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

We discuss the 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 the effect of unitarity-violating (UV) new physics. Towards this goal, a new perturbative framework is created to illuminate the effect of non-unitarity in the region of the solar-scale enhanced oscillations. We refute the skepticism about the physical reality of the $\nu$Standard Model CP phase $\delta$-$\alpha$ parameter phase correlation by analysis with the SOL convention of $U_{MNS}$, 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 $[e^{-i\delta }{\overline{\alpha }}_{\mu e},e^{-i\delta }{\overline{\alpha }}_{\tau e},{\overline{\alpha }}_{\tau \mu }]$ in the Particle Data Group convention seen in the atmospheric oscillation region. An explicit perturbative calculation to the 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.