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

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 $U_{\text{\tiny MNS}}$ 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 $\nu_{\mu} \rightarrow \nu_{e}$ 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.