In this paper we first calculate the form factors of $B\to (\pi ,K)$ and $B_s\to K$ transitions by employing the perturbative QCD (pQCD) factorization approach with the inclusion of the next-to-leading-order (NLO) corrections, and then we calculate the branching ratios of the corresponding semileptonic decays $B/B_s\to (\pi ,K)(l^{+}{l}^{-},l\nu ,\nu \overline{\nu })$ (here $l$ denotes $e$, $\mu$, and $\tau$). Based on the numerical calculations and phenomenological analysis, we find the following results: (a) For $B\to (\pi ,K)$ and $B_s\to K$ transition form factors $F_{0,+,\mathrm{T}}(q^2)$, the NLO pQCD predictions for the values of $F_{0,+,\mathrm{T}}(0)$ and their $q^2$ dependence agree well with those obtained from other methods; (b) for ${\overline{B}}^0\to {\pi }^{+}{l}^{-}{\overline{\nu }}_l$, ${\overline{K}}^0{l}^{+}{l}^{-}$ and $B^{-}\to {\pi }^0{l}^{-}{\overline{\nu }}_l$, $K^{-}{l}^{+}{l}^{-}$ decay modes, the NLO pQCD predictions for their branching ratios agree very well with the measured values; (c) by comparing the pQCD predictions for $\mathrm{Br}({\overline{B}}^0\to {\pi }^{+}{l}^{-}{\overline{\nu }}_l)$ with the measured decay rate, we extract out the magnitude of $V_{ub}$: $|V_{ub}|=({3.80}_{-0.60}^{+0.66}(\mathrm{theor})\pm 0.13)\times {10}^{-3}$; (d) we also define several ratios of the branching ratios, $R_{\nu }$, $R_C$ and $R_{N1,N2,N3}$, and present the corresponding pQCD predictions, which will be tested by LHCb and the forthcoming Super-B experiments.

• Received 30 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.114025