Decays rates for S- and P-wave bottomonium

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.