Toward diagnosing neutrino non-unitarity through CP phase correlations

Abstract

We discuss correlations between the $\nu$SM CP phase $\delta$ and the phases that originate from new physics which causes neutrino-sector unitarity violation (UV) at low energies. This study is motivated to provide one of the building pieces for a machinery to diagnose non-unitarity, our ultimate goal. We extend the perturbation theory of neutrino oscillation in matter proposed by Denton {\it et al.}~(DMP) to include the UV effect expressed by the $\alpha$ parametrization. By analyzing the DMP-UV perturbation theory to first order, we are able to draw a completed picture of the $\delta$ - UV phase correlations in the whole kinematical region covered by the terrestrial neutrino experiments. There exist the two regions with the characteristically different patterns of the correlations: (1) the chiral-type $[e^{-i\delta }{\alpha }_{\mu e},e^{-i\delta }{\alpha }_{\tau e},{\alpha }_{\tau \mu }]$ (PDG convention) correlation in the entire high-energy region $|\rho E|\text{gsim}6({\text{g/cm}}^3)$ GeV, and (2) (blobs of the $\alpha$ parameters) - $e^{\pm i\delta }$ correlation in anywhere else. Some relevant aspects for measurement of the UV parameters, such as the necessity of determining all the ${\alpha }_{\beta \gamma }$ elements at once, are also pointed out.

Comments: typo corrected, references added, version to appear in PTEP