Decay rates of various bottomonium systems

Using the Bodwin-Braaten-Lepage factorization theorem in heavy quarkonium decay and production processes, the authors calculated matrix elements associated with S- and P-wave bottomonium decays via lattice QCD simulation methods. In this work, they report preliminary results on the operator matching between the lattice expression and the continuum expression at one loop level. Phenomenological implications are discussed using these preliminary MS matrix elements