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Non-standard interaction effect on $CP$ violation in neutrino oscillation with super-beam

We have studied the $CP$ violation discovery reach in neutrino oscillation experiment with superbeam in presence of non-standard interactions of neutrinos with matter for both short and long baselines. For the most important channel of oscillation ($ν_μ\rightarrow ν_e$) for $CP$ violation discovery there is significant effect in the oscillation probability particularly due to NSIs' $\varepsilon_{eμ}$ and $\varepsilon_{eτ}$ for longer baseline and higher energy in comparison to other NSIs'. Interestingly for these two NSIs' (for real and higher allowed values) there is possibility of better discovery reach of $CP$ violation than that with only Standard Model interactions of neutrinos with matter provided that NSI values are known. For complex NSIs' we have shown the $CP$ violation discovery reach in the plane of Dirac phase $δ$ and NSI phase $ϕ_{ij}$. Our analysis indicates that for some values of some NSI phases total $CP$ violation may not be observable for any values of $δ$.