Probing T and CP Violation at DUNE and T2HK

We study the sensitivity of the DUNE and T2HK long-baseline experiments to time reversal (T) violation in neutrino oscillations. Rather than the conventional approach of exchanging initial and final neutrino flavors, we search for T violation through the $L$-dependence of the $ν_μ\to ν_e$ transition probability at fixed neutrino energy using neutrino data only. Within the standard three-flavour framework, we show that the DUNE and T2HK together can establish the presence of an $L$-odd component in the oscillation probability at up to $\sim 4σ$ significance, with the optimal sensitivity in the energy range $E_ν\in [0.68, 0.92]$ GeV. The second oscillation maximum of DUNE plays a crucial role in this analysis. We further show that DUNE is more sensitive to T violation that is running in neutrino-only mode, whereas T2HK provides better sensitivity in the conventional neutrino versus anti-neutrino comparison, making the two experiments complementary to each other in search of the CP phase $δ_{\rm CP}$.