Simple and Precise Factorization of the Jarlskog Invariant for Neutrino Oscillations in Matter

Abstract

For neutrino propagation in matter, we show that the Jarlskog invariant, which controls the size of true CP violation in neutrino oscillation appearance experiments, factorizes into three pieces: the vacuum Jarlskog invariant times two simple two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. If the solar effective matter potential and the atmospheric effective $\Delta m^2$ are chosen carefully for these two resonance factors, then the fractional corrections to this factorization are an impressive 0.04\% or smaller. We also show that the inverse of the square of the Jarlskog in matter ($1/{\hat{J}}^2$) is a fourth order polynomial in the matter potential which guarantees that it can be factored into two quadratics which immediately implies the functional form of our approximate, factorized expression.

7 pages, 3 figures; new results added, matches published version

References in corpus (4)

• Matter Density Profile Shape Effects at DUNE
• Matter Density versus Distance for the Neutrino Beam from Fermilab to Lead, South Dakota, and Comparison of Oscillations with a Variable and a Constant Density
• Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter
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