  Galaxy clusters identified with optical imaging tend to suffer from
projection effects, which impact richness (the number of member galaxies in a
cluster) and lensing coherently. Physically unassociated galaxies can be
mistaken as cluster members due to the significant uncertainties in their
line-of-sight distances, thereby changing the observed cluster richness; at the
same time, projection effects alter the weak gravitational lensing signals of
clusters, leading to a correlated scatter between richness and lensing at a
given halo mass. As a result, the lensing signals for optically selected
clusters tend to be biased high. This optical selection bias problem of cluster
lensing is one of the key challenges in cluster cosmology. Fortunately,
recently available multiwavelength observations of clusters provide a solution.
We analyze a simulated data set mimicking the observed lensing of clusters
identified by both optical photometry and gas properties, aiming to constrain
this selection bias. Assuming a redMaPPer sample from the Dark Energy Survey
with South Pole Telescope Sunyaev-Zeldovich effect observations, we find that
an overlapping survey of 1300 square deg, 0.2 < z < 0.65, can constrain the
average lensing bias to an accuracy of 5 percent. This provides an exciting
opportunity for directly constraining optical selection bias from observations.
We further show that our approach can remove the optical selection bias from
the lensing signal, paving the way for future optical cluster cosmology
analyses.
