Formulae for the analysis of the flavor-tagged decay B-s(0) -> J/psi phi - Azfar, F; Boudreau, J; Bousson, N; Fernandez, J; Gibson, K; Giurgiu, G; Gomez-Ceballos, G; Kuhr, T; Kreps, M; Liu, C; Maksimovic, P; Morlock, J; et al. (2010)
Differential rates in the decay Bs0 → J/ψφ with φ → K+K- and J/ψ → μ+μ- are sensitive to the CP-violation phase βs = arg ((-VtsVtb*)/(V csVcb*)), predicted to be very small in the standard model. The analysis of Bs0 → J/ψφ decays is also suitable for measuring the Bs0 lifetime, the decay width difference ΔΓs between the Bs0 mass eigenstates, and the Bs0 oscillation frequency Δm even if appreciable CP violation does not occur. In this paper we present normalized probability densities useful in maximum likelihood fits, extended to allow for S-wave K+K- contributions on one hand and for direct CP violation on the other. Our treatment of the S-wave contributions includes the strong variation of the S-wave/P-wave amplitude ratio with m(K+K-) across the φ resonance, which was not considered in previous work. We include a scheme for re-normalizing the probability densities after detector sculpting of the angular distributions of the final state particles, and conclude with an examination of the symmetries of the rate formulae, with and without an S-wave K+K- contribution. All results are obtained with the use of a new compact formalism describing the differential decay rate of Bs0 mesons into J/ψφ final states.