Revisiting the annihilation decay $\bar{B}_{s}\to\pi^{ + }\pi^{-}$

Abstract

It is very important to know the strength of annihilation contribution in B charmless nonleptonic decays. $\bar{B}_{s}\to \pi^{+}\pi^{-}$ process could serve a good probe of the strength. We have studied the process in QCD factorization framework. Using a gluon mass scale indicted by the studies of infrared behavior of gluon propagators to avoid enhancements in the soft end point regions, we find that the CP averaged branching ratio is about $1.24\times 10^{-7}$, the direct CP asymmetry $C_{\pi\pi}$ is about -0.05, while the mixing-induced CP asymmetry quite large with the value $S_{\pi\pi}$=0.18. The process could be measured at LHC-b experiments in the near future and would deepen our understanding of dynamics of B charmless decays.