A combined fit on the annihilation corrections inBu,d,s→PPdecays within QCDF

Abstract

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 B u,d,s → ππ, π K , KK decays, a comprehensive fit on the phenomenological parameters Xwhich are used to parameterize the endpoint singularity in annihilation amplitudes is performed with the statistical χ 2 approach. It is found that (1) flavor symmetry breaking effects are hardly to be distinguished between X i A,s and X i A,d due to the large experimental errors and theoretical uncertainties, where X i A,s and X i A,d are related to the nonfactorization annihilation contributions in B s and B u,d decay, respectively. So X i A,s X i A,d is a good approximation by now. (2) In principle, parameter X f A which is related to the factorization annihilation contributions and independent of the initial state can be regarded as the same variable for B u,d,s decays. (3) Numerically, two solutions are found, one is (ρ i A , φ i A [ • ]) = (2.98 +1.12 −0.86 , −105 +34 −24 ) and (ρ f A , φ f A [ • ]) = (1.18 +0.20 −0.23 , −40 +11 −8 ), the other is (ρ i A , φ i A [ • ]) = (2.97 +1.19 −0.90 , −105 +32 −24 ) and (ρ f A , φ f A [ • ]) = (2.80 +0.25 −0.21 , 165 +4 −3 ). Obviously, nonfactorization annihilation parameter X i A is generally unequal to factorization annihilation parameter X f A , which differs from the traditional treatment. With the fitted parameters, all results for observables of B u,d,s → ππ, π K , KK decays are in good agreement with experimental data.

Observation of the Annihilation Decay Mode B0→K+K−

“…[29], the following branching fractions are obtained: where the first uncertainty is statistical, the second systematic, and the third and fourth are due to the knowledge of [2][3][4][5]7,[31][32][33][34][35]. The pQCD estimations in Ref.…”

“…In Ref. [34], the unexpectedly large value of BðB 0 s → π þ π − Þ caused the traditional QCDF treatment for annihilation parameters to be revisited.…”

Light-front holographic distribution amplitudes of pseudoscalar mesons and their application to B -meson decays

“…From the phenomenological point of view, an annihilation amplitude with a large strong phase is generally welcome in order to fit experimental data and to explain some puzzles observed in B-meson decays [79][80][81][82][83][84]. As a result, a complex parameter X A has been introduced in the traditional parameterization scheme within the framework of QCDF [38].…”

Study of the weak annihilation contributions in charmless $$\varvec{B_s\rightarrow VV}$$ B s → V V decays

“…Theoretically, the WA contributions with possible strong phase have attracted a lot of attention in the past few years, for instance, in Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Traditionally, both ρ A and φ A are treated as universal parameters for different kinds of annihilation topologies.…”

“…Such a topologydependent parameterization scheme is also favored by most of the charmless B → P P and PV (where V stands for a light vector meson) decays, as demonstrated in Refs. [26][27][28], and it could provide a possible solution to the well-known "π K CP-asymmetry puzzle" [25]. In addition, using the recent measurements of the pure annihilation B s → π + π − and B d → K + K − decays by the CDF [36], Belle [37] and LHCb collaborations [38,39], the authors of Refs.…”