Can magnetized turbulence set the mass scale of stars?
  Understanding the evolution of self-gravitating, isothermal, magnetized gas
is crucial for star formation, as these physical processes have been postulated
to set the initial mass function (IMF). We present a suite of isothermal
magnetohydrodynamic (MHD) simulations using the GIZMO code, that resolve the
formation of individual stars in giant molecular clouds (GMCs), spanning a
range of Mach numbers found in observed GMCs. As in past works, the mean and
median stellar masses are sensitive to numerical resolution, because they are
sensitive to low-mass stars that contribute a vanishing fraction of the overall
stellar mass. The {\em mass-weighted} median stellar mass $M_\mathrm{50}$
becomes insensitive to resolution once turbulent fragmentation is
well-resolved. Without imposing Larson-like scaling laws, our simulations find
$M_\mathrm{50} \propto M_\mathrm{0} \mathcal{M}^{-3} \alpha_\mathrm{turb}
\mathrm{SFE}^{1/3}$ for GMC mass $M_\mathrm{0}$, sonic Mach number
$\mathcal{M}$, virial parameter $\alpha_\mathrm{turb}$, and star formation
efficiency $\mathrm{SFE}=M_\mathrm{\star}/M_\mathrm{0}$. This fit agrees well
with previous IMF results from the RAMSES, ORION2, and SphNG codes. Although
$M_\mathrm{50}$ has no significant dependence on the magnetic field strength at
the cloud scale, MHD is necessary to prevent a fragmentation cascade that
results in non-convergent stellar masses. For initial conditions and SFE
similar to star-forming GMCs in our Galaxy, we predict $M_\mathrm{50}$ to be
$>20 M_{\odot}$, an order of magnitude larger than observed ($\sim 2 M_\odot$),
together with an excess of brown dwarfs. Moreover, $M_\mathrm{50}$ is sensitive
to initial cloud properties and evolves strongly in time within a given cloud,
predicting much larger IMF variations than are observationally allowed. We
conclude that physics beyond MHD turbulence and gravity are necessary
ingredients for the IMF.
