Enhancement of CP Violating terms for Neutrino Oscillation in Earth Matter

Abstract

We investigate the ${\nu }_e\to {\nu }_{\mu }$ oscillation in the framework of three generations when neutrinos pass through the earth. The oscillation probability is represented by the form, $P({\nu }_e\to {\nu }_{\mu })=A\cos \delta +B\sin \delta +C$ in arbitrary matter profile by using the leptonic CP phase $\delta$. We compare our approximate formula in the previous paper with the formula which includes second order terms of $\alpha =\Delta m_{21}^2/\Delta m_{31}^2$ and $s_{13}=\sin {\theta }_{13}$. Non-perturbative effects of $\alpha$ and $s_{13}$ can be taken into account in our formula and the precision of the formula is rather improved around the MSW resonance region. Furthermore, we compare the earth matter effect of $A$ and $B$ with that of $C$ studied by other authors. We show that the magnitude of $A$ and $B$ can reach a few ten % of $C$ around the main three peaks of $C$ in the region $E>1$ GeV by numerical calculation. We give the qualitative understanding of this result by using our approximate formula. The mantle-core effect, which is different from the usual MSW effect, appears not only in $C$ but also in $A$ and $B$, although the effect is weakened.

Comments: 16 pages, 5 figures