Revisiting the pure annihilation decays $B_s\to \pi^+ \pi^-$ and $B^0 \to K^+ K^-$: the data and the pQCD predictions

Abstract

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.