Describing neutrino oscillations in matter with Magnus expansion

Abstract

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 ∆m 2 and small 1-3 mixing the approximation works well (< 3% accuracy for sin 2 θ13 = 0.01) outside the resonance region (2.7 -8) GeV.

Where are we with light sterile neutrinos?

“…where |d ln N e /dx| R is related to the radial change of electron number density. This expression provides excellent agreement with exact calculation of neutrino oscillation in matter obtained by solving the neutrino propagation equation [135][136][137].…”

Oscillations of theBe7solar neutrinos inside the Earth

“…The expression in (14) is equivalent to the result of adiabatic perturbation theory [10]: + sin 2(2θ…”

Analytical treatment of long-term observations of the day-night asymmetry for solar neutrinos

“…This approach provides the solution up to any order of approximation, as well as the constraints on the remainder terms [22]. Unfortunately, this technique [23][24][25][26], as well as other general methods (see, e.g., [27,28]), does not readily provide a way to find the solution in its explicit and practically usable form, not firmly fixing the Earth model, namely, N e (x) density distribution. It is thus desirable to find an approximate analytical solution of equation (1), which is valid under quite general assumptions about the electron density profile N e (x).…”