Will the subprocesses $\rho (770,1450{)}^0\to K^{+}{K}^{-}$ contribute large branching fractions for $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays?

Abstract

We analyze the quasi-two-body decays $B^{+}\to {\pi }^{+}\rho (770,1450{)}^0\to {\pi }^{+}{K}^{+}{K}^{-}$ in the perturbative QCD approach. The results in this work do not support that large branching fractions contributed by the resonances $\rho (770,1450{)}^0$ in the $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays. The virtual contribution for $K^{+}{K}^{-}$ from the tail of the resonance $\rho (770{)}^0$ which has been ignored in the experimental studies is about $1.5$ times of the $\rho (1450{)}^0\to K^{+}{K}^{-}$ contribution, with the predicted branching fractions ${\mathcal{B}}_v=(1.31\pm 0.27)\times 10^{-7}$ and $\mathcal{B}=(8.96\pm 2.61)\times 10^{-8}$, respectively, for these two subprocesses in the $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays. The absence of $\rho (770{)}^0\to K^{+}{K}^{-}$ for the decay amplitude of a three-body hadronic $B$ decay involving charged kaon pair could probably result in a larger proportion for the contribution from the resonance $\rho (1450{)}^0$ in the experimental analysis.

Comments: 6 pages, 3 figures, accepted for publication in Physical Review D (Rapid Communication)