The semileptonic decays $B/B_s\to (\pi ,K)(l^{+}{l}^{-},l\nu ,\nu \bar{\nu })$ in the perturbative QCD approach beyond the leading-order

Abstract

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

Comments: 21 pages, 7 figures