Effects of final state interactions in $$B^ + \to D_S^ + \bar K^0$$ decay

Abstract

We investigate the effects of final state interactions (FSI) contributions in the nonleptonic two body \(B^ + \to D_S^ + \bar K^0\) decay, however the hadronic decay of \(B^ + \to D_S^ + \bar K^0\) is analyzed by using “QCD factorization” (QCDF) method and final state interaction (FSI). First, the \(B^ + \to D_S^ + \bar K^0\) decay is calculated via QCDF method and only the annihilation graphs exist in that method. Hence, the FSI must be seriously considered to solve the \(B^ + \to D_S^ + \bar K^0\) decay and the D0π+(D0*ρ+), D+π0(D+*ρ0) and D+ηc(D+*J/ψ) via the exchange of K+(*), K0(*) and Ds+(*) mesones are chosen for the intermediate states. To estimate the intermediate states amplitudes, the QCDF method is again used. These amplitudes are used in the absorptive part of the diagrams. The experimental branching ratio of \(B^ + \to D_S^ + \bar K^0\) decay is less than 8 × 10−4 and the predicted branching ratio is 0.23 × 10−9 in the absence of FSI effects and it becomes 6.74 × 10−4 when FSI contributions are taken into account.