  We investigate potential systematic effects in constraining the amplitude of
primordial fluctuations \sigma_8 arising from the choice of halo mass function
in the likelihood analysis of current and upcoming galaxy cluster surveys. We
study the widely used N-body simulation fit of Tinker et al. (T08) and, as an
alternative, the recently proposed analytical model of Excursion Set Peaks
(ESP). We first assess the relative bias between these prescriptions when
constraining \sigma_8 by sampling the ESP mass function to generate mock
catalogs and using the T08 fit to analyse them, for various choices of survey
selection threshold, mass definition and statistical priors. To assess the
level of absolute bias in each prescription, we then repeat the analysis on
dark matter halo catalogs in N-body simulations designed to mimic the mass
distribution in the current data release of Planck SZ clusters. This N-body
analysis shows that using the T08 fit without accounting for the scatter
introduced when converting between mass definitions (alternatively, the scatter
induced by errors on the parameters of the fit) can systematically
over-estimate the value of \sigma_8 by as much as 2\sigma\ for current data,
while analyses that account for this scatter should be close to unbiased in
\sigma_8. With an increased number of objects as expected in upcoming data
releases, regardless of accounting for scatter, the T08 fit could over-estimate
the value of \sigma_8 by ~1.5\sigma. The ESP mass function leads to
systematically more biased but comparable results. A strength of the ESP model
is its natural prediction of a weak non-universality in the mass function which
closely tracks the one measured in simulations and described by the T08 fit. We
suggest that it might now be prudent to build new unbiased ESP-based fitting
functions for use with the larger datasets of the near future.
