We try a global fit of the experimental branching ratios and CP-asymmetries of the charmless B → P V decays according to QCD factorisation. We find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. The main reason for this failure is the difficulty to accomodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in B 0 → ρ + π − , which is predicted very small by QCD factorisation. Trying a fit with QCD factorisation complemented by a charming-penguin inspired model we reach a best fit which is not excluded by experiment (CL of about 8 %) but is not fully convincing. These negative results must be tempered by the remark that some of the experimental data used are recent and might still evolve significantly. *
We present a phenomenological study of the rare double radiative decay B → Kγγ in the Standard Model (SM) and beyond. Using the operator product expansion (OPE) technique, we estimate the short-distance (SD) contribution to the decay amplitude in a region of the phase space which is around the point where all decay products have energy ∼ m b /3 in the rest frame of the B-meson. At lowest order in 1/Q, where Q is of order m b , the B → Kγγ matrix element is then expressed in terms of the usual B → K form factors known from semileptonic rare decays. The integrated SD branching ratio in the SM in the OPE region turns out to be ∆B(B → Kγγ) OP E SM ≃ 1 × 10 −9 . We work out the di-photon invariant mass distribution with and without the resonant background through B → K{η c , χ c0 } → Kγγ. In the SM, the resonance contribution is dominant in the region of phase space where the OPE is valid. The present experimental upper limit on B s → τ + τ − decays, which constrains the scalar/pseudoscalar Four-Fermi operators with τ + τ − , leaves considerable room for new physics in the one-particle-irreducible contribution to B → Kγγ decays. In this case, we find that the SD B → Kγγ branching ratio can be enhanced by one order of magnitude with respect to its SM value and the SD contribution can lie outside of the resonance peaks. *
We derive model independent lower bounds on the CKM parameters (1 −ρ) andη as functions of the mixing-induced CP asymmetry S in B → π + π − and sin 2β from B → ψK S . The bounds do not depend on specific results of theoretical calculations for the penguin contribution to B → π + π − . They require only the very conservative condition that a hadronic phase, which vanishes in the heavy-quark limit, does not exceed 90 • in magnitude. The bounds are effective if − sin 2β ≤ S ≤ 1. Dynamical calculations indicate that the limits onρ andη are close to their actual values.
We analyze the extraction of weak phases from CP violation in B → π + π − decays. We propose to determine the unitarity triangle (ρ,η) by combining the information on mixing induced CP violation in B → π + π − , S, with the precision observable sin 2β obtained from the CP asymmetry in B → ψK S . It is then possible to write down exact analytical expressions forρ andη as simple functions of the observables S and sin 2β, and of the penguin parameters r and φ. As an application clean lower bounds onη and 1 −ρ can be derived as functions of S and sin 2β, essentially without hadronic uncertainty. Computing r and φ within QCD factorization yields precise determinations ofρ andη since the dependence on r and φ is rather weak. It is emphasized that the sensitivity to the phase φ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter C of direct CP violation in B → π + π − . We also discuss alternative ways to analyze S and C that can be useful if new physics affects B d -B d mixing. Predictions and uncertainties for r and φ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in 1/m b and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed.
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