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

TL;DR

This paper develops a comprehensive formalism for analyzing B_s^0 --> J/psi phi decays, incorporating S-wave contributions, CP violation effects, and detector effects, to improve measurements of CP-violation phase and decay parameters.

Contribution

It introduces a new compact formalism for the differential decay rate, including S-wave effects and re-normalization schemes, enhancing the analysis of B_s^0 decay data.

Findings

Inclusion of S-wave contributions with mass-dependent amplitude ratios.

Re-normalization method accounting for detector effects.

Framework for measuring CP violation and decay parameters.

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.