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The semileptonic decays $B/B_s \to (π, K)(l^+l^-,lν,ν\barν)$ in the perturbative QCD approach beyond the leading-order

In this paper we first calculate the form factors of $B \to (π,K)$ 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 $B/B_s \to (π, K)(l^+l^-,lν,ν\barν)$ (here $l$ denotes $e, μ$ and $τ$). Based on the numerical calculations and phenomenological analysis, we found the following results: (a) For $B \to (π, K)$ and $B_s \to K$ transition form factors $F_{0,+,\rmt}(q^2)$, the NLO pQCD predictions for the values of $F_{0,+,\rmt}(0)$ and their $q^2$-dependence agree well with those obtained from other methods; (b) For $\bar{B}^0 \to π^+l^-\barν_l, \bar{K}^0 l^+ l^- $ and $B^- \to π^0 l^-\barν_l, K^- l^+ l^-$ decay modes, the NLO pQCD predictions for their branching ratios agree very well with the measured values; (c) By comparing the pQCD predictions for $Br(\bar{B}^0 \to π^+l^-\barν_l)$ with the measured decay rate we extract out the magnitude of $V_{ub}$: $|V_{ub}|= (3.80^{+0.56}_{-0.50}(theor.)) \times 10^{-3}$; (d) We also defined several ratios of the branching ratios, $R_ν, R_C$ and $R_{N1,N2,N3}$, and presented the corresponding pQCD predictions, which will be tested by LHCb and the forthcoming Super-B experiments.