  The thermal Sunyaev-Zel'dovich (tSZ) effect signal is widely recognized as a
robust mass proxy of galaxy clusters with small intrinsic scatter. However,
recent observational calibration of the tSZ scaling relation using weak lensing
(WL) mass exhibits considerably larger scatter than the intrinsic scatter
predicted from numerical simulations. This raises a question as to whether we
can realize the full statistical power of ongoing and upcoming tSZ-WL
observations of galaxy clusters. In this work, we investigate the origin of
observed scatter in the tSZ-WL scaling relation, using mock maps of galaxy
clusters extracted from cosmological hydrodynamic simulations. We show that the
inferred intrinsic scatter from mock tSZ-WL analyses is considerably larger
than the intrinsic scatter measured in simulations, and comparable to the
scatter in the observed tSZ-WL relation. We show that this enhanced scatter
originates from the combination of the projection of correlated structures
along the line of sight and the uncertainty in the cluster radius associated
with WL mass estimates, causing the amplitude of the scatter to depend on the
covariance between tSZ and WL signals. We present a statistical model to
recover the unbiased cluster scaling relation and cosmological parameter by
taking into account the covariance in the tSZ-WL mass relation from
multi-wavelength cluster surveys.
