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In this work, we study the $S$, $P$ and $D$ wave resonance contributions tothree-body decays $B_{(s)} \to [ D^{(*)}, \bar{D}^{(*)} ] K^+K^-$ by employingthe perturbative QCD (PQCD) approach, where the kaon-kaon invariant massspectra are dominated by the $f_0(980),f_0(1370),$$\phi(1020),\phi(1680),f_2(1270),f^{\prime}_2(1525),f_2(1750)$ and $f_2(1950)$resonances. The $KK$ $S$-wave component $f_0(980)$ is modeled with the Flatt\'eformalism, while other resonances are described by the relativisticBreit-Wigner (BW) line shape. The corresponding decay channels are studied byconstructing the kaon-kaon distribution amplitude $\Phi_{KK}$, which capturesimportant final state interactions between the kaon pair in the resonantregion. We found that the PQCD predictions for the branching ratios for mostconsidered decays agree with currently available data within errors. Theassociated polarization fractions of those vector-vector and vector-tensordecay modes are also predicted, which are expected to be tested in the nearfuture experiments. The invariant mass spectra for the corresponding resonancesin the $B_{(s)} \to [D^{(*)}, \bar{D}^{(*)} ] K^+K^-$ decays are wellestablished, which can be confronted with the precise data from the LHCb andBelle II experiments.

Resonant contributions to three-body $B_{(s)} \to [ D^{(*)}, \bar{D}^{(*)} ] K^+K^-$ decays in the perturbative QCD approach

Resonant contributions to three-body $B_{(s)} \to [ D^{()}, \bar{D}^{()} ] K^+K^-$ decays in the perturbative QCD approach