  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 per shot 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.
