observations of astrophysical neutrinos., Comment: 7 pages in Revtex4.1, 6 eps figures; contribution to proceedings of XIX Workshop on High Energy Spin Physics, DSPIN-23 (September 4-8, 2023, JINR, Dubna, Russia); minimal changes; published in Phys.Atom.Nucl

We study the magnetic helicity evolution in neutron stars (NSs). First, we analyze how the surface terms affect the conservation law for the sum of the chiral imbalance of the charged particle densities and the density of the magnetic helicity. Our results are applied to a system with a finite volume, which can be a magnetized NS. We show that the contribution of these surface terms can potentially lead to the reconnection of magnetic field lines followed by X-ray or gamma bursts observed in magnetars. Comparing the new quantum surface term with the classical contribution known in the standard magnetic hydrodynamics, we obtain that its contribution dominates over the classical term only for NS with a rigid rotation. Second, we study the dynamics of chiral electrons which interact electroweakly with a background fermions having the velocity, arbitrarily depending on spatial coordinates, and the nonuniform density. We derive the the kinetic equations and the effective action for right and left particles. The correction to the Adler anomaly and to the anomalous electric current are obtained in the case of a rotating matter. Then, the obtained results are applied for the study of the magnetic helicity flow inside a magnetized rotating NS. We compute the characteristic time of the helicity change and demonstrate that it coincides with the the magnetic cycle period of certain pulsars., Comment: 29 pages in LaTeX2e, 2 eps figures; mini review based on talk given in Helicity 2020. To be published in "Helicities in Geophysics, Astrophysics, and Beyond", ed. by K.Kuzanyan, N.Yokoi, M.K.Georgoulis, and R.Stepanov (AGU, Wiley, 2024)

We study the formation of a superfluid condensate of neutrinos inside a neutrino cluster. The attractive interaction between neutrinos is mediated by a scalar boson which is lighter than a neutrino. We consider the appearance of neutrino bound states consisting of particles with oppositely directed spins. The gap equation for such a system is derived. Based on numerical simulations of the neutrino distribution in a cluster, we find the phase transition temperature and the coherence length inside such a cluster for various parameters of the system. The constraints on the parameters of the Yukawa interaction, resulting in the neutrino superfluidity, are derived. We obtain that the cosmic neutrino background can contribute to the superfluid condensate inside a neutrino cluster having realistic characteristics. The mechanism of the neutrino cluster cooling in the early universe, based on the plasmons \v{C}erenkov radiation, is proposed., Comment: 14 pages in LaTeX2e, 9 eps figures

We study the gravitational scattering of ultrarelativistic neutrinos off a rotating supermassive black hole (BH) surrounded by a thick magnetized accretion disk. Neutrinos interact electroweakly with background matter and with the magnetic field in the disk since neutrinos are supposed to possess nonzero magnetic moments. The interaction with external fields results in neutrino spin oscillations. We find that the toroidal magnetic field, inherent in the magnetized Polish doughnut, does not cause a significant spin-flip for any reasonable strengths of the toroidal component. The reduction of the observed neutrino flux, owing to neutrino spin oscillations, is predicted. A poloidal component of the magnetic field gives the main contribution to the modification of the observed flux. The neutrino interaction with matter, rotating with relativistic velocities, also changes the flux of neutrinos. We briefly discuss the idea of the neutrino tomography of magnetic field distributions in accretion disks near BHs., Comment: 18 pages in JCAP LaTeX style, 15 eps figures; text is revised slightly, several new references are added, version published in JCAP

We study spin and flavor oscillations of astrophysical neutrinos under the influence of external fields in curved spacetime. First, we consider spin oscillations in case of neutrinos gravitationally scattered off a rotating supermassive black hole surrounded by a thin magnetized accretion disk. We find that the gravitational interaction only does not result in the spin-flip of scattered ultrarelativistic neutrinos. Realistic magnetic fields lead to the significant reduction of the observed flux of neutrinos possessing reasonable magnetic moments. Second, we study neutrino flavor oscillations in stochastic gravitational waves (GWs). We derive the effective Hamiltonian for neutrinos interacting with a plane GW having an arbitrary polarization. Then, we consider stochastic GWs with arbitrary correlators of amplitudes. The equation for the density matrix for neutrino oscillations is solved analytically and the probabilities to detect certain neutrino flavors are derived. We find that the interaction of neutrinos, emitted by a core-collapsing supernova, with the stochastic GW background results in the several percent change of the neutrino fluxes. The observability of the predicted effects is discussed., Comment: 8 pages in LaTeX2e, 8 eps figures, contribution to proceedings of International Conference on Quantum Field Theory, High-Energy Physics, and Cosmology (July 18-21, 2022; JINR, Dubna, Russia), to be published in Phys. Part. Nucl. Lett

We study the time evolution of magnetic fields in various configurations of spatially inhomogeneous pseudoscalar fields, which are the coherent superposition of axions. The new induction equation for the magnetic field, which accounts for this inhomogeneity, is derived for such systems. Based on this equation, we study, first, the evolution of two Chern-Simons (CS) waves interacting with a linearly decreasing pseudoscalar field. The nonzero gradient of the pseudoscalar field results in the mixing between these CS waves. Then, we consider the problem in a compact domain, when an initial CS wave is mirror symmetric. In this situation, the inhomogeneity of a pseudoscalar field acts as the effective modification of the $\alpha$-dynamo parameter. Thus, we conclude that the influence of a spatially inhomogeneous pseudoscalar field on the magnetic field evolution strongly depends on the geometry of the system., Comment: 18 pages in pdf LaTeX, 6 pdf figures; title is changed, text is significantly modified; version to be published in Int.J.Mod.Phys.D

We study the evolution of hypermagnetic fields (HMFs) in random plasma in the symmetric phase of the early universe. The system of kinetic equations for the spectra of the energy density and the helicity, as well as the particles asymmetries is derived. We also formulate the initial condition which involve the Kazantsev and Kolmogorov spectra of the seed HMFs. This system is solved numerically. We predict the energy spectrum of primeval gravitational waves which are produced by these HMFs. Additionally, the baryon asymmetry of the universe, generated by the lepton asymmetries, is obtained. These results allow us to constrain the strength of seed HMFs., Comment: 10 pages in LaTeX2e, 6 eps figures; contribution to proceedings of the 6th International Conference on Particle Physics and Astrophysics (November 29 - December 2, 2022, Moscow, Russia); minimal changes in the text; to be published in Phys.Atom.Nucl

We study spin effects in the neutrino gravitational scattering by a supermassive black hole with a magnetized accretion disk having a finite thickness. We exactly describe the propagation of ultrarelativistic neutrinos on null geodesics and solve the spin precession equation along each neutrino trajectory. The interaction of neutrinos with the magnetic field is owing to the nonzero diagonal magnetic moment. Additionally, neutrinos interact with plasma of the accretion disk electroweakly within the Fermi approximation. These interactions are obtained to change the polarization of incoming neutrinos, which are left particles. The fluxes of scattered neutrinos, proportional to the survival probability of spin oscillations, are derived for various parameters of the system. In particular, we are focused on the matter influence on the outgoing neutrinos flux. The possibility to observe the predicted effects for astrophysical neutrinos is briefly discussed., Comment: 14 pages in World Scientific LaTeX style, 14 eps figures; minimal changes, version to be published in special issue of Int.J.Mod.Phys.D

The neutrino propagation and oscillations in various gravitational fields are studied. First, we consider the neutrino scattering off a black hole accounting for the neutrino spin precession. Then, we study the evolution of flavor neutrinos in stochastic gravitational waves. The astrophysical applications of the obtained results are considered., Comment: 3 pages in Revtex, 3 eps figures, contribution to the proceedings of 20th Lomonosov Conference on Elementary Particle Physics (August 19-25, 2021, Moscow, Russia), to be published in Moscow University Physics Bulletin

We study neutrinos gravitationally scattered off a rotating supermassive black hole which is surrounded by a thin accretion disk with a realistic magnetic field. Neutrinos are supposed to be Dirac particles having a nonzero magnetic moment. Neutrinos move along arbitrary trajectories, with the incoming flux being parallel to the equatorial plane. We exactly account for the influence of both gravity and the magnetic field on the neutrino motion and its spin evolution. The general statement that the helicity of an ultrarelativistic neutrino is constant in the particle scattering in an arbitrary gravitational field is proven within the quasiclassical approach. We find the measurable fluxes of outgoing neutrinos taking into account the neutrino spin precession in the external field in curved spacetime. These fluxes turn out to be significantly suppressed for some parameters of the system. Finally, we discuss the possibility to observe the predicted phenomena for core-collapsing supernova neutrinos in our Galaxy., Comment: 16 pages in LaTeX2e, 11 eps figures; paper is significantly extended, Fig. 3 is added, new appendix is included; version to be published in Classical and Quantum Gravity

We study the evolution of random hypermagnetic fields (HMFs) in the symmetric phase of the early universe before the electroweak phase transition. The behavior of HMFs is driven by the analog of the chiral magnetic effect accounting for the asymmetries of leptons and Higgs bosons. These asymmetries are also dynamical variables of the model and evolve together with HMFs. Moreover, we account for the contribution of the hyper-MHD turbulence in the effective diffusion coefficient and the $\alpha$-dynamo parameter. The realistic spectrum of seed HMFs consists of two branches: Batchelor and Kolmogorov ones. The impact of HMFs on the production of relic gravitational waves (GWs) and the baryon asymmetry of the universe (BAU), as well as flavor oscillations of supernova neutrinos in the stochastic GWs generated, are considered. We establish the constraint on the strength of the seed HMF comparing the spectral density of produced GWs with the observations of the LIGO-Virgo-KAGRA collaborations. The stronger upper bound on the seed HMF is obtained from the condition of not exceeding the observed value of BAU., Comment: 25 pages in World Scientific LaTeX style, 21 eps figures, 1 table; text is revised significantly, several new references are added, version published in Int.J.Mod.Phys.D

We study the system of interacting axions and magnetic fields in the early universe after the quantum chromodynamics phase transition, when axions acquire masses. Both axions and magnetic fields are supposed to be spatially inhomogeneous. We derive the equations for the spatial spectra of these fields, which depend on conformal time. In case of the magnetic field, we deal with the spectra of the energy density and the magnetic helicity density. The evolution equations are obtained in the closed form within the mean field approximation. We choose the parameters of the system and the initial condition which correspond to realistic primordial magnetic fields and axions. The system of equations for the spectra is solved numerically. We compare the cases of inhomogeneous and homogeneous axions. The evolution of the magnetic field in these cases is different only within small time intervals. Generally, magnetic fields are driven mainly by the magnetic diffusion. We find that the magnetic field instability takes place for the amplified initial wavefunction of the homogeneous axion. This instability is suppressed if we account for the inhomogeneity of the axion., Comment: 14 pages in LaTeX2e, 9 eps figures; paper was significantly revised, Sec. 6 was completely rewritten, matches the version published in Phys. Lett. B

We study the production of relic gravitational waves (GWs) in turbulent hypermagnetic fields (HMFs) in the symmetric phase of the early universe before the electroweak phase transition (EWPT). The noise of HMFs is modeled by the analog of the magnetic hydrodynamics turbulence. The evolution of HMFs is driven by the analogs of the chiral magnetic effect and the Adler anomalies in the presence of the nonzero asymmetries of leptons and Higgs bosons. We track the evolution of the energy density of GWs from 10 TeV down to EWPT and analyze its dependence on the parameters of the system. We also discuss the possibility to observe the predicted GW background by the current GW detectors., Comment: 17 pages in jcap LaTeX style, 13 eps figures; paper is significantly revised, Secs. 3 and 4 are modified, new Fig. 2 is included, several new references are added; version published in JCAP

We study a matter turbulence caused by strong random hypermagnetic fields (HMFs ) that influence the baryon asymmetry evolution due to the Abelian anomalies in the symmetric phase in the early Universe. Such a matter turbulence is stipulated by the presence of the advection term in the induction equation for which a fluid velocity is dominated by the Lorentz force in the Navier-Stokes equation. For random HMFs, having nonzero mean squared strengths, we calculate the spectra for the HMF energy and the HMF helicity densities. The latter function governs the evolution of the fermion asymmetries in the symmetric phase before the electroweak phase transition (EWPT). In the simplest model based on the first SM generation for the lepton asymmetries of $e_\mathrm{R,L}$ and $\nu_{e_\mathrm{L}}$, we calculate a decline of all fermion asymmetries including the baryon asymmetry, given by the `t Hooft conservation law, when one accounts for a turbulence of HMFs during the universe cooling down to EWPT. We obtain that the stronger the mean squared strength of random initial HMFs is, the deeper the fermion asymmetries decrease, compared to the case in the absence of any turbulence., Comment: 15 pages, 8 eps figures, LaTeX2e; minimal changes; version published in Eur.Phys.J.C

We examine the propagation and flavor oscillations of neutrinos under the influence of gravitational waves (GWs) with an arbitrary polarization. We rederive the effective Hamiltonian for the system of three neutrino flavors using the perturbative approach. Then, using this result, we consider the evolution of neutrino flavors in stochastic GWs with a general energy density spectrum. The equation for the density matrix is obtained and solved analytically in the case of three neutrino flavors. As an application, we study the evolution of the flavor content of a neutrino beam emitted in a core-collapsing supernova. We obtain the analytical expressions for the contributions of GWs to the neutrino fluxes and for the damping decrement, which describes the attenuation of the fluxes to their asymptotic values. We find that the contribution to the evolution of neutrino fluxes from GWs, emitted by merging supermassive black holes, dominates over that from black holes with stellar masses. The implication of the obtained results for the measurement of astrophysical neutrinos with neutrino telescopes is discussed., Comment: 10 pages in RevTeX, 2 eps figures; paper is significantly revised, especially Sec. III, new Fig. 2 is added; matches version published in PRD

We study the neutrino scattering off a rotating black hole with a realistic accretion disk permeated by an intrinsic magnetic field. Neutrino trajectories in curved spacetime as well as the particle spin evolution in dense matter of an accretion disk and in the magnetic field are accounted for exactly. We obtain the fluxes of outgoing ultrarelativistic neutrinos taking into account the change of the neutrino polarization owing to spin oscillations. Using the conservative value of the neutrino magnetic moment and realistic radial distributions of the matter density and the magnetic field strength, we get that these fluxes are reduced by several percent compared to the case when no spin oscillations are accounted for. In some situations, there are spikes in the neutrino fluxes because of the neutrino interaction with the rotating plasma of an accretion disk. Taking into account the uncertainties in the astrophysical neutrino fluxes, the predicted effects turn out to be quite small to be observed with the current neutrino telescopes., Comment: 15 pages in LaTeX, JCAP LaTeX style, 14 eps figures; text is revised; matches the version published in JCAP

We reconsider the problem of the birefringence of electromagnetic (EM) waves in a medium consisting of a plasma and a $\nu\bar{\nu}$-gas within the Standard Model of particle physics. The considered effect arises in such a medium due to the parity violation for the electroweak neutrino-electron interaction. Our recent calculations of the electroweak correction to the photon polarization operator in the electroweak plasma allow us to significantly improve some previous estimates of such effect in astrophysics. We estimate the rotary power for EM waves propagating in a non-relativistic plasma in the intergalactic space and interacting with the gas of relic neutrinos and antineutrinos there. We show that, in presence of a plasma, the EM wave birefringence effect in a $\nu\bar{\nu}$-gas exceeds significantly that effect in a $\nu\bar{\nu}$-gas in empty space considered earlier. These previous treatments of the birefringence relied on the calculations of the refraction index for on-shell photons in vacuum using the forward scattering amplitude $\gamma\nu\to \gamma\nu$ with virtual charged leptons in Feynman diagrams. The possibility to observe experimentally the new effect suggested here is discussed., Comment: 12 pages in Latex, 1 eps figure, JCAP LaTeX style; title has been changed, minor corrections in the text; version published in JCAP

We study the evolution of axions interacting with primordial magnetic fields (PMFs) starting just from the QCD phase transition in the expanding universe. This interaction is owing to the Primakoff effect. Adopting the zero mode approximation for axions, we derive the system of equations for axions and magnetic fields, where the expansion of the universe and the spectra of magnetic fields are accounted for exactly. We find that the contribution of the Primakoff effect to the dynamics of axions and magnetic fields is rather weak. It confirms some previous estimates leading to analogous conclusions, when accounting here for the Hubble expansion both for an uniform axion field and non-uniform PMFs using Fourier spectra for their energy and helicity densities. We solve the corresponding system of the evolution equations and find that the axion zero mode, when evolving during radiation era, has its amplitude at the level sufficient for that axion to be a good candidate for the cold dark matter., Comment: 8 pages in Revtex, 4 eps figures; accepted for publication in Phys.Rev.D

We study the evolution and oscillations of fixed massive neutrinos interacting with stochastic gravitational waves (GWs). The energy spectrum of these GWs is Gaussian, with the correlator of the amplitudes being arbitrary. We derive the equation for the density matrix for flavor neutrinos in this case. In the two flavors approximation, this equation can be solved analytically. We find the numerical solution for the density matrix in the general case of three neutrino flavors. We consider merging binary black holes as sources of stochastic GWs with realistic spectra. Both normal and inverted mass orderings are analyzed. We discuss the relaxation of the neutrino fluxes in stochastic GWs emitted mainly by supermassive black holes. In this situation, we obtain the range of energies and the propagation lengths for which the relaxation process is the most efficient. We discuss the application of our results for the observation of fluxes of astrophysical neutrinos., Comment: 13 pages in JCAP LaTeX style, 6 eps figures, 2 tables; paper is revised, appendix is added, results are slightly modified; version published in JCAP

Spin oscillations of neutrinos, gravitationally scattered off a black hole (BH), are studied. The cases of nonrotating and rotating BHs are analyzed. We derive the analytic expressions for the transition and survival probabilities of spin oscillations when neutrinos interact with these gravitational backgrounds. The obtained transition probabilities depend on the impact parameter, as well as the neutrino energy and the particle mass. We find that there is a possibility of spin oscillations of ultrarelativistic neutrinos scattering off a rotating BH. Then, considering the neutrino scattering off BH surrounded by background matter, we derive the effective Schrodinger equation for spin oscillations. The numerical solution of this equation is obtained in the case of a supermassive BH with a realistic accretion disk. Spin effects turn out to be negligible in the neutrino scattering in the Schwarzschild metric. In the Kerr metric, we find that the observed neutrino fluxes can be reduced almost 10% because of spin oscillations when ultrarelativistic neutrinos experience gravitational scattering. The neutrino interaction with an accretion disk results in the additional modification of the intensities of outgoing neutrino fluxes. We consider the applications of the obtained results for the neutrino astronomy., Comment: 22 pages, 20 eps figures, LaTeX2e, published version. arXiv admin note: substantial text overlap with arXiv:1911.08317

We study chiral fermions electroweakly interacting with a background matter having the nonuniform density and the velocity arbitrarily depending on coordinates. The dynamics of this system is described approximately by finding the Berry phase. The effective action and the kinetic equations for right and left particles are derived. In the case of a rotating matter, we obtain the correction to the anomalous electric current and to the Adler anomaly. Then we study some astrophysical applications. Assuming that the chiral imbalance in a rotating neutron star vanishes, we obtain the rate of the magnetic helicity change owing to the interaction of chiral electrons with background neutrons. The characteristic time of the helicity change turns out to coincide with the period of the magnetic cycle of some pulsars., Comment: 14 pages in LaTeX2e, 1 eps figure, to be published in Nucl.Phys.B

We propose the mean field dynamo model for the generation of strongest magnetic fields, $B\sim 10^{15}\,{\rm G}$, in a neutron star (NS) accounting for the chiral magnetic effect (CME) driven by the shock in a supernova (SN) progenitor of that NS. The temperature jump at a narrow shock front, where an initial magnetic field existing in inflowing matter rises sharply, is the source of the CME that prevails significantly the erasure of the CME due to the spin-flip through Coulomb collisions in plasma. The growth of the magnetic field just behind the shock given by the instability term $\nabla\times (\alpha {\bf B})$ in induction equation, stops after a successful SN explosion that throws out the mantle of a protoneutron star. As a result, such an explosion interrupts the transfer of strongly magnetized plasma from the shock onto NS surface and leads to the saturation of the magnetic field. Assuming the rigid protostar rotation, we employ the mean field dynamo, which is similar to the $\alpha^2$-dynamo known in the standard magnetohydrodynamics (MHD). The novelty of our model is that $\alpha^2$-dynamo is based on concepts of particle physics, applied in MHD, rather than by a mirror asymmetry of convective vortices in the rotating convection., Comment: 18 pages, 8 eps figures, LaTeX2e. arXiv admin note: text overlap with arXiv:1909.03236

The Adler-Bell-Jackiw anomaly for massive particles is studied in an external magnetic field. The contributions of the mean spin and the pseudoscalar are accounted for in the quasiclassical approximation. The equation for the evolution of the magnetic helicity with the new quantum corrections is derived. We show that the quantum contribution to the helicity evolution can overcome the classical one in the dense degenerate matter which can be present in the core of a neutron star. The application of the obtained results for the interpretation of magnetar bursts are discussed., Comment: 6 pages in pdflatex, 1 pdf figure; contribution to the proceedings of the 4th International conference on particle physics and astrophysics (October 22-26, 2018, Moscow, Russia)

We review the application of the relativistic quantum mechanics method for the description of neutrino oscillations for the studies of spin-flavor oscillations in background matter under the influence of a plane electromagnetic wave. Basing on the new exact solution of the Dirac-Pauli equation for a massive neutrino in the given external fields, we derive the transition probabilities for spin and spin-flavor oscillations. The obtained expressions are analyzed for different types of the neutrino magnetic moments. Our results are compared with findings of other authors., Comment: 4 pages, 2 eps figures, contribution to the proceedings of the 19th Lomonosov Conference on Elementary Particle Physics (Moscow, Russia, August 22-28, 2019)

We study spin oscillations of neutrinos gravitationally scattered off a nonrotating black hole (BH). We derive the transition and survival probabilities of spin oscillations in quadratures when neutrinos interacts with BH only. The dependence of the probabilities on the impact parameter is analyzed. Then, we obtain the effective Schr\"{o}dinger equation for neutrino spin oscillations in neutrino scattering off BH surrounded by background matter. This equation is solved numerically in the case of a supermassive BH with a realistic accretion disk. We find that the observed neutrino fluxes can be reduced almost 20% because of spin oscillations when neutrinos experience gravitational scattering. The neutrino interaction with an accretion disk results in the additional asymmetry in the intensities of outgoing fluxes depending on the neutrino trajectory., Comment: 16 pages in LaTeX2e, 20 eps figures

We study spin and flavor oscillations of neutrinos under the influence of gravitational waves (GWs). We rederive the quasiclassical equation for the evolution of the neutrino spin in various external fields in curved spacetime starting from the Dirac equation for a massive neutrino. Then, we consider neutrino spin oscillations in nonmoving and unpolarized matter, a transverse magnetic field, and a plane GW. We show that a parametric resonance can take place in this system. We also study neutrino flavor oscillations in GWs. The equation for the density matrix of flavor neutrinos is solved when we discuss the neutrino interaction with stochastic GWs emitted by coalescing supermassive black holes. We find the fluxes of cosmic neutrinos, undergoing flavor oscillations in such a gravitational background, which can be potentially measured by a terrestrial detector. Some astrophysical applications of our results are considered., Comment: 6 pages, pdflatex, 4 pdf figures, J.Phys.Conf.Ser. LaTeX style; contribution to proceedings of DSPIN-2019 (JINR, Dubna, Russia, September 2-6 2019)

We suggest a new mean field dynamo model in anomalous MagnetoHydroDynamics (AMHD) accounting for the mean spin (polarization) of the magnetized chiral (ultrarelativistic) plasma of a neutron star (NS). For simplicity we consider a non-superfluid NS with its rigid rotation neglecting also any matter turbulence (convection) within a star. On this way, we recover the Chiral Magnetic Effect (CME) as a possible source for the amplification of a seed, sufficiently strong magnetic field, $B\sim 10^{13}\,\text{G}$, up to values $B\gtrsim 10^{18}\,\text{G}$ in old NS's, having ages $t\gtrsim 10^6\,\text{yr}$. The important issue in AMHD model suggested is the continuous evolution of the chiral imbalance providing the CME for these ages, $\partial_t\mu_5 (t)\neq 0$, in spite of the fast spin-flip in Coulomb collisions in the dense NS plasma that leads to vanishing $\mu_5\to 0$ at an earlier epoch in the corresponding protoneutron star. In contrast to the conventional mean-field dynamos, the dynamo drivers in the model are produced due to magnetic field generated at the previous stages of stellar evolution. It makes our model basically nonlinear., Comment: 14 pages in LaTeX2e, JCAP LaTeX style, 6 eps figures. The paper has been withdrawn since the main results are incorrect. We have partly corrected them in arXiv:2001.08139

We study neutrino flavor oscillations in a plane gravitational wave (GW) with circular polarization. For this purpose we use the solution of the Hamilton-Jacobi equation to get the contribution of GW to the effective Hamiltonian for the neutrino mass eigenstates. Then, considering stochastic GWs, we derive the equation for the density matrix for flavor neutrinos and analytically solve it in the two flavors approximation. The equation for the density matrix for the three neutrino flavors is also derived and solved numerically. In both cases of two and three neutrino flavors, we predict the ratios of fluxes of different flavors at a detector for cosmic neutrinos with relatively low energies owing to the interaction with such a GW background. The obtained results are compared with the recent observation of the flavor content of the astrophysical neutrino fluxes., Comment: 11 pages in Revtex4.1, 4 eps figures; paper is significantly revised, 3 flavors oscillations are studied, new figures are included, new Sec. IV is added; version to be published in Phys.Rev.D

We suggest the generalization of the Anomalous Magneto-Hydro-Dynamics (AMHD) in the chiral plasma of a neutron star (NS) accounting for the mean spin in the ultrarelativistic degenerate electron gas within the magnetized NS core as a continuing source of the chiral magnetic effect. Using the mean field dynamo model generalized in AMHD, one can obtain the growth of a seed magnetic field up to $10^{18}\,\text{G}$ for an old non-superfluid NS at its neutrino cooling era $t < 10^6\,\text{yr}$, while neglecting any matter turbulence within its core and assuming the rigid NS rotation. The application of the suggested approach to the evolution of magnetic fields observed in magnetars, $B\sim 10^{15}\,\text{G}$, should be self-consistent with all approximations used in the suggested laminar dynamo, at least, up to the jumps of growing fields., Comment: 15 pages, 9 eps figures, JCAP latex style; title is modified, minimal changes in the text; version published in JCAP

We study spin oscillations of massive Dirac neutrinos in background matter, electromagnetic and gravitational fields. First, using the Dirac equation for a neutrino interacting with the external fields in curved spacetime, we rederive the quasiclassical equation for the neutrino spin evolution, which was proposed previously basing on principles of the general covariance. Then, we apply this result for the description of neutrino spin oscillations in nonmoving and unpolarized matter under the influence of a constant transverse magnetic field and a gravitational wave. We derive the effective Schr\"odinger equation for neutrino oscillations in these external fields and solve it numerically. Choosing realistic parameters of external fields, we show that the parametric resonance can take place in spin oscillations of low energy neutrinos. Some astrophysical applications are briefly discussed., Comment: 11 pages in Revtex, 4 pdf figures; paper is significantly revised; figures are replotted; the discussion on spin evolution in curved spacetime is extended; Sec. III, where astrophysical applications are considered, is significantly revised; version to be published in Phys.Rev.D

We study oscillations of Dirac neutrinos in background matter and a plane electromagnetic wave. First, we find the new exact solution of the Dirac-Pauli equation for a massive neutrino with the anomalous magnetic moment electroweakly interacting with matter under the influence of a plane electromagnetic wave with the circular polarization. We use this result to describe neutrino spin oscillations in the external fields in question. Then we consider several neutrino flavors and study neutrino spin-flavor oscillations in this system. For this purpose we formulate the initial condition problem and solve it accounting for the considered external fields. We derive the analytical expressions for the transition probabilities of spin-flavor oscillations for different types of neutrino magnetic moments. These analytical expressions are compared with the numerical solutions of the effective Schr\"odinger equation and with the findings of other authors. In particular, we reveal that a resonance in neutrino spin-flavor oscillations in the considered external fields cannot happen contrary to the previous claims. Finally, we briefly discuss some possible astrophysical applications., Comment: 18 pages in LaTeX, 4 eps fugures; more detailed comparison with previous studies is added, several new references are included, multiple typos are corrected; matches the version to be published in PRD

We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation, are derived for different spectral zones. We are particularly interested in the spectral regions which are localized near the lowest and the maximal frequencies, as well as in the vicinity of a central frequency. The cases of discrete orthogonal grids with dimensions from 1 to 4 are analyzed. The possibility of the propagation of waves in the considered situations is substantiated by numerical simulations., Comment: 16 pages in LaTeX, 17 pdf figures, 2 tables; matches the published version, which can be retrieved here http://jomardpublishing.com/UploadFiles/Files/journals/AMMAV1N1/V3N3/DvornikovS.pdf

We study the generation of an electric current, along the external magnetic field, of fermions, interacting by parity violating electroweak forces with background matter. First, we discuss the situation of massive particles with nonzero anomalous magnetic moments. We show that the induced current is vanishing for such particles in the state of equilibrium. Then, the case of massless fermions is studied. We demonstrate that the contribution of the electroweak interaction is washed out from the expression for the current, which turns out to coincide with the prediction of the chiral magnetic effect. Our results are compared with findings of other authors., Comment: 8 pages in LaTeX; EPJ Web of Conferences style; contribution to proceedings of Quarks-2018: 20th International Seminar on High Energy Physics (May, 27 - June, 2 2018, Valday, Russia)

We study spin and spin-flavor oscillations of Dirac neutrinos in a plane electromagnetic wave with circular polarization. The evolution of massive neutrinos with nonzero magnetic moments in the field of an electromagnetic wave is based on the exact solution of the Dirac-Pauli equation. We formulate the initial condition problem to describe spin-flavor oscillations in an electromagnetic wave. The transition probabilities for spin and spin-flavor oscillations are obtained. In case of spin-flavor oscillations, we analyze the transition and survival probabilities for different neutrino magnetic moments and various channels of neutrino oscillations. As an application of the obtained results, we study the possibility of existence of $\nu_{e\mathrm{L}}\to\nu_{\mu\mathrm{R}}$ oscillations in an electromagnetic wave emitted by a highly magnetized neutron star. Our results are compared with findings of other authors., Comment: 23 pages in LaTeX2e, 23 eps figures; paper was significantly extended, new Sec. 5 was added, several new figures and references were included; version published in PRD

We analyze the role of the surface terms in the conservation law for the sum of the magnetic helicity density and the chiral imbalance of the charged particle densities. These terms are neglected in the Anomalous MagnetoHydroDynamics (AMHD), where infinite volume is considered typically. We discuss a finite volume system, such as a magnetized neutron star (NS), and study the contribution of the surface terms to the evolution of the magnetic helicity. Accounting for the fast washing out of the chiral imbalance in a nascent NS, we demonstrate that the surface terms contribution can potentially lead to the reconnection of magnetic field lines and subsequent gamma or X-ray bursts observed from magnetars. We derive the additional surface terms originated by the mean spin flux through a volume boundary arising due to macroscopic spin effects in electron-positron plasma. Then, comparing this quantum surface term with the classical one known in standard MHD, we find that the new quantum contribution prevails over classical term for the rigid NS rotation only., Comment: 16 pages in pdflatex, 1 pdf figure, jcap latex style; paper was significantly revised, Sec. 3 was extended, some notations were improved; version published in JCAP

We study the excitation of the electric current of chiral fermions along the external magnetic field, known as the chiral magnetic effect, in the presence of the background axial-vector field. The calculation of the current is based on the exact solution of the Dirac equation for these fermions accounting for the external fields. First, this solution was obtained for massive particles and, then, we consider the chiral limit, which is used in the anomalous current computation. We obtain that, in this situation, the anomalous current does not contain the direct contribution of the axial-vector field. This result is compared with findings of other authors., Comment: 13 pages in pdflatex, 2 pdf figures; paper was significantly revised, Sec. 4 was extended by the discussion of the applicability of chiral phenomena to neutron star physics; matches the version to be published in Phys.Rev.D

We study the possibility of the existence of the electric current, formed by massive electrons and positrons, flowing along an external magnetic field. The charged fermions are supposed to have nonzero anomalous magnetic moments and electroweakly interact with background matter. The expression for the current is obtained on the basis of the exact solution of the Dirac equation in the corresponding external fields. We demonstrate that, in the state of equilibrium, such a current is vanishing for any characteristics of the electron-positron plasma as well as the external fields. Our results are compared with the recent findings of other authors., Comment: 14 pages in LaTeX2e; paper was significantly extended; matches the variant published in IJMPA

We review the results in our recent works on the generation of strong magnetic fields in compact stars driven by the parity violating electroweak interactions between background fermions. The cases of a neutron star, a hybrid star, and a quark star are considered. We formulate the system of kinetic equations for the description of the spectra of the magnetic energy and the magnetic helicity, as well as for the chiral imbalances. Turbulence effects, which can be important for the evolution of small-scale magnetic field, are also taken into account. We find the numerical solution of these equations in case of large- and small-scale magnetic fields in quark matter. The applications of the obtained results for the generation of large-scale magnetic fields in magnetars and for the explanation of magnetar bursts are discussed., Comment: 5 pages in LaTeX2e, 8 eps figures; contribution to the proceedings of the International Conference "Modern Trends in Physics" (Baku, Azerbaijan, April 20-22, 2017)

The neutrino asymmetry in the early universe plasma, $n_\nu - n_{\bar \nu}$, is calculated both before and after the electroweak phase transition (EWPT). In the Standard Model before EWPT, the leptogenesis is well known to be driven by the abelian anomaly in a massless hypercharge field. The generation of the neutrino asymmetry in the Higgs phase after EWPT, in its turn, has not been considered previously because of the absence of any quantum anomaly in an external electromagnetic field for such electroneutral particles as neutrino, unlike the Adler-Bell-Jackiw anomaly for charged left and right polarized massless electrons in the same electromagnetic field. Using the neutrino Boltzmann equation, modified by the Berry curvature term in the momentum space, we establish the violation of the macroscopic neutrino current in plasma after EWPT and exactly reproduce the nonconservation of the lepton current in the symmetric phase before EWPT arising in quantum field theory due to the nonzero lepton hypercharge and corresponding triangle anomaly in an external hypercharge field. In the last case, the non-conservation of the lepton current is derived through the kinetic approach without a computation of corresponding Feynman diagrams. Then the new kinetic equation is applied for the calculation of the neutrino asymmetry accounting for the Berry curvature and the electroweak interaction with background fermions in the Higgs phase. Such an interaction generates a neutrino asymmetry through the electroweak coupling of neutrino currents with electromagnetic fields in plasma, which is $\sim G_\mathrm{F}^2$. It turns out that this effect is especially efficient for maximally helical magnetic fields., Comment: 18 pages in LaTeX2e, 4 eps figures; based on talk given on the 3rd International Conference on Particle Physics and Astrophysics ICPPA-2017 (October 2-5, 2017, Moscow, Russia); to be published in the special issue of Int.J.Mod.Phys.D

We consider the system of massive electrons, possessing nonzero anomalous magnetic moments, which electroweakly interact with background neutrons under the influence of an external magnetic field. The Dirac equation for such electrons is exactly solved. Basing on the obtained solution, we find that a nonzero electric current of these electrons can flow along the magnetic field. Accounting for the new current in the Maxwell equations, we demonstrate that a magnetic field in this system appears to be unstable. Then we consider a particular case of a degenerate electron gas, which may well exist in a neutron star, and show that a seed magnetic field can be amplified by more than one order of magnitude. Finally we discuss the application of our results for the explanation of the electromagnetic radiation emitted by magnetars., Comment: 10 pages in LaTeX, 2 eps figures; contribution to the proceedings of 52nd Rencontres de Moriond "Very High Energy Phenomena in the Universe" (La Thuile, Italy, March 18-25, 2017)

We describe the generation of the electric current flowing along the external magnetic field in the system of massive charged fermions, possessing anomalous magnetic moments and electroweakly interacting with background matter. This current is shown to result in the instability of the magnetic field leading to its growth. Some astrophysical applications are discussed., Comment: 3 pages in LaTeX, 2 eps figures; Contribution to the proceedings of 18th Lomonosov Conference on Elementary Particle Physics (Moscow, Russia, August 24-30, 2017)

A model of a stable plasma formation, based on radial quantum oscillations of charged particles, is discussed. The given plasmoid is described with the help of the nonlinear Schr\"odinger equation. A new phenomenon of the effective attraction between oscillating charged particles is considered within the framework of the proposed model. The possible existence of a composite plasma structure is also discussed. Hypothesis about using the obtained results to describe natural long-lived plasma formations, which can serve as alternative energy sources, is put forward., Comment: 6 pages in pdf; mini review to be published in Russian Physics Journal

We study the evolution of magnetic fields in turbulent hot plasma of the early Universe accounting for the chiral magnetic effect. The magnetohydrodynamic turbulence is modeled by replacing the matter velocity in the advection term in the Faraday equation with the Lorentz force. The system of the kinetic equations for the spectra of the densities of the magnetic helicity and the magnetic energy, as well as for the chiral imbalance, is derived. The amplification of the magnetic field is shown to result from the presence of the chiral magnetic effect solely. The system of the kinetic equations is solved numerically in primordial plasma after the electroweak phase transition. The influence of the matter turbulence on the magnetic field evolution is examined for different seed magnetic fields., Comment: 5 pages in LaTeX2e, 6 eps figures; J. Phys. Conf. Ser. LaTeX style; Contribution to the proceedings of the 3rd International Conference on Particle Physics and Astrophysics (October 2-5, 2017; Moscow, Russia)

We study neutrino spin oscillations in background matter under the influence of strong electromagnetic and gravitational fields. The neutrino spin evolution is treated quasiclassically. We derive the effective Hamiltonian governing spin oscillations of a neutrino moving in the vicinity of a black hole and interacting with a relativistic magnetized accretion disk around a black hole. Applications for the studies of spin oscillations of astrophysical neutrinos are considered., Comment: 6 pages, 2 eps figires, J.Phys.Conf.Ser. LaTeX style; Contribution to the proceedings of DSPIN-2017, September 11-15, 2017, Dubna, Russia

It is shown that the electric current of massive fermions along the external magnetic field can be excited in the case when particles possess anomalous magnetic moments and electroweakly interact with background matter. This current is calculated on the basis of the exact solution of the Dirac equation in the external fields. It is shown that the magnetic field becomes unstable if this current is taken into account in the Maxwell equations. Considering a particular case of a degenerate electron gas, which can be found in a neutron star, it is revealed that the seed magnetic field can be significantly enhanced. The application of the results to astrophysics is also discussed., Comment: 9 pages in LaTeX2e, 2 eps figures; paper is significantly revised, the comparison with the chiral magnetic effect is added; version to be published in JETP Letters