Resonances $\phi(1020)$ and $\phi(1680)$ contributions for the three-body decays $B^+ \to D_s^+K\bar K$

TL;DR

This paper investigates the contributions of the resonances $\,phi(1020)$ and $\,phi(1680)$ to the three-body decay processes of $B^+$ mesons into $D_s^+$ and kaon pairs, providing theoretical predictions for branching ratios using the perturbative QCD approach.

Contribution

It offers the first detailed calculation of $\,phi(1680)$ resonance contributions in these decay channels and predicts their branching ratios, expanding understanding of resonance effects in B meson decays.

Findings

Branching ratio for $B^+ o D_s^+\,phi(1020) o D_s^+ K^+K^-$ is about $1.53 imes 10^{-7}$.

Branching ratio for $B^+ o D_s^+\,phi(1680)$ is approximately $6.94 imes 10^{-9}$.

$\,phi(1680)$ contribution is about 5% of the $\,phi(1020)$ contribution.

Abstract

We study the resonances $\phi(1020)$ and $\phi(1680)$ contributions for the three-body decays $B^+ \to D_s^+K\bar K$ in the perturbative QCD approach. The branching ratios for $B^+ \to D_s^+\phi(1020) \to D_s^+ K^+K^-$ and $B^+ \to D_s^+\phi(1020) \to D_s^+ K^0\bar{K}^0$ are predicted to be $(1.53\pm0.23) \times 10^{-7}$ and $(1.02^{+0.19}_{-0.13} )\times 10^{-7}$, respectively. The decay $B^+ \to D_s^+\phi(1680)$ with $\phi(1680)$ decays into $K^+K^-$ or $K^0\bar{K}^0$, has the branching fraction $(6.94^{+1.83}_{-2.02})\times 10^{-9}$, which is about $5\%$ of the result for $B^+ \to D_s^+\phi(1020) \to D_s^+ K^+K^-$.