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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 $ν$SM- and the $α$ 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 $ν$SM CP $δ$ - $α$ parameter phase correlation by analysis with the SOL convention of $U_{\text{\tiny MNS}}$ in which $e^{ \pm i δ}$ is attached to $s_{12}$. Then, a comparative study between the solar- and atmospheric-scale oscillation regions allowed by the framework reveals a dynamical $δ-$(blobs of the $α$ parameters) correlation in the solar oscillation region, in sharp contrast to the ``chiral'' type phase correlation $[e^{- i δ} \barα_{μe}, e^{ - i δ} \barα_{τe}, \barα_{τμ}]$ in the PDG convention seen in the atmospheric oscillation region. An explicit perturbative calculation to first order in the $ν_μ \rightarrow ν_{e}$ 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 $α_{βγ}$ parameters.