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Particles and Fields

Eur. Phys. J. C 24, 361-371 (2002)
DOI: 10.1007/s10052-002-0956-4

Bayesian analysis of the constraints on $\gamma$ from $B \rightarrow K\pi$ rates and CP asymmetries in the flavor-SU(3) approach

M. Bargiotti1, A. Bertin1, M. Bruschi1, M. Capponi1, S. De Castro1, L. Fabbri1, P. Faccioli1, D. Galli1, B. Giacobbe1, U. Marconi1, I. Massa1, M. Piccinini1, M. Poli2, 3, N. Semprini Cesari1, R. Spighi1, V. Vagnoni1, S. Vecchi1, M. Villa1, A. Vitale1 and A. Zoccoli1

1  Dipartimento di Fisica dell'Università di Bologna and INFN Sezione di Bologna, 40126 Bologna, Italy
2  Dipartimento di Energetica "Sergio Stecco" dell'Università di Firenze, 50139 Firenze, Italy
3  INFN Sezione di Bologna, 40126 Bologna, Italy

(Received: 22 March 2002 / Published online: 7 June 2002 )

The relation between the branching ratios and direct CP asymmetries of $B \rightarrow K\pi$ decays and the angle $\gamma$ of the CKM unitarity triangle is studied numerically in the general framework of the SU(3) approach, with minimal assumptions about the parameters not fixed by flavor-symmetry arguments. Experimental and theoretical uncertainties are subjected to a statistical treatment according to the Bayesian method. In this context, the experimental limits recently obtained by CLEO, BaBar and Belle for the direct CP asymmetries are translated into the bound $\vert\gamma - 90^{\circ}\vert > 21^{\circ}$ at the 95% C.L. A detailed analysis is carried out to evaluate the conditions under which measurements of the CP averaged branching ratios may place a significant constraint on $\gamma$. Predictions for the ratios of charged ( Rc) and neutral ( Rn) $B \rightarrow K\pi$ decays are also presented.

© Società Italiana di Fisica, Springer-Verlag 2002