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In the framework of three generations, we consider the CP violation inneutrino oscillation with matter effects. At first, we show that thenon-perturbative effects of two small parameters, \Delta m_{21}^2/\Deltam_{31}^2 and \sin \theta_{13}, become more than 50% in certain ranges of energyand baseline length. This means that the non-perturbative effects should beconsidered in detailed analysis in the long baseline experiments. Next, wepropose a method to include these effects in approximate formulas foroscillation probabilities. Assuming the two natural conditions,\theta_{23}=45^\circ and the fact that the matter density is symmetric, a setof approximate formulas, which involve the non-perturbative effects, has beenderived in all channels.Comment: 25 pages, 4 figures, version to appear in JHE

the journal of high energy physics/the journal of high energy physics

Large non-perturbative effects of small Δm221/Δm231and sin θ13on neutrino oscillation and CP violation in matter