${\cal B}(\bar{B}_d^0 \to K^+ K^-)$ $=$ $(0.10^{+0.03+0.03}_{-0.02-0.03}) \times 10^{-6}$ [@Cheng2]. It is obvious that the QCDF prediction of ${\cal B}(\bar{B}_d^0 \to K^+ K^-)$ agrees well with the data Eq.(\[HFAGKK\]), but the one of ${\cal B}(\bar{B}_s^0 \to \pi^+ \pi^-)$ is much smaller than the present experimental measurement Eq.(\[HFAGpipi\]). This discrepancy kindles the passions of restudy on annihilation contributions [@zhu1; @zhu2; @chang1].

At present, there are two major issues among the well-concerning focus on the annihilation contributions within the QCDF framework, one is whether $X_A(\rho_A,\phi_A)$ is universal for $B$ decays, and the other is what its value should be. As to the first issue, there is no an imperative reason for the annihilation parameters $\rho_A$ and $\phi_A$ to be the same for different $B_{u,d,s}$ decays, even for different annihilation topologies, although they were usually taken to be universal in the previous numerical calculation for simplicity [@du1; @Beneke2]. Phenomenologically, it is almost impossible to account for all of the well-measured two-body charmless $B$ decays with the universal values of $\rho_A$ and $\phi_A$ based on the QCDF approach [@zhu2; @chang1; @Beneke2; @Cheng2]. In addition, the pQCD study on $B$ meson decays also indicate that the annihilation parameters $\rho_A$ and $\phi_A$ should be process-dependent. In 