Probing Non-unitary $CP$ Violation effects in Neutrino Oscillation Experiments

In the present work, we have considered minimal unitarity violation(MUV) scheme, to obtain the general expression for ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillation probability, in vacuum. For this channel, we have investigated the sensitivities to non-unitary parameters $\mathrm{\mid }{\rho }_{\mu \tau }\mathrm{\mid }$ and ${\omega }_{\mu \tau }$ with short baseline(SBL) experiments for normal as well as inverted hierarchical neutrino masses. We also check how the sensitivity to non-unitary parameters get modified for ${\theta }_{23}$ above and below maximality. We find that the $3\sigma$ sensitivity towards $\mathrm{\mid }{\rho }_{\mu \tau }\mathrm{\mid }$ is maximum for non-unitary phase ${\omega }_{\mu \tau }=0$, whereas it is minimum for ${\omega }_{\mu \tau }=\pm \pi$ in case of normal hierarchy(NH). However, the sensitivity is minimum at ${\omega }_{\mu \tau }=0$ and maximum for ${\omega }_{\mu \tau }=\pm \pi$ for inverted hierarchy(IH). We observe that for unitary $CP$ phase $\delta =0$ and $\delta =\pi \mathrm{/}2$, the sensitivity to measure non-unitarity remains same in both the cases. We, also, explore wide range of $L\mathrm{/}E$ to forecast, in principle, the possibilities to observe $CP$-violation due to unitary($\delta$) and non-unitary(${\omega }_{\mu \tau }$) phases. We find that the both phases can be disentangled, in principle, from each other, for the $L\mathrm{/}E$ range less than 200 km/GeV for ${\nu }_{\mu }\to {\nu }_{\tau }$ channel.