The Effective $\Delta m_{ee}^2$ in Matter

Abstract

In this paper we generalize the concept of an effective $\Delta m_{ee}^2$ for ${\nu }_e/{\bar{\nu }}_e$ disappearance experiments, which has been extensively used by the short baseline reactor experiments, to include the effects of propagation through matter for longer baseline ${\nu }_e/{\bar{\nu }}_e$ disappearance experiments. This generalization is a trivial, linear combination of the neutrino mass squared eigenvalues in matter and thus is not a simple extension of the usually vacuum expression, although, as it must, it reduces to the correct expression in the vacuum limit. We also demonstrated that the effective $\Delta m_{ee}^2$ in matter is very useful conceptually and numerically for understanding the form of the neutrino mass squared eigenstates in matter and hence for calculating the matter oscillation probabilities. Finally we analytically estimate the precision of this two-flavor approach and numerically verify that it is precise at the sub-percent level.

arXiv comment9 pages, 6 figures, 1 table, comments welcome

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Cited by in corpus (6)

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• Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes
• Interplay between the factorization of the Jarlskog Invariant and location of the Solar and Atmospheric Resonances for Neutrino Oscillations in Matter
• A Modern Look at the Oscillation Physics Case for a Neutrino Factory
• Neutrino Oscillations in the Three Flavor Paradigm