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

TL;DR

This paper develops more accurate analytical approximations for matter effects on CP violation in low-energy neutrino oscillations, aiding experimental analysis and understanding of matter-induced phenomena.

Contribution

It introduces improved analytical formulas for neutrino oscillation probabilities in matter at energies below 1 GeV, surpassing previous approximations in accuracy.

Findings

Analytical approximations are more accurate than previous models.

The matter-corrected Jarlskog parameter peaks at specific resonance energies.

Medium-baseline experiments in the 0.12-0.28 GeV range can effectively explore CP violation.

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.