  We estimate the bias on weak lensing mass measurements of shear-selected
galaxy cluster samples. The mass bias is expected to be significant because
constructions of cluster samples from peaks in weak lensing mass maps and
measurements of cluster masses from their tangential shear profiles share the
same noise. We quantify this mass bias from large sets of mock cluster samples
with analytical density profiles and realistic large-scale structure noise from
ray-tracing simulations. We find that, even for peaks with signal-to-noise
ratio larger than $4.0$ in weak lensing mass maps constructed in a deep survey
with a high source galaxy number density of $30~\mathrm{arcmin}^{-2}$, derived
weak lensing masses for these shear-selected clusters are still biased high by
$\sim55\%$ on average. Such a large bias mainly originates from up-scattered
low mass objects, which is an inevitable consequence of selecting clusters with
a noisy observable directly linked to the mass measurement. We also investigate
the dependence of the mass bias on different physical and observational
parameters, finding that the mass bias strongly correlates with cluster
redshifts, true halo masses, and selection signal-to-noise thresholds, but
having moderate dependence on observed weak lensing masses and survey depths.
This bias, albeit considerable, can still be modeled accurately in statistical
studies of shear-selected clusters as the intrinsic scatter around the mean
bias is found to be reasonable in size. We demonstrate that such a bias can
explain the deviation in X-ray properties previously found on a shear-selected
cluster sample. Our result will be useful for turning large samples of
shear-selected clusters available in future surveys into potential probes of
cosmology and cluster astrophysics.
