Abstract
Differential rates in the decay B 0s → J/ψϕ with ϕ →K + K −and J/ψ →μ+μ−are sensitive to the CP -violation phase β s = arg((−V ts V tb ∗)/(V cs V cb ∗)), predicted to be very small in the standard model. The analysis of B 0s → J/ψϕ decays is also suitable for measuring the B 0s lifetime, the decay width difference ΔΓ s between the B 0s mass eigenstates, and the B s 0 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 0s mesons into J/ψϕ final states.
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References
A.S. Dighe, I. Dunietz and R. Fleischer, Extracting CKM phases and \( {B_s} - {\overline B_s} \) mixing parameters from angular distributions of nonleptonic B decays, Eur. Phys. J. C6 (1999) 647 [hep-ph/9804253] [SPIRES].
A. Lenz and U. Nierste, T heoretical update of \( {B_s} - {\overline B_s} \) mixing, JHEP 06 (2007) 072 [hep-ph/0612167] [SPIRES].
CDF collaboration, T. Aaltonen et al., Measurement of lifetime and decay-width difference in B 0s →J/ψϕ decays, Phys. Rev. Lett. 100 (2008) 121803 [arXiv:0712.2348] [SPIRES].
D0 collaboration, V.M. Abazov et al., Lifetime difference and CP-violating phase in the B 0s system, Phys. Rev. Lett. 98 (2007) 121801 [hep-ex/0701012] [SPIRES].
CDF collaboration, T. Aaltonen et al., First Flavor-Tagged Determination of Bounds on Mixing-Induced CP-violation in B 0s → J/ψϕ Decays, Phys. Rev. Lett. 100 (2008) 161802 [arXiv:0712.2397] [SPIRES].
D0 collaboration, V.M. Abazov et al., Measurement of B 0s mixing parameters from the flavor-tagged decay B 0s → J/ψϕ, Phys. Rev. Lett. 101 (2008) 241801 [arXiv:0802.2255] [SPIRES].
I. Dunietz, R. Fleischer and U. Nierste, In pursuit of new physics with B s decays, Phys. Rev. D 63 (2001) 114015 [hep-ph/0012219] [SPIRES].
S. Stone and L. Zhang, S-waves and the Measurement of CP-violating Phases in B s Decays, Phys. Rev. D 79 (2009) 074024 [arXiv:0812.2832] [SPIRES].
A.S. Dighe, I. Dunietz, H.J. Lipkin and J.L. Rosner, Angular distributions and lifetime differences in B s → J/ψϕ decays, Phys. Lett. B 369 (1996) 144 [hep-ph/9511363] [SPIRES].
M. Kobayashi and T. Maskawa, CP-Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652.
UTfit collaboration, M. Bona et al., T he unitarity triangle fit in the standard model and hadronic parameters from lattice QCD: A reappraisal after the measurements of Δm s and BR \( \left( {B \to \tau {\nu_\tau }} \right) \), JHEP 10 (2006) 081 [hep-ph/0606167] [SPIRES].
CDF collaboration, A. Abulencia et al., Observation of \( B_s^0 - \overline B_s^0 \) oscillations, Phys. Rev. Lett. 97 (2006) 242003 [hep-ex/0609040] [SPIRES].
W. Gautschi, Efficient Computation of the Complex Error Function, SIAM J. Numer. Anal. 7 (1970) 187.
M. Gronau and J.L. Rosner, Flavor symmetry for strong phases and determination of β s , ΔΓ in B s → J/ψϕ, Phys. Lett. B 669 (2008) 321 [arXiv:0808.3761] [SPIRES].
Y. Xie, P. Clarke, G. Cowan and F. Muheim, Determination of 2β s in B s → J/ψ K + K − Decays in the Presence of a K + K − S-Wave Contribution, JHEP 09 (2009) 074 [arXiv:0908.3627] [SPIRES].
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ArXiv ePrint:1008.4283
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Azfar, F., Boudreau, J., Bousson, N. et al. Formulae for the analysis of the flavor-tagged decay B 0s → J/ψϕ. J. High Energ. Phys. 2010, 158 (2010). https://doi.org/10.1007/JHEP11(2010)158
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DOI: https://doi.org/10.1007/JHEP11(2010)158