The Discovery reach of $CP$ violation in neutrino oscillation with non-standard interaction effects

We have studied the $CP$ violation discovery reach in neutrino oscillation experiment with superbeam, neutrino factory and monoenergetic neutrino beam. For NSI satisfying model-dependent bound for shorter baselines (like CERN-Fr\'ejus set-up ) there is insignificant effect of NSI on the the discovery reach of $CP$ violation due to $\delta$. Particularly, for superbeam and neutrino factory we have also considered relatively longer baselines for which there could be significant NSI effects on $CP$ violation discovery reach for higher allowed values of NSI. For monoenergetic beam only shorter baselines are considered to study $CP$ violation with different nuclei as neutrino sources. Interestingly for non-standard interactions - $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$ of neutrinos with matter during propagation in longer baselines in superbeam, there is possibility of better discovery reach of $CP$ violation than that with only Standard Model interactions of neutrinos with matter. For complex NSI we have shown the $CP$ violation discovery reach in the plane of Dirac phase $\delta$ and NSI phase $\phi_{ij}$. The $CP$ violation due to some values of $\delta $ remain unobservable with present and near future experimental facilities in superbeam and neutrino factory . However, in presence of some ranges of off-diagonal NSI phase values there are some possibilities of discovering total $CP$ violation for any $\delta_{CP}$ value at $5 \sigma$ for neutrino factory. Our analysis indicates that for some values of NSI phases total $CP$ violation may not be at all observable for any values of $\delta $. Using a neutrino beam from electron capture process for nuclei $^{110}_{50}$Sn and $^{152}$Yb, we have shown the discovery reach of $CP$ violation in neutrino oscillation experiment.