Projection effects of large-scale structures on weak-lensing peak
  abundances
  High peaks in weak lensing (WL) maps originate dominantly from the lensing
effects of single massive halos. Their abundance is therefore closely related
to the halo mass function and thus a powerful cosmological probe. On the other
hand, however, besides individual massive halos, large-scale structures (LSS)
along lines of sight also contribute to the peak signals. In this paper, with
ray tracing simulations, we investigate the LSS projection effects. We show
that for current surveys with a large shape noise, the stochastic LSS effects
are subdominant. For future WL surveys with source galaxies having a median
redshift $z_{\mathrm{med}}\sim1$ or higher, however, they are significant. For
the cosmological constraints derived from observed WL high peak counts, severe
biases can occur if the LSS effects are not taken into account properly. We
extend the model of \citet{Fan2010} by incorporating the LSS projection effects
into the theoretical considerations. By comparing with simulation results, we
demonstrate the good performance of the improved model and its applicability in
cosmological studies.
