Abstract
In this paper we review different expansions for neutrino oscillation probabilities in matter in the context of long-baseline neutrino experiments. We examine the accuracy and computational efficiency of different exact and approximate expressions. We find that many of the expressions used in the literature are not precise enough for the next generation of long-baseline experiments, but several of them are while maintaining comparable simplicity. The results of this paper can be used as guidance to both phenomenologists and experimentalists when implementing the various oscillation expressions into their analysis tools.
Highlights
Over the last two decades neutrino oscillation measurements have become increasingly precise and are entering the precision era
Most of the current data coming from experiments using neutrinos from the sun, reactors, the atmosphere and particle accelerators can be described in terms of three-neutrino oscillations, which depend on the six oscillation parameters: two mass splittings m231, m221, three mixing angles θ12, θ13 and θ23 and a CPviolating phase δ
We focus on the oscillation maxima because the heights of the maxima are an important test for CP violation [48] and the locations of the maxima are an important test for the atmospheric mass splitting [49]
Summary
Over the last two decades neutrino oscillation measurements have become increasingly precise and are entering the precision era. Most of the current data coming from experiments using neutrinos from the sun, reactors, the atmosphere and particle accelerators can be described in terms of three-neutrino oscillations, which depend on the six oscillation parameters: two mass splittings m231, m221, three mixing angles θ12, θ13 and θ23 and a CPviolating phase δ. Many of these parameters are measured rather well as of [1].
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