Model-independent search for T violation with T2HK and DUNE

We consider the time reversal (T) transformation in neutrino oscillations in a model-independent way by comparing the observed transition probabilities at two different baselines at the same neutrino energy. We show that, under modest model assumptions, if the transition probability $P_{{\nu }_{\mu }\to {\nu }_e}$ around $E_{\nu }\simeq 0.86$ GeV measured at DUNE is smaller than the one at T2HK the T symmetry has to be violated. Experimental requirements needed to achieve good sensitivity to this test for T violation are to obtain enough statistics at DUNE for $E_{\nu }\lesssim 1$ GeV (around the 2nd oscillation maximum), good energy resolution (better than 10%), and near-detector measurements with a precision of order 1% or better.