High-precision measurement of atmospheric mass-squared splitting with T2K and NOvA

A precise measurement of the atmospheric mass-squared splitting |\Delta m^2_{\mu\mu}| is crucial to establish the three-flavor paradigm and to constrain the neutrino mass models. In addition, a precise value of |\Delta m^2_{\mu\mu}| will significantly enhance the hierarchy reach of future medium-baseline reactor experiments like JUNO and RENO-50. In this work, we explore the precision in |\Delta m^2_{\mu\mu}| that will be available after the full runs of T2K and NOvA. We find that the combined data will be able to improve the precision in |\Delta m^2_{\mu\mu}| to sub-percent level for maximal 2-3 mixing. Depending on the true value of \sin^2\theta_{23} in the currently-allowed 3 sigma range, the precision in |\Delta m^2_{\mu\mu}| will vary from 0.87% to 1.24%. We further demonstrate that this is a robust measurement as it remains almost unaffected by the present uncertainties in \theta_{13}, \delta_{CP}, the choice of mass hierarchy, and the systematic errors.