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.

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

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• Resonances $\rho (1450{)}^{+}$ and $\rho (1700{)}^{+}$ in $B\to DKK$ decays
• Role of $f_0(980)$ and $a_0(980)$ in the $B^{-}\to {\pi }^{-}{K}^{+}{K}^{-}$ and $B^{-}\to {\pi }^{-}{K}^0{\bar{K}}^0$ reactions
• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays
• The $\rho (770,1450)\to \omega \pi$ contributions for three-body decays $B\to {\bar{D}}^{(\ast )}\omega \pi$
• Contributions of $\rho (770,1450)\to \omega \pi$ for the Cabibbo-favored $D\to h\omega \pi$ decays
• Resonance contributions from ${\chi }_{c0}$ in the charmless three-body hadronic $B$ meson decays
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays
• Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays