  We use two-dimensional transverse laser cooling to produce an ultracold beam
of YbF molecules. Through experiments and numerical simulations, we study how
the cooling is influenced by the polarization configuration, laser intensity,
laser detuning and applied magnetic field. The ultracold part of the beam
contains more than $2 \times 10^5$ molecules and has a temperature below 200
$\mu$K, and the cooling yields a 300-fold increase in the brightness of the
beam. The method can improve the precision of experiments that use molecules to
test fundamental physics. In particular, the beam is suitable for measuring the
electron electric dipole moment with a statistical precision better than
$10^{-30}$ e cm.
