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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…
We further develop and extend a recent perturbative framework for neutrino oscillations in uniform matter density so that the resulting oscillation probabilities are accurate for the complete matter potential versus baseline divided by…
Exact analytical expressions in terms of generalized confluent hypergeometric functions for the transition amplitudes of neutrino oscillations in presence of matter are computed for an arbitrary number of species. The density of matter is…
A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of…
We present a formalism for the matter effects in the Earth on low energy neutrino fluxes which is both accurate and has all advantages of a full analytic treatment. The oscillation probabilities are calculated up to second order term in…
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
We present a new treatment of the Earth matter effects on the neutrino oscillations that is valid for an arbitrary density profile. When applied to the the study of the day-night effect on the solar neutrino flux it renders us a simple…
We present approximative solutions to the neutrino evolution equation calculated by different methods. In a two neutrino framework, using the physical parameters which gives the main effects to neutrino oscillations from nu{e} to another…
We argue that the neutrino oscillation probabilities in matter are best understood by allowing the mixing angles and mass-squared differences in the standard parametrization to `run' with the matter effect parameter $a=2\sqrt{2}G_F N_e E$,…
We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric $\Delta m^2$ scales. Unlike previous works, we use a renormalized basis in which certain…
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a…
We give a perturbation theory of neutrino oscillation in the Earth. The perturbation theory is valid for neutrinos with energy $E \gsim 0.5$ GeV. It is formulated using trajectory dependent average potential. Non-adiabatic contributions are…
As the increasing of neutrino energy or matter density, the neutrino oscillation in matter may undergo "vacuum-dominated", "resonance" and "matter-dominated" three different stages successively. Neutrinos endure very different matter…
We present a semi-analytical derivation of the survival probability of solar neutrinos in the three generation scheme, based on the Magnus approximation of the evolution operator of a three level system, and assuming a mass hierarchy among…
Atmospheric neutrinos at low energies, $E \lsim 500$ MeV, is known to be a rich source of information of lepton mixing parameters. We formulate a simple perturbative framework to elucidate the characteristic features of neutrino oscillation…
Motivated by tremendous progress in neutrino oscillation experiments, we derive a new set of simple and compact formulas for three-flavor neutrino oscillation probabilities in matter of a constant density. A useful definition of the…
Analytic formulas are presented for three flavor neutrino oscillations in matter in the plane wave approximation. We calculate in particular the time evolution operator in both mass and flavor bases. We also find the transition…
Neutrino oscillations are one of the most studied and successful phenomena since the establishment of the solar neutrino problem in late 1960's. In this work we discuss the exact expressions for the probability P_{\alpha\beta} in a constant…
We examine the reliability of the theoretical methods presently used for analysis and prediction of neutrino oscillation phenomena. Of particular interest are the limitations imposed by branch points when expansions in one of the small…
This is revision of the S-Matrix theory of neutrino oscillations used for many years. We evaluate the transition probability of a $\mu$ to $e$ neutrino without an approximation used for many theoretical studies, and find important…