Effects of final-state interactions in pure annihilation decay of B ⁰ _s → π+π ⁻

Abstract

The hadronic decay of B ⁰ _s → π ⁺ π ⁻ is analyzed by using “QCD factorization” (QCDF) method and final-state interaction (FSI). First, the B ⁰ _s → π ⁺ π ⁻ decay is calculated via QCDF method and the annihilation graphs only exist in this method. Hence, the FSI must be seriously considered to solve the B ⁰ _s → π ⁺ π ⁻ decay and the K ^+(*) K ^−(*) and $K^{0(*)} K^{\bar 0(*)}$ via the exchange of K ^0(*) and K ^−(*) mesons are chosen for the intermediate states. To estimate the intermediate state amplitudes, the QCDF method is again used. These amplitudes are used in the absorptive part of the diagrams. The experimental branching ratio of B ⁰ _s → π ⁺ π ⁻ decay is less than 1.2 × 10⁻⁶ and our results according to the QCDF method and FSI are 0.68 × 10⁻⁸ and 1.18 × 10⁻⁶, respectively.