  The neutrino mass ordering is one of the principal unknowns in the neutrino
sector. Long baseline neutrino experiments have the potential of resolving this
issue as they are sensitive to large matter effects. The superbeam experiment
DUNE is one of the most promising candidates to study the neutrino mass
hierarchy, along with NO$\nu$A and T2K. But in the presence of non unitarity of
the leptonic mixing matrix, the capability of such experiments to discriminate
between the two hierarchies gets suppressed. The mass hierarchy sensitivity of
DUNE decreases in the presence of new physics. In this paper we analyze the
origin and extent of this loss of sensitivity at the level of oscillation
probabilities, events, mass hierarchy sensitivity and the discovery reach of
DUNE, NO$\nu$A and T2K.
