Contributions for the kaon pair from $\rho (770)$, $\omega (782)$ and their excited states in the $B\to K\bar{K}h$ decays

Abstract

We study the resonance contributions for the kaon pair originating from the intermediate states $\rho (770,1450,1700)$ and $\omega (782,1420,1650)$ for the three-body hadronic decays $B\to K\bar{K}h$ in the perturbative QCD approach, where $h=(\pi ,K)$. The branching fractions of the virtual contributions for $K\bar{K}$ from the Breit-Wigner formula tails of $\rho (770)$ and $\omega (782)$ which have been ignored in experimental and theoretical studies for these decays are found larger than the corresponding contributions from the resonances $\rho (1450,1700)$ and $\omega (1420,1650)$. The differential branching fractions for $B\to \rho (770)h\to K\bar{K}h$ and $B\to \omega (782)h\to K\bar{K}h$ are found nearly unaffected by the quite different values of the full widths for $\rho (770)$ and $\omega (782)$ in this paper. The predictions in this work for the branching fractions of the quasi-two-body decays $B^{+}\to {\pi }^{+}\rho (1450{)}^0\to {\pi }^{+}{K}^{+}{K}^{-}$ and $B^{+}\to {\pi }^{+}\rho (1450{)}^0\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ meet the requirement of $SU(3)$ symmetry relation.

Comments: 25 pages, 3 figures, typos in Eq.(25) corrected