Abstract
Given an accelerator-based neutrino experiment with the beam energy E \lesssim 1 GeV, we expand the probabilities of \nu_\mu \to \nu_e and \overline {\nu}_\mu \to \overline {\nu}_e oscillations in matter in terms of two small quantities \Delta_{21}/\Delta_{31} and A/\Delta_{31}, where \Delta_{21} \equiv m^2_2 - m^2_1 and \Delta_{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.
Highlights
JHEP07(2016)011 become invalid when E approaches vanishing.1 The reason is that mainly the longbaseline neutrino oscillation experiments with E 1 GeV were considered in those works
As a by-product, the new analytical approximations help us to understand why the matter-corrected Jarlskog parameter J peaks at the resonance energy E∗ 0.14 GeV for the normal neutrino mass hierarchy, and how the three Dirac unitarity triangles are deformed due to the terrestrial matter contamination
We affirm that a medium-baseline neutrino oscillation experiment with the beam energy E lying in the E∗ E 2E∗ range is capable of exploring leptonic CP violation with little matter-induced suppression
Summary
Given the effective neutrino masses mi and the effective lepton flavor mixing matrix U which have accommodated the matter-induced corrections to mi and U , the effective Hamiltonian responsible for the propagation of a neutrino beam in matter can be written as [21, 22]. Taking the best-fit values of θ12, θ13, ∆21 and ∆31 for example, we obtain E∗ 0.140 GeV (or 0.123 GeV) and J∗/J 1.10 (or 1.07) for the normal (or inverted) neutrino mass ordering from the analytical formulas in eqs. Because the next-to-leading-order terms of E∗ and J∗/J are both proportional to the expansion parameter α = ∆21/∆31 ±1/30, they exhibit a small but appreciable difference in figure 2 with respect to the normal and inverted neutrino mass hierarchies This observation indicates that even a low-energy neutrino oscillation experiment could have the potential to probe the CP- and T-violating effects and the neutrino mass ordering. Since E0 2E∗ holds as a good approximation, one could consider to set the neutrino beam energy E in the E∗ E 2E∗ range when designing a realistic medium-baseline oscillation experiment to probe the J /J 1 region of CP violation. The typical beam energies of the proposed MOMENT [13] and ESSνSM [14] experiments just lie in such an interesting region
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