The Extreme Tail of the Non-Gaussian Mass Function
  Number counts of massive high-redshift clusters provide a window to study
primordial non-Gaussianity. The current quality of data, however, forces the
statistical analysis to probe a region of parameter space -- the extreme tail
of the mass function -- which is neither accessible in any of the currently
available theoretical prescriptions for calculating the mass function, nor
calibrated in N-body simulations. In this work we present a new analytical
prescription for calculating a "resummed" non-Gaussian halo mass function,
which is constructed to remain stable in the extreme tail. We show that the
prescription works well in the parameter regime that has been currently
explored in simulations. We then use Fisher matrix techniques to compare our
prescription with an extrapolated fit to N-body simulations, which has recently
been used to obtain constraints from data collected by the South Pole Telecope.
We show that for the current data, both prescriptions would lead to
statistically consistent constraints. As the data improve, however, there is a
possibility of introducing a statistically significant bias in the constraints
due to the choice of prescription, especially if non-Gaussianity is scale
dependent and becomes relatively large on cluster scales. It would then be
necessary to test the accuracy of the prescriptions in N-body simulations that
can probe clusters with high masses and redshifts in the presence of large
non-Gaussianity.
