The matter effect to T-violation at a neutrino factory

Abstract

We analyzed T-violation in neutrino oscillation by using perturbation methods with respect to $\Delta m_{21}^{2}L/2E$ and $\delta a(x)L/2E$, where $\delta a(x)$ represents the matter density fluctuation from its average value. We found that the matter contribution to T-violation arises from interferences between $\Delta m_{21}^{2}L/2E$ and $\delta a(x)L/2E$. In the 2nd order, the symmetric and asymmetric matter density fluctuations give effects to the $\sin \delta$ (intrinsic) and the $\cos \delta$ (fake) parts of T-violation. We give their analytic forms and analyze the matter contribution to the $\sin \delta$ and $\cos \delta$ terms. We found that, for L=3000km, both the symmetric and asymmetric matter density fluctuations give negligible contributions to T-violation, and that thus the constant (average) matter density gives a good approximation. On the other hand, we argue that, for L=7000km or longer length, T-violation turns out to become very small due to cancellation between the 1st and the 2nd order terms. This shows that the constant (average) matter approximation is not valid.

Latex, 30 pages, 6 figures

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