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We study the effects of non-standard interactions (NSI) and the genuine CPphase $\delta_D$ in neutrino oscillations at low, $E_\nu \lesssim1\,\mbox{GeV}$, and very low, $E_\nu \lesssim 0.1\,\mbox{GeV}$, energies. Forexperimental setup with baseline and neutrino energy tuned to the first 1-3oscillation maximum, we develop a simple analytic formalism to show the effectsof NSI. The vacuum mimicking and its violation as well as the use of theseparation basis play a central role in our formalism. The NSI corrections thataffect the CP phase measurement mainly come from the violation of vacuummimicking as well as from the corrections to the 1-3 mixing angle andmass-squared difference. We find that the total NSI correction to the $\nu_\mu- \nu_e$ probability $P_{\mu e}$ can reach $20\% - 30\%$ ($1 \sigma$) atT2(H)K. Correspondingly, the correction to the CP phase can be as large as$50^\circ$ and hence significantly deteriorates the CP sensitivity at T2(H)K.The proposed TNT2K experiment, a combination of T2(H)K and the short baselineexperiment $\mu$Kam that uses the Super-K/Hyper-K detector at Kamioka tomeasure the oscillation of the antineutrinos from muon decay at rest($\mu$DAR), can substantially reduce the degeneracy between NSI and the genuineCP phase $\delta_D$ to provide high CP sensitivity. The NSI correction to$P_{\mu e}$ is only $2\%$ ($1 \sigma$) for $\mu$DAR neutrinos.

Non-standard interactions and the CP phase measurements in neutrino oscillations at low energies