  Experimentally, baryon number minus lepton number, $B-L$, appears to be a
good global symmetry of nature. We explore the consequences of the existence of
gauge-singlet scalar fields charged under $B-L$ -- dubbed lepton-number-charged
scalars, LeNCS -- and postulate that these couple to the standard model degrees
of freedom in such a way that $B-L$ is conserved even at the non-renormalizable
level. In this framework, neutrinos are Dirac fermions. Including only the
lowest mass-dimension effective operators, some of the LeNCS couple
predominantly to neutrinos and may be produced in terrestrial neutrino
experiments. We examine several existing constraints from particle physics,
astrophysics, and cosmology to the existence of a LeNCS carrying $B-L$ charge
equal to two, and discuss the emission of LeNCS's via "neutrino beamstrahlung,"
which occurs every once in a while when neutrinos scatter off of ordinary
matter. We identify regions of the parameter space where existing and future
neutrino experiments, including the Deep Underground Neutrino Experiment, are
at the frontier of searches for such new phenomena.
