Toward diagnosing neutrino non-unitarity through CP phase correlations

TL;DR

This paper explores how the CP phase in neutrino oscillations correlates with new physics phases indicating non-unitarity, extending perturbation theory to analyze these correlations across experimental conditions.

Contribution

It extends the DMP perturbation theory to include UV effects, providing a comprehensive analysis of CP phase correlations with new physics parameters in neutrino experiments.

Findings

Identifies two distinct correlation patterns between CP phase and UV parameters.

Highlights the importance of measuring all UV parameters simultaneously.

Provides a framework for diagnosing neutrino non-unitarity in experiments.

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 $\vert \rho E \vert \gsim 6~(\text{g/cm}^3)$ 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.