Perturbing neutrino oscillations around the solar resonance

Atmospheric neutrinos at low energies, $E \lsim 500$ MeV, is known to be a rich source of information of lepton mixing parameters. We formulate a simple perturbative framework to elucidate the characteristic features of neutrino oscillation at around the solar-scale enhancement due to the matter effect. The clearest message we could extract from our perturbation theory is that CP violation in the appearance oscillation probability is large, a factor of $\sim 10$ times larger than CP violation at around the atmospheric-scale oscillation maximum. Underlying mechanism for it is that one of the suppression factors on the CP phase dependent terms due to smallness of $\Delta m^2_{21} / \Delta m^2_{31}$ are dynamically lifted by the solar-scale enhancement. Our framework has a unique feature as a perturbation theory in which large $\Delta m^2_{31}$ term outside the key 1-2 sector for the solar-scale resonance does not yield sizeable corrections. On the contrary, the larger the $\Delta m^2_{31}$, the smaller the higher order corrections.