  Assuming that there is a sterile neutrino, we ask what then is the ability of
long-baseline experiments to i) establish that neutrino oscillation violates
CP, ii) determine the three-neutrino mass ordering, and iii) determine which
CP-violating phase or phases are the cause of any CP violation that may be
observed. We find that the ability to establish CP violation and to determine
the mass ordering could be very substantial. However, the effects of the
sterile neutrino could be quite large, and it might prove very difficult to
determine which phase is responsible for an observed CP violation. We explain
why a sterile neutrino changes the long-baseline sensitivities to CP violation
and to the mass ordering in the ways that it does. We note that long-baseline
experiments can probe the presence of sterile neutrinos in a way that is
different from, and complementary to, the probes of short-baseline experiments.
We explore the question of how large sterile-active mixing angles need to be
before long-baseline experiments can detect their effects, or how small they
need to be before the interpretation of these experiments can safely disregard
the possible existence of sterile neutrinos.
