A simple relation for B_s-mixing

We reinvestigate a simple relation between the semileptonic CP asymmetry a_{sl}^s, the decay rate difference \Delta \Gamma_s, the mass difference \Delta M_s and S_{\psi \phi} extracted from the angular analysis of the decay B_s \to \psi \phi, which is regularly used in the literature. We find that this relation is not suited to eliminate the theory prediction for \Gamma_{12}, it can, however be used to determine the size of the penguin contributions to the decay B_s \to \psi \phi. Moreover we comment on the current precision of the theory prediction for \Gamma_{12}.