# Jarlskog Invariant of the Neutrino Mapping Matrix - High Energy Physics - Phenomenology

Abstract: The Jarlskog Invariant $J { u-map}$ of the neutrino mapping matrix iscalculated based on a phenomenological model which relates the smallness oflight lepton masses $m e$ and $m 1$ of $u 1$ with the smallness of $T$violation. For small $T$ violating phase $\chi l$ in the lepton sector,$J { u-map}$ is proportional to $\chi l$, but $m e$ and $m 1$ are proportionalto $\chi l^2$. This leads to $J { u-map} \cong{1-6}\sqrt{\frac{m e}{m \mu}}+O \bigg\sqrt{\frac{m em \mu}{m \tau^2}}\bigg+O\bigg\sqrt{\frac{m 1m 2}{m 3^2}}\bigg$. Assuming$\sqrt{\frac{m 1m 2}{m 3^2}}<<\sqrt{\frac{m e}{m \mu}}$, we find$J { u-map}\cong 1.16\times 10^{-2}$, consistent with the present experimentaldata.

Author: R. Friedberg, T. D. Lee

Source: https://arxiv.org/