Recently, the Belle II Collaboration reported the branching fraction $\mathcal{B}(B^{+}\to K^{+}\nu \overline{\nu })=(2.3\pm 0.7)\times {10}^{-5}$ with a significance of $3.5\sigma$, which is $2.7\sigma$ above the Standard Model expectation. Motivated by this measurement, we calculate this decay channel at the next-to-leading order and twist-three level using the perturbative QCD approach. By combining lattice QCD data with our results, we obtain form factors with improved reliability. Using these form factors, we estimate the branching ratios of $B^{+}\to K^{+}$ semileptonic flavor-changing neutral current decays, including $B^{+}\to K^{+}\nu \overline{\nu }$ and $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$. To address the anomalies in these two processes, we introduce a leptoquark model as a new physics scenario. Analyzing five possible types of leptoquarks, we successfully explain the latest experimental measurements and derive further constraints on the leptoquarks. Furthermore, the single leptoquark model becomes invalid once the stringent constraints from process $B_s\to {\mu }^{+}{\mu }^{-}$ and $B_s-\overline{B_s}$ mixing is taken into account.

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• Extensions of gauge sector
• Extensions of scalar sector
• Flavor changing neutral currents
• Form factors
• Particle decays