  We establish upper limits on branching fractions for B0 decays to final
states where the decay products are purely invisible (i.e., no observable final
state particles) and for B0 decays to nu nubar gamma. Within the Standard
Model, these decays have branching fractions that are below current
experimental sensitivity, but various models of physics beyond the Standard
Model predict significant contributions from these channels. Using 88.5 million
B Bbar pairs collected at the Y(4S) resonance by the BaBar experiment at the
PEP-II e+e- storage ring at the Stanford Linear Accelerator Center, we
establish upper limits at the 90% confidence level of 22 x 10^-5 for the
branching fraction of B0 -> invisible and 4.7 x 10^-5 for the branching
fraction of B0 -> nu nubar gamma.
