Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E \lesssim 1 GeV

Abstract

Given an accelerator-based neutrino experiment with the beam energy E \lesssim 1 GeV, we expand the probabilities of ν_μ\to ν_e and \overline ν_μ\to \overline ν_e oscillations in matter in terms of two small quantities Δ_{21}/Δ_{31} and A/Δ_{31}, where Δ_{21} \equiv m^2_2 - m^2_1 and Δ_{31} \equiv m^2_3 - m^2_1 are the neutrino mass-squared differences, and A measures the strength of terrestrial matter effects. Our analytical approximations are numerically more accurate than those made by Freund in this energy region, and thus they are particularly applicable for the study of leptonic CP violation in the low-energy MOMENT, ESS\nuSM and T2K oscillation experiments. As a by-product, the new analytical approximations help us to easily understand why the matter-corrected Jarlskog parameter \widetilde{\cal J} peaks at the resonance energy E_* \simeq 0.14 GeV (or 0.12 GeV) for the normal (or inverted) neutrino mass hierarchy, and how the three Dirac unitarity triangles are deformed due to the terrestrial matter contamination. We also affirm that a medium-baseline neutrino oscillation experiment with the beam energy E lying in the E_* \lesssim E \lesssim 2 E_* range is capable of exploring leptonic CP violation with little matter-induced suppression.

36 pages, 11 figures. A crucial mistake removed, highlights changed, and a comparison with Freund's result made

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Cited by in corpus (18)

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• Renormalization-Group Equations of Neutrino Masses and Flavor Mixing Parameters in Matter
• Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter
• Signatures of the genuine and matter-induced components of the CP violation asymmetry in neutrino oscillations
• Neutrino Oscillation in Dense Matter
• On the Properties of the Effective Jarlskog Invariant for Three-flavor Neutrino Oscillations in Matter
• Looking into Analytical Approximations for Three-flavor Neutrino Oscillation Probabilities in Matter
• A compact analytical approximation for a light sterile neutrino oscillation in matter
• Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations
• Sum rules and asymptotic behaviors of neutrino mixing in dense matter
• Leptonic unitarity triangles: RGE running effects and $\mu$-$\tau$ reflection symmetry breaking
• Connecting Leptonic Unitarity Triangle to Neutrino Oscillation with CP Violation in Vacuum and in Matter
• Radiative corrections to the lepton flavor mixing in dense matter
• Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter
• A Nearest-neighbor Expansion of Lepton Flavor Mixing in Powers of the $\mu$-$\tau$ Permutation Symmetry Breaking Effect