We show that the Standard Model electroweak interaction of ultrarelativistic electrons with nucleons (the eN interaction) in a neutron star (NS) permeated by a seed large-scale helical magnetic field provides its growth up to > 1 0 15 G during a time comparable with the ages of young magnetars ~104 yr. The magnetic field instability originates from the parity violation in the eN interaction entering the generalized Dirac equation tor right and left massless electrons in an external uniform magnetic field. We calculate the average electric current given by the solution of the modified Dirac equation containing an extra current for right and left electrons (positrons), which turns out to be directed along the magnetic field. Such a current includes both a changing chiral imbalance of electrons and the eN potential given by a constant neutron density in a NS. Then we derive the system of the kinetic equations for the chiral imbalance and the magnetic helicity which accounts for the eN interaction. By solving this system, we show that a sizable chiral imbalance arising in a neutron protostar due to the Urea process e[ + p -> N + veL diminishes very rapidly because of a huge chirality-flip rate. Thus the eN term prevails over the chiral effect, providing a huge growth of the magnetic helicity and the helical magnetic field. Som e neutron stars, called m agnetars, having m agnetic fields B ~ 1015-10 16 G, can be considered the strongest m agnets in our U niverse [1], Despite the existence o f various m odels for the generation o f such strong fields, based, e.g., on the turbulent dynam o [2], the origin of magnetic fields in m agnetars is still an open problem. Recently, in Ref. [3] the authors tried to apply the chiral magnetic effect [4,5], adapted successfully for the QCD plasm a [6], to tackle the problem o f m agnetic fields in magnetars. The approach o f Ref. [3] im plies the chiral kinetic theory, where the Vlasov equation is m odified when adding the Berry curvature term to the Lorentz force [7], The fate o f such a chiral plasm a instability is based on the A dler anom aly in QED with the nonconservation of the pseudovector current for m assless ferm ions y/Y rfsV in external electrom agnetic fields. Since this current is the difference o f right j f and left j]y currents, the assum ption o f a seed im balance betw een their densities given by the difference o f chem ical potentials, (nR -nL) ~ p s = {Br ~ Rl ) / 2 7* 0, w here « R L are the densities o f right and left ferm ions (electrons) andare their chem ical potentials, could lead to the m agnetic field instability we study here adding electrow eak interactions in the Standard M odel (SM).The same effect (while w ithout weak interactions) was used in Ref.[8] to study the self-consistent evolution of * maxim, dvomikov @ usp.br 'semikoz @ yandex.ru the magnetic helicity in the hot plasm a o f the early Universe driven by the change o f the lepton asym m etryIn it was shown that such an asym m etry dim inishes, p 5 -> 0, due to the growth o f the chirality...

We study neutrino spin oscillations in gravitational fields. The quasi-classical approach is used to describe the neutrino spin evolution. First we examine the case of a weak gravitational field. We obtain the effective Hamiltonian for the description of neutrino spin oscillations. We also receive the neutrino transition probability when a particle propagates in the gravitational field of a rotating massive object. Then we apply the general technique to the description of neutrino spin oscillations in the Schwarzschild metric. The neutrino spin evolution equation for the case of the neutrino motion in the vicinity of a black hole is obtained. The effective Hamiltonian and the transition probability are also derived. We examine the neutrino oscillations process on different circular orbits and analyze the frequencies of spin transitions. The validity of the quasi-classical approach is also considered.

We study the instability of magnetic fields in a neutron star core driven by the parity violating part of the electron-nucleon interaction in the Standard Model. Assuming a seed field of the order 10 12 G, that is a common value for pulsars, one obtains its amplification due to such a novel mechanism by about five orders of magnitude, up to 10 17 G, at time scales ∼ (10 3 − 10 5 ) yr. This effect is suggested to be a possible explanation of the origin of the strongest magnetic fields observed in magnetars. The growth of a seed magnetic field energy density is stipulated by the corresponding growth of the magnetic helicity density due to the presence of the anomalous electric current in the Maxwell equation. Such an anomaly is the sum of the two competitive effects: (i) the chiral magnetic effect driven by the difference of chemical potentials for the right and left handed massless electrons and (ii) constant chiral electroweak electron-nucleon interaction term, which has the polarization origin and depends on the constant neutron density in a neutron star core. The remarkable issue for the decisive role of the magnetic helicity evolution in the suggested mechanism is the arbitrariness of an initial magnetic helicity including the case of non-helical fields from the beginning. The tendency of the magnetic helicity density to the maximal helicity case at large evolution times provides the growth of a seed magnetic field to the strongest magnetic fields in astrophysics.

The derivation of the quasiclassical Lorentz invariant neutrino spin evolution equation taking into account general types of neutrino non-derivative interactions with external fields is presented. We discuss the constraints on the characteristics of matter and neutrino under which this quasiclassical approach is valid. The application of the obtained equation for the case of the Standard Model neutrino interactions with moving and polarized background matter is considered.It is commonly believed that neutrino physics provides strong evidence for physics beyond the Standard Model. In different extensions of the Standard Model new types of interactions are predicted for massive neutrinos. The problem of neutrino propagation in matter in the case of a general set of interactions with the background fermions has attracted considerable attention (see, for example [1,2]). Recently, we have developed the Lorentz invariant formalism for description of neutrino spin-flavor and flavor oscillations with the Standard Model vector and axial-vector interactions in moving matter under the influence of an arbitrary electromagnetic fields [3,4,5]. In particular, we have derived, within general assumption like Lorentz invariance and linearity over neutrino spin vector S µ and also over such characteristics of matter like fermions currents and polarizations, the evolution equation for the neutrino spin. We have used this evolution equation for description of neutrino oscillations in electromagnetic fields accounting for neutrino vector and axial-vector interactions with background fermions that corresponds to the case of the Standard Model weak interactions. Note that quasiclassical approach to the problem of neutrino spin relaxation in stochastic electromagnetic fields was used in ref. [6]. However, the problem of the neutrino spin evolution equation accounting also for more general new types of neutrino interactions is still remained open.We discuss below neutrino spin evolution in background matter in the case of a new physics model that admits a general set of new neutrino interac-1

We consider the massive Dirac neutrino electric charge and magnetic moment within the context of the standard model supplied with SU(2)-singlet right-handed neutrino in arbitrary R ξ gauge. Using the dimensional-regularization scheme we start with the calculations of the one-loop contributions to the neutrino electromagnetic vertex function exactly accounting for the neutrino mass. We examine the decomposition of the massive neutrino electromagnetic vertex function. It is found by means of direct calculations that the massive neutrino vertex function contains only the four form factors. Then we derive the closed integral expressions for different contributions to the neutrino electric form factor, electric charge, and magnetic moment. For several one-loop contributions to the neutrino charge and magnetic moment, that were calculated previously with mistakes by the other authors, we find the correct results. We show that the electric charge for the massive neutrino is a gauge independent and vanishing parameter in the first two orders of the expansion over the neutrino mass parameter b = (mν/MW ) 2 . From the obtained closed two-integral expression for a massive neutrino electric form factor it is also possible to derive the neutrino charge radius. In the particular choice of the 't Hooft-Feynman gauge we also demonstrate that the neutrino charge is zero in all orders of expansion over b, i.e. for arbitrary mass of neutrino. For each of the diagrams contributing to the neutrino magnetic moment, we obtain the expressions accounting for the leading (zeroth) and next-to-leading (first) order in b, where the gauge dependence is shown explicitly. Each of the contributions is finite and the sum of all contributions turns out to be gauge-independent. Our calculations also enable us to obtain the neutrino magnetic moment in theoretical models that differ from each other by the values of particles' masses, including the case of a very heavy neutrino. The general expression for the massive neutrino magnetic form factor is presented.

We study the magnetic field generation in a neutron star within the model based on the magnetic field instability in the nuclear matter owing to the electron-nucleon parity violating interaction. We suggest that the growing magnetic field takes the energy from thermal background fermions in the neutron star matter. The system of kinetic equations for the spectra of the magnetic helicity density and magnetic energy density as well as the chiral imbalance are solved numerically accounting for this energy source. We obtain that, for the initial conditions corresponding to a typical neutron star, the large scale magnetic field ∼ 10 15 G is generated during (10 4 − 10 5 ) yr. We suggest that the proposed model describes strong magnetic fields observed in magnetars.PACS numbers: 97.60. Jd, 11.15.Yc, 95.30.Qd The most plausible explanation of radiation of soft gamma repeaters [1] and anomalous X-ray pulsars [2] is the presence of strong magnetic fields B 10 15 G in a neutron star (NS). Such highly magnetized NSs are called magnetars. Various models, explaining the origin of such strong astrophysical magnetic fields, were reviewed in Ref. [3]. Nevertheless, the issue of the magnetic fields generation in magnetars still remains open.Recently in Refs. [4,5] we proposed the new model for the generation of strong magnetic fields in magnetars based on the instability of magnetic fields in dense degenerate matter composed of nonrelativistic neutrons and ultrarelativistic electrons interacting by parity violating electroweak forces. The idea that electroweak interaction can induce the magnetic field instability was put forward first in Ref. [6]. Within our model, basing on quite natural assumptions about the neutron star structure, we could describe the generation of large scale magnetic fields, with magnitudes predicted in magnetars, during time intervals comparable with magnetars ages.Despite the plausibility of the model developed in Refs. [4,5], it has a significant disadvantage. The instability of a magnetic field, proposed in Refs. [4,5], is a necessary but not a sufficient condition for the magnetic field growth. To describe the magnetic field generation in magnetars one should indicate the source which feeds the magnetic field growth. This issue is addressed in the present work.In this paper we further develop the model in Refs. [4,5]. We start with a brief description of the basic features of our model. Then we propose that magnetic fields can take the energy from the thermal motion of particles in the NS matter. We modify the kinetic equations, derived * maxdvo@izmiran.ru † semikoz@yandex.ru

The magnetohydrodynamics (MHD) is modified to incorporate the parity violation in the Standard Model leading to a new instability of magnetic fields in the electroweak plasma in the presence of nonzero neutrino asymmetries. The main ingredient for such a modified MHD is the antisymmetric part of the photon polarization tensor in plasma, where the parity violating neutrino interaction with charged leptons is present. We calculate this contribution to the polarization tensor connected with the Chern-Simons term in effective Lagrangian of the electromagnetic field. The general expression for such a contribution which depends on the temperature and the chemical potential of plasma as well as on the photon's momentum is derived. The instability of a magnetic field driven by the electron neutrino asymmetry for the ν-burst during the first second of a supernova explosion can amplify a seed magnetic field of a protostar, and, perhaps, can explain the generation of strongest magnetic fields in magnetars. The growth of a cosmological magnetic field driven by the neutrino asymmetry density ∆n ν = n ν − nν = 0 is provided by a lower bound on |ξ νe | = |µ νe |/T which is consistent with the well-known Big Bang nucleosynthesis (upper) bound on neutrino asymmetries in a hot universe plasma.

We study lepton asymmetry evolution in plasma of the early Universe before the electroweak phase transition (EWPT) accounting for chirality flip processes via Higgs decays (inverse decays) entering equilibrium at temperatures below TRL ≃ 10 TeV, TEW < T < TRL. We solve appropriate kinetic equations for leptons and Higgs bosons taking into account the lepton number violation due to Abelian anomalies for right and left electrons and neutrinos in the self-consistent hypercharge field obeying Maxwell equations modified by the contribution of the Standard Model of electroweak interactions. The violation of left lepton numbers and the corresponding violation of the baryon number due to sphaleron processes in symmetric phase is taken into account as well. Assuming the Chern-Simons wave configuration of the seed hypercharge field, we get the estimates of baryon and lepton asymmetries evolved from the primordial right electron asymmetry existing alone as partial asymmetry at T ≥ TRL. One finds a strong dependence of the asymmetries on the Chern-Simons wave number. We predict a nonzero chiral asymmetry ∆µ = µe R − µe L = 0 in this scenario evolved down to the EWPT moment that can be used as an initial value for the Maxwellian field evolution after EWPT.