A combined fit on the annihilation corrections in Bu,d,s→PPBu,d,s→PP decays within QCDF

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→ππ,πK,KKBu,d,s→ππ,πK,KK decays, a comprehensive fit on the phenomenological parameters XAi,f (or ρAi,f and ϕAi,f) which are used to parameterize the endpoint singularity in annihilation amplitudes is performed with the statistical χ2χ2 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 BsBs and Bu,dBu,d decay, 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,sBu,d,s decays. (3) Numerically, two solutions are found, one is (ρAi,ϕAi[°])=(2.98−0.86+1.12,−105−24+34) and (ρAf,ϕAf[°])=(1.18−0.23+0.20,−40−8+11), the other is (ρAi,ϕAi[°])=(2.97−0.90+1.19,−105−24+32) and (ρAf,ϕAf[°])=(2.80−0.21+0.25,165−3+4). Obviously, nonfactorization annihilation parameter XAi is generally unequal to factorization annihilation parameter XAf, which differs from the traditional treatment. With the fitted parameters, all results for observables of Bu,d,s→ππ,πK,KKBu,d,s→ππ,πK,KK decays are in good agreement with experimental data.