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We give a perturbation theory of neutrino oscillation in the Earth. Theperturbation theory is valid for neutrinos with energy $E \gsim 0.5$ GeV. It isformulated using trajectory dependent average potential. Non-adiabaticcontributions are included as the first order effects in the perturbationtheory. We analyze neutrino oscillation with standard matter effect and withnon-standard matter effect. In a three flavor analysis we show that theperturbation theory gives a precise description of neutrino conversion in theEarth. Effect of the Earth matter is substantially simplified in thisformulation.

Precise Formulation of Neutrino Oscillation in the Earth