  Cosmological tests based on cluster counts require accurate calibration of
the space density of massive halos, but most calibrations to date have ignored
complex gas physics associated with halo baryons. We explore the sensitivity of
the halo mass function to baryon physics using two pairs of gas-dynamic
simulations that are likely to bracket the true behavior. Each pair consists of
a baseline model involving only gravity and shock heating, and a refined
physics model aimed at reproducing the observed scaling of the hot,
intracluster gas phase. One pair consists of billion-particle re-simulations of
the original 500 Mpc/h Millennium Simulation of Springel et al. (2005), run
with the SPH code Gadget-2 and using a refined physics treatment approximated
by preheating (PH) at high redshift. The other pair are high-resolution
simulations from the adaptive-mesh refinement code ART, for which the refined
treatment includes cooling, star formation, and supernova feedback (CSF). We
find that, although the mass functions of the gravity-only (GO) treatments are
consistent with the recent calibration of Tinker et al. (2008), both pairs of
simulations with refined baryon physics show significant deviations. Relative
to the GO case, the masses of ~10^{14} Msun/h halos in the PH and CSF
treatments are shifted by averages of -15 \pm 1 percent and +12 \pm 5 percent,
respectively. These mass shifts cause ~ 30% deviations in number density
relative to the Tinker function, significantly larger than the 5% statistical
uncertainty of that calibration.
