Updating B --> PP, VP decays in the framework of flavor symmetry

Abstract

Current data of charmless B meson decays to two pseudoscalar mesons (PP) and one vector and one pseudoscalar mesons (VP) are analyzed within the framework of flavor SU(3) symmetry, a working principle that we have tested by allowing symmetry breaking factors in the decay amplitudes and found to be a good approximate symmetry. In the PP sector, the color-suppressed tree amplitude is found to be larger than previously known and has a strong phase of ~ -70^o relative to the color-favored tree amplitude. We have extracted for the first time the W-exchange and penguin-annihilation amplitudes. The former has a size of about the QCD-penguin amplitude and a phase opposite to that of the color-favored tree amplitude, while the latter is suppressed in magnitude but gives the dominant contribution to the $B_s^0\to {\pi }^{+}{\pi }^{-}$ and ${\pi }^0{\pi }^0$ decays. In the VP sector, one striking feature is that the color-suppressed tree amplitude with the spectator quark ending up in the vector meson has a large size and a strong phase of ~ -90^o relative to the color-favored tree amplitudes. The associated electroweak penguin amplitude also has a similar strong phase and a magnitude comparable to the corresponding QCD penguin amplitude. This leads to a large branching fraction of order 10^{-6} for $B_s^0\to \varphi {\pi }^0$. In contrast, the color-suppressed tree, QCD penguin, and electroweak penguin amplitudes with the spectator quark ending up in the pseudoscalar meson have magnitudes more consistent with naive expectations. Besides, current data are not sufficiently precise for us to fix the W-exchange amplitudes. For both the PP and VP sectors, predictions of all the decay modes are made based upon our preferred fit results and compared with data and those made by perturbative approaches. We have identified a few observables to be determined experimentally in order to discriminate among theory calculations.

34 pages, 19 tables; references updated

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