Calibration of bias and scatter involved in cluster mass measurements
  using optical weak gravitational lensing
  Cosmological inference from cluster number counts is systematically limited
by the accuracy of the mass calibration, i.e. the empirical determination of
the mapping between cluster selection observables and halo mass. In this work
we demonstrate a method to quantitatively determine the bias and uncertainties
in weak-lensing mass calibration. To this end, we extract a library of
projected matter density profiles from hydrodynamical simulations. Accounting
for shear bias and noise, photometric redshift uncertainties, mis-centering,
cluster member contamination, cluster morphological diversity, and
line-of-sight projections, we produce a library of shear profiles. Fitting a
one-parameter model to these profiles, we extract the so-called \emph{weak
lensing mass} $M_\text{WL}$. Relating the weak-lensing mass to the halo mass
from gravity-only simulations with the same initial conditions as the
hydrodynamical simulations allows us to estimate the impact of hydrodynamical
effects on cluster number counts experiments. Creating new shear libraries for
$\sim$1000 different realizations of the systematics, provides a distribution
of the parameters of the weak-lensing to halo mass relation, reflecting their
systematic uncertainty. This result can be used as a prior for cosmological
inference. We also discuss the impact of the inner fitting radius on the
accuracy, and determine the outer fitting radius necessary to exclude the
signal from neighboring structures. Our method is currently being applied to
different Stage~III lensing surveys, and can easily be extended to Stage~IV
lensing surveys.
