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.