  A method of sideband Raman cooling to the vibrational ground state of the
$m=0$ Zeeman sublevel in a far-detuned two-dimensional optical lattice is
proposed. In our scheme, the Raman coupling between vibrational manifolds of
the adjacent Zeeman sublevels is shifted to the red sideband due to the ac
Stark effect induced by a weak pump field. Thus, cooling and optical pumping to
$m=0$ is achieved by purely optical means with coplanar cw laser beams. The
optical lattice and cooling parameters are estimated in the framework of simple
theoretical models. An application of the transverse sideband cooling method to
frequency standards is discussed. Coherent population trapping for the sideband
Raman transitions between the degenerate vibrational levels is predicted.
