Measuring sin 2βin Bs(t) -> phi K_s

We show that, unlike other pure b -> d penguin processes, the decay Bs(t) -> phi K_s is dominated by a single amplitude, that of the internal t-quark. The contributions of the u- and c-quark operators each vanish due to a cancellation between the (V-A) \otimes (V-A) and (V-A) \otimes (V+A) matrix elements. Thus, the indirect CP asymmetry in this decay probes sin 2β. Although this cancellation is complete only for certain values of the s- and b-quark masses, the theoretical uncertainty on sin 2βis still less than 10% over most (~80%) of the parameter space. By measuring the direct CP asymmetry, one can get a better idea of the probable error on sin 2β.

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