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The conventional approximate formula for neutrino oscillation in matter whichis obtained from the expansion in terms of the ratio of mass square differences$\alpha=\Delta m_{21}^{2}/\Delta m_{31}^{2}\approx0.03$, first proposed byCervera, et al and Freund, turns out to be an accurate formula for acceleratorneutrino experiments. Originally it required the neutrino energy to be wellabove the solar resonance to validate the expansion but it is found to be stillvery accurate when the formula is extrapolated to the resonance, which ispractically important for the T2K experiment. This paper shows that theaccuracy is guaranteed by cancellations of branch cut singularities and also,for the first time, analytically computes the actual error of the formula. Theactual error implies that the original requirement can be safely removed incurrent experiments.

Why Is The Neutrino Oscillation Formula Expanded In $\Delta m_{21}^{2}/\Delta m_{31}^{2}$ Still Accurate Near The Solar Resonance In Matter?