# Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with *E* ≲ 1 GeV

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## Abstract

Given an accelerator-based neutrino experiment with the beam energy *E* ≲ 1 GeV, we expand the probabilities of *ν* _{ μ } → *ν* _{ e } and \( {\overline{\nu}}_{\mu}\to {\overline{\nu}}_e \) oscillations in matter in terms of two small quantities Δ_{21} */*Δ_{31} and *A/*Δ_{31}, where *Δ* _{21}≡*m* _{2} ^{2} − *m* _{1} ^{2} and *Δ* _{31}≡*m* _{3} ^{2} − *m* _{1} ^{2} 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*ν*SM and T2K oscillation experiments. As a by-product, the new analytical approximations help us to easily understand why the matter-corrected Jarlskog parameter \( \tilde{\mathcal{J}} \) peaks at the resonance energy *E* _{∗} ≃ 0*.*14GeV (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* _{∗} ≲ *E* ≲ 2*E* _{∗} range is capable of exploring leptonic CP violation with little matter-induced suppression.

## Keywords

CP violation Neutrino Physics## Notes

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