  In this work, we recalculate the charmless pure annihilation decays $B_s\to
\pi^+ \pi^-$ and $B^0 \to K^+ K^-$ by using the perturbative QCD (pQCD)
factorization approach, and compare the pQCD predictions with currently
available experimental measurements. We used the same set of relevant input
parameters and wave functions to make the calculations for the considered decay
modes and found the following results: (a) one can provide a consistent pQCD
interpretation for both the measured $Br(B_s^0 \to \pi^+ \pi^-)$ and $Br(B_d^0
\to K^+ K^-)$ simultaneously; (b) the pQCD predictions for $Br(B_s^0 \to
\pi^+\pi^-)$ obtained by different authors are well consistent with each other;
(c) our new pQCD prediction for $Br(B_d^0 \to K^+K^-)$ agree very well with the
measured values from CDF and LHCb Collaboration; and (d) the CP-violating
asymmetry ${\cal A}_{CP}(B_d^0 \to K^+K^-) \approx 16%$, which is large and may
be detected at the LHCb experiment.
