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We find an analytical expression of neutrino evolution operator in the Earthmatter using perturbative approach in the context of three neutrinooscillations. We find that our analytical expression is highly accurate bycomparing its results with the numerical solutions of neutrino evolutionequation at energy scales relevant for solar, reactor, atmospheric, andaccelerator neutrinos. Using our analytical approach we study the accuracy ofhypothesis of treating the Earth density piecewise constant. We also study howthe Earth matter effect can change the sensitivity to CP phase parameter$\delta _{CP}$. Through nadir angle averaged conversion probabilities ofneutrino and anti-neutrino, we find that the sensitivity to $\delta _{CP}$ ismaximum in the energy range 0.2 to 1 GeV and through energy averaged conversionprobabilities, we find that the sensitivity is maximum about nadir angle$72.5^{\text{o}}$ for neutrinos oscillating in the Earth matter.

The Effect of the Earth Matter on Three Neutrino Oscillations and Sensitivity to CP Phase Parameter