Formulae for the analysis of the flavor-tagged decay Bs0 → J/ψϕ

Abstract

Differential rates in the decay B_s⁰ → J/ψϕ with ϕ →K⁺K⁻and J/ψ →μ⁺μ⁻are sensitive to the CP -violation phase β_s = arg((−V_tsV_tb^∗)/(V_csV_cb^∗)), predicted to be very small in the standard model. The analysis of B_s⁰ → J/ψϕ decays is also suitable for measuring the B_s⁰ lifetime, the decay width difference ΔΓ_s between the B_s⁰ mass eigenstates, and the B_s⁰ 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 B_s⁰ mesons into J/ψϕ final states.