Perturbative exponential expansion and matter neutrino oscillations

Abstract

We derive an analytical description of neutrino oscillations in matter based on the Magnus exponential representation of the time evolution operator. Our approach is valid in a wide range of the neutrino energies and properly accounts for the modifications that the respective probability transitions suffer when neutrinos originated in different sources traverse the Earth. The present approximation considerably improves over other perturbative treatments existing in the current literature. Furthermore, the analytical expressions derived inside the Magnus framework are remarkably simple, which facilitates their practical use. When applied to the calculation of the day-night asymmetry in the solar neutrino flux our result reproduces the numerical calculation with an accuracy better than 1% for the first order approximation. When the approximation is extended to the second order, the accuracy of the method is further improved by almost one order of magnitude, and it is still better than 5% even for neutrino energies as large as 100 MeV. In the GeV regime characteristic of atmospheric and accelerator neutrinos this accuracy is complemented by a good reproduction of the position of the maxima in the flavor transition probabilities.

Physical Review D 78, 045024 (2008)

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Cited by in corpus (7)

• The Magnus expansion and some of its applications
• Neutrino flavour transformation in supernovae
• Three Flavor Neutrino Oscillations in Matter: Flavor Diagonal Potentials, the Adiabatic Basis and the CP phase
• Associated production of prompt photons and heavy quarks in off-shell gluon-gluon fusion
• Analytical treatment of long-term observations of the day-night asymmetry for solar neutrinos
• Does the Borexino experiment have enough resolution to detect the neutrino flavor day-night asymmetry?
• Efficient numerical integration of neutrino oscillations in matter