Limitations in Measuring the Angle $β$ by Using $SU(3)$ Relations for $B$-Meson Decay-Amplitudes

Details Limitations in Measuring the Angle $β$ by Using $SU(3)$ Relations for $B$-Meson Decay-Amplitudes Limitations in Measuring the Angle $β$ by Using $SU(3)$ Relations for $B$-Meson Decay-Amplitudes

1994-09-07

arxiv.org/abs/hep-ph/9409244v1

Phys.Lett.B341:379-385,1995

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages (LaTeX) + 5 figures included, Munich Technical University preprint TUM-T31-69/94

Scientific paper

10.1016/0370-2693(94)01314-3

Flavour $SU(3)$ symmetry of strong interactions and certain dynamical assumptions have been used in a series of recent publications to extract weak CKM phases from $B$-decays into $\{\pi\pi,\pi K, K\bar K\}$ final states. We point out that irrespectively of $SU(3)$-breaking effects the presence of QCD-penguin contributions with internal $u$- and $c$-quarks precludes a clean determination of the angle $\beta$ in the unitarity triangle by using the branching ratios only. This difficulty can be overcome by measuring in addition the ratio $x_d/x_s$ of $B^0_d-\bar B^0_d$ to $B^0_s-\bar B^0_s$ mixings. The measurement of the angle $\gamma$ is unaffected by these new contributions. Some specific uncertainties related to $SU(3)$-breaking effects and electroweak penguin contributions are briefly discussed.

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