25023 2407.05807 10.1007/JHEP12(2024)014 14 14 T violation at a future neutrino factory Regular Article - Theoretical Physics 1 19 2024 12 3 2024 7 10 2024 9 25 2024 11 5 2024 12 3 The Author(s) 2024 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2024 2024 12 12 Ryuichiro Kitano ryuichiro.kitano@kek.jp Joe Sato sato-joe-mc@ynu.ac.jp Sho Sugama sugama-sho-hp@ynu.jp https://ror.org/01g5y5k24 grid.410794.f 0000 0001 2155 959X KEK Theory Center Tsukuba 305-0801 Japan https://ror.org/0516ah480 grid.275033.0 0000 0004 1763 208X Graduate University for Advanced Studies (Sokendai) Tsukuba 305-0801 Japan https://ror.org/03zyp6p76 grid.268446.a 0000 0001 2185 8709 Department of Physics, Facility of Engineering Science Yokohama National University Yokohama 240-8501 Japan Abstract 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 → ν μ oscillation probabilities can be measured with a good accuracy at the Hyper-Kamiokande detector. By comparing with the probability of the time-reversal process, ν μ → ν e , 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, à la the CPT theorem, provides us with a non-trivial check of the three neutrino paradigm based on the quantum field theory. Keywords CP Violation Neutrino Mixing ArXiv ePrint: 2407.05807