Primordial star formation appears to result in stars at least an order of magnitude more massive than modern star formation. It has been proposed that the transition from primordial to modern initial mass functions occurs due to the onset of effective metal line cooling at a metallicity Z/Z_sun = 10^{-3.5}. However, these simulations neglected molecular hydrogen cooling. We perform simulations using the same initial conditions, but including molecular cooling, using a complex network that follows molecular hydrogen formation and also directly follows carbon monoxide and water. We find that molecular hydrogen cooling allows roughly equivalent fragmentation to proceed even at zero metallicity for these initial conditions. The apparent transition just represents the point where metal line cooling becomes more important than molecular cooling. In all cases, the fragments are massive enough to be consistent with models of primordial stellar masses, suggesting that the transition to the modern initial mass function may be determined by other physics such as dust formation. We conclude that such additional cooling mechanisms, combined with the exact initial conditions produced by cosmological collapse are likely more important than metal line cooling in determining the initial mass function, and thus that there is unlikely to be a sharp transition in the initial mass function at Z/Z_sun = 10^{-3.5}.
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