Expectation value of the axial-vector current in the external electromagnetic field

We are calculated the expectation value of the axial-vector current induced by the vacuum polarization effect of the Dirac field in constant external electromagnetic field. In calculations we use Schwingers proper time method. The effective Lagrangian has very simple Lorenz invariant form. Along with the anomaly term, it also contains two Lorenz invariant terms. The result is compared with our previous calculation of the photon - Z boson mixing in the magnetic field.

Transition Radiation by Standard Model Neutrinos at an Interface

We discuss the transition radiation process $ u to u gamma$ at an interface of two media. The medium fulfills the dual purpose of inducing an effective neutrino-photon vertex and of modifying the photon dispersion relation. The transition radiation occurs when at least one of those quantities have different values in different media. We present a result for the probability of the transition radiation which is both accurate and analytic. For $E_ u =1$MeV neutrino crossing polyethylene-vacuum interface the transition radiation probability is about $10^{-39}$ and the energy intensity (deposition) is about $10^{-34}$eV. At the surface of the neutron stars the transition radiation probability may be $sim 10^{-20}$. Our result on three orders of magnitude is larger than the results of previous calculations.}

Transition Radiation by Neutrinos

We calculate the transition radiation process $ u to u gamma$ at an interface of two media. The neutrinos are taken to be with only standard-model couplings. The medium fulfills the dual purpose of inducing an effective neutrino-photon vertex and of modifying the photon dispersion relation. The transition radiation occurs when at least one of those quantities have different values in different media. The neutrino mass is ignored due to its negligible contribution. We present a result for the probability of the transition radiation which is both accurate and analytic. For $E_ u =1$ MeV neutrino crossing polyethylene-vacuum interface the transition radiation probability is about $10^{-39}$ and the energy intensity is about $10^{-34}$ eV. At the surface of the neutron stars the transition radiation probability may be $sim 10^{-20}$. Our result on three orders of magnitude is larger than the results of previous calculations.

Describing neutrino oscillations in matter with Magnus expansion

We present new formalism for description of the neutrino oscillations in matter with varying density. The formalism is based on the Magnus expansion and has a virtue that the unitarity of the S-matrix is maintained in each order of perturbation theory. We show that the Magnus expansion provides better convergence of series: the restoration of unitarity leads to smaller deviations from the exact results especially in the regions of large transition probabilities. Various expansions are obtained depending on a basis of neutrino states and a way one splits the Hamiltonian into the self-commuting and non-commuting parts. In particular, we develop the Magnus expansion for the adiabatic perturbation theory which gives the best approximation. We apply the formalism to the neutrino oscillations in matter of the Earth and show that for the solar oscillation parameters the second order Magnus adiabatic expansion has better than 1% accuracy for all energies and trajectories. For the atmospheric $Delta m^2$ and small 1-3 mixing the approximation works well ($< 3 %$ accuracy for $sin^2 theta_{13} = 0.01$) outside the resonance region (2.7 - 8) GeV.