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We study the contributions of the kaon pair originating from the resonance$\rho(770)$ for the three-body decays $B \to D K\bar{K}$ by employing theperturbative QCD approach. According to the predictions in this work, thecontributions from the intermediate state $\rho(770)^0 $ are relatively smallfor the three-body decays such as $B^0 \to \bar{D}^0 K^+ K^-$, $B_s^0 \to\bar{D}^0 K^+ K^-$, and $B^+ \to D_s^+ K^+K^-$, while about $20\%$ of the totalthree-body branching fraction for $B^+ \to \bar{D}^0 K^+ \bar{K}^0$ couldpossibly come from the subprocess $\rho(770)^+\to K^+ \bar{K}^0$. We alsoestimate the branching fractions for $\rho(770)^\pm$ decay into the kaon pairto be about $1\%$, and that for the neutral $\rho(770)$ decay into $K^+K^-$ or$K^0\bar{K}^0$ to be about $0.5\%$, which will be tested by future experiments.

Contributions of the kaon pair from $\rho(770)$ for the three-body decays $B \to D K\bar{K}$