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Formulae for the analysis of the flavor-tagged decay \(B_{s}^{0} \to J/{\psi}\phi\). (English) Zbl 1294.81379

Summary: Differential rates in the decay \(B_{s}^{0} \to J/\psi\phi\) with \(\phi \to K^{+}K^{-}\) and \(J/\psi \to \mu^{+}\mu ^{-}\) are sensitive to the \(CP\) -violation phase \(\beta_{s} = \arg((-V_{ts}V_{tb}^{\ast}) / (V_{cs}V_{cb}^{\ast}))\), predicted to be very small in the standard model. The analysis of \(B_{s}^{0} \to J/\psi\phi\) decays is also suitable for measuring the \(B_{s}^{0}\) lifetime, the decay width difference \(\Delta \Gamma_{s}\) between the \(B_{s}^{0}\) mass eigenstates, and the \(B_{s}^{0}\) 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 \(K^{+}K^{-}\) 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 \(\phi\) 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 \(K^{+}K^{-}\) contribution. All results are obtained with the use of a new compact formalism describing the differential decay rate of \(B_{s}^{0}\) mesons into \(J/\psi\phi\) final states.

MSC:

81V35 Nuclear physics
81U99 Quantum scattering theory
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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