  Measurements of the electron's electric dipole moment (eEDM) are demanding
tests of physics beyond the Standard Model. We describe how ultracold YbF
molecules could be used to improve the precision of eEDM measurements by two to
three orders of magnitude. Using numerical simulations, we show how the
combination of magnetic focussing, two-dimensional transverse laser cooling,
and frequency-chirped laser slowing, can produce an intense, slow,
highly-collimated molecular beam. We show how to make a magneto-optical trap of
YbF molecules and how the molecules could be loaded into an optical lattice.
eEDM measurements could be made using the slow molecular beam or using
molecules trapped in the lattice. We estimate the statistical sensitivity that
could be reached in each case and consider how sources of noise can be reduced
so that the shot-noise limit of sensitivity can be reached. We also consider
systematic effects due to magnetic fields and vector light shifts and how they
could be controlled.
