  Stellar evolution models predict the existence of a gap in the black hole
mass spectrum from $\sim55 M_\odot - 120 M_\odot$ due to pair-instability
supernovae (PISNe). We investigate the possible existence of such an "upper"
mass gap in the second gravitational wave transient catalog (GWTC-2) by
hierarchically modeling the astrophysical distribution of black hole masses. We
extend the Truncated and Powerlaw+Peak mass distribution families to allow for
an explicit gap in the mass distribution, and apply the extended models to
GWTC-2. We find that with the Truncated model there is mild evidence favoring
an upper mass gap with log Bayes Factor $\ln \mathcal{B} = 2.79$, inferring the
lower and upper bounds at $56.12_{-4.38}^{+7.54} M_\odot$, and
$103.74_{-6.32}^{+17.01} M_\odot$ respectively. When using the Powerlaw+Peak
model, we find no preference for the gap. When imposing tighter priors on the
gap bounds centered on the expected PISN gap bounds, the log Bayes factors in
favor of a gap mildly increase. These results are however contingent on the
parameter inference for the most massive binary, GW190521, for which follow up
analyses showed the source may be an intermediate mass ratio merger that has
component masses straddling the gap. Using the GW190521 posterior samples from
the analysis in Nitz & Capano (2021), we find an increase in Bayes factors in
favor of the gap. However, the overall conclusions are unchanged: There is no
preference for a gap when using the Powerlaw+Peak model. This work paves the
way for constraining the physics of pair-instability and pulsational
pair-instability supernovae and high-mass black hole formation.
