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We formulate a perturbative framework for the flavor transformation of thestandard three active neutrinos but with non-unitary flavor mixing matrix, asystem which may be relevant for leptonic unitarity test. We use the $\alpha$parametrization of the non-unitary matrix and take its elements $\alpha_{\beta\gamma}$ ($\beta,\gamma = e,\mu,\tau$) and the ratio $\epsilon \simeq \Deltam^2_{21} / \Delta m^2_{31}$ as the small expansion parameters. Qualitativelynew two features that hold in all the oscillation channels are uncovered in theprobability formula obtained to first order in the expansion: (1) The phases ofthe complex $\alpha$ elements always come in into the observable in theparticular combination with the $\nu$SM CP phase $\delta$ in the form $[e^{- i\delta } \bar{\alpha}_{\mu e}, ~e^{ - i \delta} \bar{\alpha}_{\tau e},~\bar{\alpha}_{\tau \mu}]$ under the PDG convention of unitary $\nu$SM mixingmatrix. (2) The diagonal $\alpha$ parameters appear in particular combinations$\left( a/b - 1 \right) \alpha_{ee} + \alpha_{\mu \mu}$ and $\alpha_{\mu \mu} -\alpha_{\tau \tau}$, where $a$ and $b$ denote, respectively, the matterpotential due to CC and NC reactions. This property holds only in the unitaryevolution part of the probability, and there is no such feature in the genuinenon-unitary part, while the $\delta$ - $\alpha$ parameter phase correlationexists for both. The reason for such remarkable stability of the phasecorrelation is discussed.

Standard versus Non-Standard CP Phases in Neutrino Oscillation in Matter with Non-Unitarity