Matter Enhancement of T Violation in Neutrino Oscillation

We study the matter enhancement of T violation in neutrino oscillation with three generations. The magnitude of T violation is proportional to Jarlskog factor J . Recently, the elegant relation, (∆m)12(∆m)23(∆m)31Jm = ∆12∆23∆31J , is derived, where ∆ij = ∆m 2 ij/(2E) and the subscript m denotes the quantities in matter. Using this relation, we reconsider how Jm changes as the function of the matter potential a under the approximation |∆m2 12 | ≪ |∆m2 13 |. We show that the number of maxima for Jm depends on the magnitude of sin 2 2θ13 and there are two maxima considering the constraint to sin 2θ13 from CHOOZ experiment. One maximum of Jm at a = O(∆12) is given by J/ sin 2θ12, which leads to the large enhancement of Jm in the case of SMA MSW solution. The other maximum at a = O(∆13) is |∆12/∆13|J/ sin 2θ13 and the enhancement is possible if sin 2θ13 is small enough. These maximal values are consistent with the results obtained by other methods.