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

TL;DR

This paper calculates form factors and branching ratios for semileptonic B and Bs decays using NLO pQCD, finding good agreement with other methods and experiments, and providing predictions for future tests.

Contribution

It provides NLO pQCD calculations of form factors and branching ratios for B and Bs semileptonic decays, improving accuracy and consistency with experimental data.

Findings

NLO pQCD form factors agree with other methods.

Predicted branching ratios match experimental measurements.

Extracted |V_ub| consistent with other determinations.

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 $F_{0,+,\rmt}(q^2)$, 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 \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 $V_{ub}$: $|V_{ub}|= (3.80^{+0.56}_{-0.50}(theor.)) \times 10^{-3}$; (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.