Formulae for the Analysis of the Flavor-Tagged Decay B^0_s --> Jpsi phi

Abstract

Differential rates in the decay B^0_s --> Jpsi phi, with phi --> K^+K^- and Jpsi --> mu^+ mu^- are sensitive to the CP-violation phase beta_s, predicted to be very small in the standard model. The analysis of B^0_s --> Jpsi phi decays is also suitable for measuring the B^0_s lifetime, the decay width difference DeltaGamma_s between the B^0_s mass eigenstates, and the B^0_s oscillation frequency Delta m 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 contributions on one hand and for the effects of 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 phi 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 contribution. All results are obtained with the use of a new compact formalism describing the differential decay rate of B^0_s mesons into Jpsi phi final states.