CP-Violating and Charged Current Neutrino Non-standard Interactions in CE$\nu$NS

Neutrino non-standard interactions (NSI) can be constrained using coherent elastic neutrino-nucleus scattering. We discuss here two aspects in this respect, namely the effects of (i) charged current NSI in neutrino production and (ii) CP-violating phases associated with neutral current NSI in neutrino detection. Effects of CP-phases require the simultaneous presence of two different flavor-changing neutral current NSI parameters. Applying these two scenarios to the COHERENT measurement, we derive limits on charged current NSI and find that more data is required to compete with the existing limits. Regarding CP-phases, we show how the limits on the NSI parameters depend dramatically on the values of the phases. Accidentally, the same parameters influencing coherent scattering also show up in neutrino oscillation experiments. We find that COHERENT provides complementary constraints on the set of NSI parameters that can explain the discrepancy in the best-fit value of the standard CP-phase obtained by T2K and NO$\nu$A, while the significance with which the LMA-Dark solution is ruled out can be weakened by the presence of additional NSI parameters introduced here.