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 $U_{{\tiny MNS}}$, 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 Particle Data Group convention seen in the atmospheric oscillation region. An explicit perturbative calculation to the 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.

LOCAL DEMANDS ON STERILE NEUTRINOS

In a model-independent manner, we explore the local implications of a single neutrino oscillation measurement which cannot be reconciled within a three-neutrino theory. We examine this inconsistency for a single region of baseline to neutrino energy L/E. Assuming that sterile neutrinos account for the anomaly, we find that the local demands of this datum can require the addition to the theory of one to three sterile neutrinos. We examine the constraints which can be used to determine when more than one neutrino would be required. The results apply only to a given region of L/E. The question of the adequacy of the sterile neutrinos to satisfy a global analysis is not addressed here. Finally, using the results of a 3+2 analysis, we indicate values for unknown mixing matrix elements which would require two sterile neutrinos due to local demands only.