  Although weak lensing (WL) is a powerful method to estimate a galaxy cluster
mass without any dynamical assumptions, a model bias can arise when the cluster
density profile departs from the assumed model profile. In a merging system,
the bias is expected to become most severe because the constituent halos
undergo significant structural changes. In this study, we investigate WL mass
bias in binary cluster mergers using a suite of idealized hydrodynamical
simulations. Realistic WL shear catalogs are generated by matching the source
galaxy properties, such as intrinsic shape dispersion, measurement noise,
source densities, etc., to those from Subaru and {\it Hubble Space Telescope}
observations. We find that, with the typical mass-concentration ($M$-$c$)
relation and the Navarro-Frenk-White (NFW) profile, the halo mass bias depends
on the time since the first pericenter passage and increases with the mass of
the companion cluster. The time evolution of the mass bias is similar to that
of the concentration, indicating that, to first order, the mass bias is
modulated by the concentration change. For a collision between two
$\sim10^{15}~M_{\odot}$ clusters, the maximum bias amounts to $\sim60\%$. This
suggests that previous WL studies may have significantly overestimated the mass
of the clusters in some of the most massive mergers. Finally, we apply our
results to three merger cases: Abell 2034, MACS J1752.0+4440, and ZwCl
1856.8+6616, and report their mass biases at the observed epoch, as well as
their pre-merger masses, utilizing their merger shock locations as tracers of
the merger phases.
