  We use the Bodwin-Braaten-Lepage factorization scheme to separate the long-
and short-distance factors that contribute to the decay rates of $\Upsilon$,
$\eta_b$ (S-wave) and $\chi_b$,$h_b$ (P-wave). The long distance matrix
elements are calculated on the lattice in the quenched approximation using a
non-relativistic formulation of the $b$ quark dynamics.
