Discovery reach of $CP$ violation and non-standard interactions in low energy neutrino factory

In low energy neutrino factory ($E_{\mu }<10$GeV) using MIND detector, we have studied the optimization of $CP$ violation discovery reach in the leptonic sector for different baselines and different parent muon energy considering only Standard Model interactions of neutrinos with matter. Considering such optimized experimental set-up of baseline and energy we have addressed the question of how $CP$ violation discovery reach could get affected by the presence of non-standard interactions of neutrinos with matter during the propagation of neutrinos. For off diagonal NSI elements there could be complex phases ${\varphi }_{ij}$ which could also lead to $CP$ violation. In presence of these complex phases we have shown the contours showing the discovery reach of $\delta$ and ${\varphi }_{ij}$. We have also shown the discovery reach of NSIs in the same experimental set-up which is optimized for discovery of $CP$ violation in the leptonic sector.