Missing energy and the measurement of the CP-violating phase in neutrino oscillations

In the next generation of long-baseline neutrino oscillation experiments, aiming to determine the charge-parity violating phase $\delta_{CP}$ in the appearance channel, fine-grained time-projection chambers are expected to play an important role. In this Letter, we analyze an influence of realistic detector capabilities on the $\delta_{CP}$ sensitivity for a setup similar to that of the Deep Underground Neutrino Experiment. We find that the effect of the missing energy, carried out by undetected particles, is sizable. Although the reconstructed neutrino energy can be corrected for the missing energy, the accuracy of such procedure has to exceed 20\%, to avoid a sizable bias in the extracted $\delta_{CP}$ value.