Non-standard interactions and the CP phase measurements in neutrino oscillations at low energies
We study the effects of non-standard interactions (NSI) and the genuine CP phase $\delta_D$ in neutrino oscillations at low, $E_\nu \lesssim 1\,\mbox{GeV}$, and very low, $E_\nu \lesssim 0.1\,\mbox{GeV}$, energies. For experimental setup with baseline and neutrino energy tuned to the first 1-3 oscillation maximum, we develop a simple analytic formalism to show the effects of NSI. The vacuum mimicking and its violation as well as the use of the separation basis play a central role in our formalism. The NSI corrections that affect the CP phase measurement mainly come from the violation of vacuum mimicking as well as from the corrections to the 1-3 mixing angle and mass-squared difference. We find that the total NSI correction to the $\nu_\mu - \nu_e$ probability $P_{\mu e}$ can reach $20\% - 30\%$ ($1 \sigma$) at T2(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 baseline experiment $\mu$Kam that uses the Super-K/Hyper-K detector at Kamioka to measure the oscillation of the antineutrinos from muon decay at rest ($\mu$DAR), can substantially reduce the degeneracy between NSI and the genuine CP phase $\delta_D$ to provide high CP sensitivity. The NSI correction to $P_{\mu e}$ is only $2\%$ ($1 \sigma$) for $\mu$DAR neutrinos.