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

TL;DR

This paper analyzes three-body B meson decays involving D mesons and kaon pairs, focusing on resonance contributions using the perturbative QCD approach, and predicts decay rates and spectra consistent with current data.

Contribution

It introduces a detailed PQCD framework for modeling resonance effects in B decays with kaon pairs, including the kaon-kaon distribution amplitude and resonance line shapes.

Findings

Predicted branching ratios agree with current experimental data.

Provided polarization fractions for vector-vector and vector-tensor decay modes.

Established invariant mass spectra for resonances in B decays, testable by LHCb and Belle II.

Abstract

In this work, we study the $S$, $P$ and $D$ wave resonance contributions to three-body decays $B_{(s)} \to [ D^{(*)}, \bar{D}^{(*)} ] K^+K^-$ by employing the perturbative QCD (PQCD) approach, where the kaon-kaon invariant mass spectra 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\'e formalism, while other resonances are described by the relativistic Breit-Wigner (BW) line shape. The corresponding decay channels are studied by constructing the kaon-kaon distribution amplitude $\Phi_{KK}$, which captures important final state interactions between the kaon pair in the resonant region. We found that the PQCD predictions for the branching ratios for most considered decays agree with currently available data within errors. The associated polarization fractions of those vector-vector and vector-tensor decay modes are also predicted, which are expected to be tested in the near future experiments. The invariant mass spectra for the corresponding resonances in the $B_{(s)} \to [D^{(*)}, \bar{D}^{(*)} ] K^+K^-$ decays are well established, which can be confronted with the precise data from the LHCb and Belle II experiments.