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.

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

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Cited by in corpus (21)

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• Four-body decays $B_{(s)}\to (K\pi {)}_{S/P}(K\pi {)}_{S/P}$ in the perturbative QCD approach
• Contributions for the kaon pair from $\rho (770)$, $\omega (782)$ and their excited states in the $B\to K\bar{K}h$ decays
• Analysis of three-body charmed B meson decays under the factorization-assisted topological-amplitude approach
• Resonance contributions $\varphi (1020,1680)\to K\bar{K}$ for the three-body decays $B\to K\bar{K}h$
• Contributions of the kaon pair from $\rho (770)$ for the three-body decays $B\to DK\bar{K}$
• Is $f_X(1500)$ observed in the $B\to \pi (K)KK$ decays ${\rho }^0(1450)$?
• The PQCD approach towards to next-to-leading order: a short review
• Analysis of three-body charmless $B$-meson decays under the factorization-assisted topological-amplitude approach
• The role of $D_{(s)}^{\ast }$ and their contributions in $B_{(s)}\to D_{(s)}h{h}^{\prime }$ decays
• Global determination of two-meson distribution amplitudes from three-body $B$ decays in the perturbative QCD approach
• Resonances $\rho (1450{)}^{+}$ and $\rho (1700{)}^{+}$ in $B\to DKK$ decays
• Resonant contributions to three-body $B_{(s)}\to [D^{(\ast )},{\bar{D}}^{(\ast )}]K^{+}{K}^{-}$ decays in the perturbative QCD approach
• 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
• 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
• The $\rho (770,1450)\to \omega \pi$ contributions for three-body decays $B\to {\bar{D}}^{(\ast )}\omega \pi$
• Resonances $\varphi (1020)$ and $\varphi (1680)$ contributions for the three-body decays $B^{+}\to D_s^{+}K\bar{K}$
• Contributions of $\rho (770,1450)\to \omega \pi$ for the Cabibbo-favored $D\to h\omega \pi$ decays
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays
• Resonance contributions from ${\chi }_{c0}$ in the charmless three-body hadronic $B$ meson decays
• Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays