Implications of Cp Asymmetry Limits for B →

The decays of B mesons to the charmless final states ππ and Kπ are a rich source of information on the fundamental parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, but the extraction of this information from data requires the separation of weak interaction effects from strong-interaction quantities such as magnitudes of operator matrix elements and strong phases. A number of model-independent analyses of these systems [1, 2, 3, 4] have shown that when one combines data on CP asymmetries with branching ratios of CP-averaged final states, one can separate the strong interaction effects from fundamental CKM parameters, obtaining useful information on both sets of quantities. In the present paper we apply several of these analyses [1, 2, 3] to the decays B → Kπ and B → ππ, using new upper limits quoted by the CLEO [5], BaBar [6, 7], and Belle [8] Collaborations for several CP-violating asymmetries in these decays, as well as updated CP-averaged branching ratios for these states. Comparison of the CPaveraged rate for B → Kπ with that for B → Kπ, given a small strong phase difference, excludes 31 ≤ γ ≤ 60 for the weak phase γ ≡ Arg(−V ∗ ubVud/V ∗ cbVcd), while comparison of B → Kπ with B → Kπ sets a 1σ lower limit of γ > 50. Present 1σ bounds on the asymmetry parameter Sππ in B 0 → ππ exclude roughly half the CKM parameter space allowed by other measurements.