T violation at a future neutrino factory

We study the possibility of measuring T (time reversal) violation in a future long baseline neutrino oscillation experiment. By assuming a neutrino factory as a staging scenario of a muon collider at the J-PARC site, we find that the νₑ → νμ oscillation probabilities can be measured with a good accuracy at the Hyper-Kamiokande detector. By comparing with the probability of the time-reversal process, νμ → νₑ, measured at the T2K/T2HK experiments, one can determine the CP phase δ in the neutrino mixing matrix if | sin(δ)| is large enough. The determination of δ can be made with poor knowledge of the matter density of the earth as T violation is almost insensitive to the matter effects. The comparison of CP and T-violation measurements, \`a\ la the CPT theorem, provides us with a non-trivial check of the three neutrino paradigm based on the quantum field theory.