\label{HFAGpipi},$$ $${\cal B}(\bar{B}_{d}^{0}{\to}K^{+}K^{-})
  =(0.12{\pm}0.05){\times}10^{-6}
  \label{HFAGKK}.$$ Such results, if confirmed, imply unexpectedly large annihilation contributions in $B$ decays and significant flavour symmetry breaking effects between the annihilation amplitudes of $B_{u,d}$ and $B_{s}$ decays, which attract much attention recently, for instance Refs. [@zhu1; @zhu2; @chang1; @xiao1].

Theoretically, as noticed already in Refs. [@pqcd; @relaRef; @du1; @Beneke2], even though the annihilation contributions are formally $\Lambda_{QCD}/m_b$ power suppressed, they are very important and indispensable for charmless $B$ decays. By introducing the parton transverse momentum and the Sudakov factor to regulate the endpoint divergence, there is a large complex annihilation contribution within the perturbative QCD (pQCD) approach [@pqcd; @relaRef]. The latest renewed pQCD estimations ${\cal B}(\bar{B}_s^0 \to \pi^+ \pi^-)$ $=$ $(5.10^{+1.96+0.25+1.05+0.29}_{-1.68-0.19-0.83-0.20}) \times 10^{-7}$ and ${\cal B}(\bar{B}_d^0 \to K^+ K^-)$ $=$ $(1.56^{+0.44+0.23+0.22+0.13}_{-0.42-0.22-0.19-0.09}) \times 10^{-7}$ [@xiao1] give an appropriate account of the CDF and LHCb measurements within uncertainties. In the QCD factorization (QCDF) framework [@Beneke1], the endpoint divergence in annihilation amplitudes is usually parameterized by $X_{A}(\rho_A,\phi_A)$ (see Eq.(\[XA\])). The parameters $\rho_A$ $\sim$ $1$ and $\phi_A$ $\sim$ $-55^{\circ}$ (scenario S4) [@Beneke2] are adopted conservatively in evaluating the amplitudes of $B$ $\to$ $PP$ decays, which lead to the predictions ${\cal B}(\bar{B}_s^0 \to \pi^+ \pi^-)$ $=$ $(0.26^{+0.00+0.10}_{-0.00-0.09}) \times 10^{-6}$ and 