Physics of parameter correlations around the solar-scale enhancement in neutrino theory with unitarity violation

Abstract

We discuss physics of the three neutrino flavor transformation with non-unitary mixing matrix, with particular attention to the correlation between the $\nu$SM- and the $\alpha$ parameters which represent effect of unitarity violating (UV) new physics. Toward the goal, a new perturbative framework is created to illuminate the effect of non-unitarity in region of the solar-scale enhanced oscillations. We refute the skepticism about the physical reality of the $\nu$SM CP $\delta$ - $\alpha$ parameter phase correlation by analysis with the SOL convention of $U_{\text{MNS}}$ in which $e^{\pm i\delta }$ is attached to $s_{12}$. Then, a comparative study between the solar- and atmospheric-scale oscillation regions allowed by the framework reveals a dynamical $\delta -$(blobs of the $\alpha$ parameters) correlation in the solar oscillation region, in sharp contrast to the ``chiral'' type phase correlation $[e^{-i\delta }{\bar{\alpha }}_{\mu e},e^{-i\delta }{\bar{\alpha }}_{\tau e},{\bar{\alpha }}_{\tau \mu }]$ in the PDG convention seen in the atmospheric oscillation region. An explicit perturbative calculation to first order in the ${\nu }_{\mu }\to {\nu }_e$ channel allows us to decompose the UV related part of the probability into the unitary evolution part and the genuine non-unitary part. We observe that the effect of non-unitarity tends to cancel between these two parts, as well as between the different ${\alpha }_{\beta \gamma }$ parameters.

Title changed, physics discussions added, text 32 and total 45 pages