Enhancement of CP violating terms for neutrino oscillation in Earth matter

We investigate the v(e) --> v(u) oscillation in the framework of three generations when neutrinos pass through the Earth. The oscillation probability is represented by the form, P(v(e) --> v(u)) = A cosdelta + B sindelta + 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 = Deltam(21)(2)/Deltam(31)(2) and s(13) = sintheta(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. (C) 2004 Elsevier B.V. All rights reserved.