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

TL;DR

This paper develops a perturbative framework for neutrino oscillations with non-unitary mixing in matter, revealing new phase correlations and parameter combinations relevant for testing leptonic unitarity.

Contribution

It introduces a novel perturbative approach incorporating non-unitarity in neutrino oscillations, highlighting specific phase correlations and parameter combinations in matter.

Findings

Phases of non-unitary parameters combine with the standard CP phase in observable ways.

Diagonal non-unitary parameters appear in specific matter-dependent combinations.

Phase correlations between standard and non-unitary parameters are stable and discussed in detail.

Abstract

We formulate a perturbative framework for the flavor transformation of the standard three active neutrinos but with non-unitary flavor mixing matrix, a system 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 $\epsilon \simeq \Delta m^2_{21} / \Delta m^2_{31}$ as the small expansion parameters. Qualitatively new two features that hold in all the oscillation channels are uncovered in the probability formula obtained to first order in the expansion: (1) The phases of the complex $\alpha$ elements always come in into the observable in the particular 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 mixing matrix. (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 matter potential due to CC and NC reactions. This property holds only in the unitary evolution part of the probability, and there is no such feature in the genuine non-unitary part, while the $\delta$ - $\alpha$ parameter phase correlation exists for both. The reason for such remarkable stability of the phase correlation is discussed.