Toward diagnosing neutrino non-unitarity through CP phase correlations

Abstract

We discuss correlations between the νSM CP phase δ 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 et al. (DMP) to include the UV effect expressed by the α parametrization. By analyzing the DMP-UV perturbation theory to first order, we are able to draw a completed picture of the δ -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 chiraltype [e −iδ α µe , e −iδ α τ e , α τ µ ] (PDG convention) correlation in the entire high-energy region |ρE| > ∼ 6 (g/cm 3 ) GeV, and (2) (blobs of the α parameters) -e ±iδ correlation in anywhere else. Some relevant aspects for measurement of the UV parameters, such as the necessity of determining all the α βγ elements at once, are also pointed out.