Matter versus vacuum oscillations at long-baseline accelerator neutrino experiments

The neutrino oscillation probabilities at the long-baseline accelerator neutrino experiments are expected to be modified by matter effects. We search for evidence of such modification in the data of T2K and NO nu A, by fitting the data to the hypothesis of (a) matter modified oscillations and (b) vacuum oscillations. We find that vacuum oscillations provide as good a fit to the data as matter modified oscillations. Even extended runs of T2K and NO nu A, with five years in neutrino mode (5 nu) and five years in anti-neutrino mode (5 nu), cannot make a 3 sigma distinction between vacuum and matter modified oscillations. The future experiment DUNE, with neutrino and anti-neutrino runs of five years each (5 nu + 5 nu), can rule out vacuum oscillations by itself at 5 sigma if the hierarchy is normal. If the hierarchy is inverted, a 5 sigma discrimination against vacuum oscillations requires the combination of (5 nu + 5 nu) runs of T2K, NO nu A and DUNE.