processes, and that a fine-tuning of the phase $\phi_A$ is required to be reconciled with experimental data when $\rho_A$ is significantly larger than 1 [@Beneke2]. The recent study on the annihilation contributions show that $\rho_A$ $>$ $2$ and ${\vert}\phi_A{\vert}$ $\geq$ $30^{\circ}$ are acceptable, even necessary, to reproduce the data for some two-body nonleptonic $B_{u,d,s}$ decay modes [@zhu2; @chang1]. In this paper, we will perform a fitting on the parameters $\rho_A$ and $\phi_A$ by considering $B$ ${\to}$ ${\pi}{\pi}$, ${\pi}K$ and $K \bar{K}$ decay modes, on one hand, to investigate the strength of annihilation contribution, on the other hand, to study their effects on the anomalies in $B$ physics, such as the well-known ${\pi}K$ and ${\pi}{\pi}$ puzzles.

The so-called ${\pi}K$ puzzle is reflected by the difference between the direct $CP$ asymmetries for $B^{-}$ ${\to}$ $K^{-}\pi^{0}$ and $\bar{B}^{0}$ ${\to}$ $K^{-}\pi^{+}$ decays. With the up-to-date HFAG results [@HFAG], we get $$\Delta A \equiv A_{CP}(B^{-} {\to} K^{-} {\pi}^{0})
   - A_{CP}(\bar{B}^{0} \to K^{-} \pi^{+})
   = (12.2 \pm 2.2) \%
 \label{acppi},$$ which differs from zero by about $5.5\sigma$. However, the direct $CP$ asymmetries of $A_{CP}(B^{-} \to K^{-} \pi^{0})$ and $A_{CP}(\bar{B}^{0} \to K^{-} \pi^{+})$ are expected to be approximately equal with the isospin symmetry in the SM, numerically 