A Combined Fit on the Annihilation Corrections in Bᵤ,d,ₛ → PP Decays Within QCDF

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Motivated by the possible large annihilation contributions implied by recent CDF and LHCb measurements on nonleptonic annihilation B meson decays, and the refined experimental measurements on hadronic B meson decays, we study the strength of annihilation contributions within QCD factorization (QCDF) in this paper. With the available measurements of two-body Bᵤ,d,ₛ -> pi pi, pi K, K K decays, a comprehensive fit on the phenomenological parameters Xₐⁱ,ᶠ (or rhoₐⁱ,ᶠ and phiₐⁱ,ᶠ) which are used to parameterize the endpoint singularity in annihilation amplitudes is performed with the statistical chi² approach. It is found that (1) flavor symmetry breaking effects are hardly to be distinguished between Xₐ,ₛⁱ and Xₐ,dⁱ due to the large experimental errors and theoretical uncertainties, where Xₐ,ₛⁱ and Xₐ,dⁱ are related to the nonfactorization annihilation contributions in Bₛ and Bᵤ,d decays, respectively. So Xₐ,ₛⁱ = Xₐ,dⁱ is a good approximation by now. (2) In principle, parameter Xₐᶠ which is related to the factorization annihilation contributions and independent of the initial state can be regarded as the same variable for Bᵤ,d,ₛ decays. (3) Numerically, two solutions are found, one is (rhoₐⁱ, phiₐⁱ) = (2.98+1.12-0.86,-105+34-24) and (rhoₐᶠ, phiₐᶠ) = (1.18+0.20-0.23,-40+11-8), the other is (rhoₐⁱ, phiₐⁱ) = (2.97+1.19-0.90,-105+32-24) and (rhoₐᶠ, phiₐᶠ) = (2.80+0.25-0.21,165+4-3). Obviously, nonfactorization annihilation parameter Xₐⁱ is generally unequal to factorization annihilation parameter Xₐᶠ, which differ from the traditional treatment. With the fitted parameters, all results for observables of Bᵤ,d,ₛ ->pi pi, pi K, K K decays are in good agreement with experimental data.