T violation at a future neutrino factory (Contribution to the 25th International Workshop on Neutrinos from Accelerators)

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 $ν_e \to ν_μ$ oscillation probabilities can be measured with good accuracy at the Hyper-Kamiokande detector. By comparing with the probability of the time-reversal process, $ν_μ\to ν_e$, measured at the T2K/T2HK, 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, {\it à la} the CPT theorem, provides us with a non-trivial check of the three neutrino paradigm based on the quantum field theory. This proceeding is based on JHEP 12 (2024), 014 [arXiv:hep-ph/2407.05807].