Probing muonic charged current non-standard interactions at Muon Decay at Rest facility in conjunction with T2HK.

The muon decay-at-rest ($\mu$-DAR) facility provides us with an ideal platform to probe purely muonic charged-current non-standard neutrino interactions (NSIs). We probe this class of NSI effects using antineutrinos from a muon decay-at-rest ($\mu$-DAR) source. Even though muonic NSI are absent in neutrino production at the future Tokai to Kamioka superbeam experiment with megaton Hyper Kamiokande detector (T2HK), we show that our proposed hybrid set-up comprising of $\mu$-DAR and T2HK helps in alleviating the parameter degeneracies that are present in data. Analytic considerations reveal that oscillation probability is most sensitive to the NSI parameter in the $\mu$-e sector. For this parameter, we show, that the $\mu$-DAR setup can improve on the existing bounds down to around 0.01, especially when the data is combined with neutrino data from T2HK experiment due to the lifting of parameter degeneracies. The high precision with which $\mu$-DAR can measure $\delta_{\rm{CP}}$ is shown to be robust even in the presence of the considered NSIs. Finally, we show that the combination of $\mu$-DAR along with T2HK can also be used to put mild constraints on the NSI phase in the vicinity of the maximal CP-violating value.