论文标题
$ \ bar {b} _s \ to k^{（*）} \ ell^+ \ ell^ - $ $ $ pqcd分解方法的研究，使用晶格QCD输入，
Study of $\bar{B}_s\to K^{(*)}\ell^+ \ell^-$ decays in the PQCD factorization approach with the lattice QCD input
论文作者
论文摘要
在本文中，我们从系统地研究了半肌衰减$ \ bar {b} _s \ to k^{（*）} \ ell^+ \ ell^ - $ with $ l^ - =（e^ - ，μ^ - ，μ^ - ，τ^ - ）$，通过使用逆向QCD（pqcd）和“ pqcd+ lattice” fince+ lattication。我们首先使用PQCD方法在低$ q^2 $区域中评估了所有相关的形式$ f_i（q^2）$，我们还将可用的晶格QCD结果在终点$ q^2_ {max} $中作为其他输入，以提高形式的额外量为高$ q^2 $区域。我们计算了分支比率和其他十二种物理可观察物。从我们的研究中，我们可以找到以下几点：（a）对于$ \ bar {b} _s \至k l^+ l^ - $衰减，pqcd和“ pqcd+ lattice”分支率（brs）$ {\ cal b}（\ bar b} _s {b} _s _s \ to br b l l l^l^l^l^l^ - ） $ r_k^{eμ} $和$ r_k^{μτ} $，以及leptons $ p_l $的纵向极化不对称在错误中同意； （b）CP平均分支比率$ {\ cal B}（\ bar {b} _S \ to K^*μ^+μ^ - ）$是$（3.17^{+0.95} _ { - 0.78} $ 10^^$ 88， $（2.48^{+0.56} _ { - 0.50}）\ times 10^{ - 8} $，与LHCB测量值$（2.9 \ pm 1.1）\ times 10^{ - 8} $和轻单键（LCSR规则（LCSR）预测非常吻合； （c）对于比率，$ r_ {k^\ ast}^{eμ} $和$ r_ {k^\ ast}^{μτ} $，pqcd和“ pqcd+lattice”预测彼此同意，并且彼此的误差很小，并且小于$ 10 \％$ $; （d）对于直接CP不对称的$ {\ cal a} _ {cp} $的所有被考虑的衰减模式，它们总是按预期很小：小于$ 5 \％$ $ b。 （e）对于Angular Observables $ P_ {1,2,3} $和$ P^\ prime_ {4,5,6,8} $，我们对每种Lepton的理论预测在错误中都是一致的。我们认为，未来的LHCB和Belle-II实验可以测试上述预测。
In this paper, we studied systematically the semileptonic decays $\bar{B}_s \to K^{(*)} \ell^+ \ell^-$ with $l^-=(e^-,μ^-,τ^-)$ by using the perturbative QCD (PQCD) and the "PQCD+Lattice" factorization approach, respectively. We first evaluated all relevant form factors $F_i(q^2)$ in the low $q^2$ region using the PQCD approach, and we also take the available Lattice QCD results at the end point $q^2_{max}$ as additional inputs to improve the extrapolation of the form factors to the high $q^2$ region. We calculated the branching ratios and other twelve kinds of physical observables. From our studies, we find the following points: (a) for $ \bar{B}_s \to K l^+ l^-$ decays, the PQCD and "PQCD+Lattice" predictions for branching ratios (BRs) ${\cal B}(\bar{B}_s \to K l^+ l^-)$, the ratios of the BRs $R_K^{eμ}$ and $R_K^{μτ}$, and the longitudinal polarization asymmetry of the leptons $P_L$ agree well within errors; (b) the PQCD and "PQCD+Lattice" predictions for the CP averaged branching ratio ${\cal B}(\bar{B}_s \to K^* μ^+ μ^-)$ are $(3.17^{+0.95}_{-0.78})\times 10^{-8}$ and $(2.48^{+0.56}_{-0.50})\times 10^{-8}$ respectively, which agree well with the LHCb measured value $(2.9\pm 1.1) \times 10^{-8}$ and the light-cone sum rule (LCSR) prediction; (c) for the ratios $R_{K^\ast}^{eμ}$ and $R_{K^\ast}^{μτ}$, the PQCD and "PQCD+Lattice" predictions agree well with each other and have a small error less than $10\%$; (d) for the direct CP asymmetries ${\cal A}_{CP}$ of all considered decay modes, they are always very small as expected: less than $5\%$ in magnitude; and (e) for the angular observables $P_{1,2,3}$ and $P^\prime_{4,5,6,8}$ , our theoretical predictions for each kind of lepton are consistent within errors. We believe that above predictions could be tested by future LHCb and Belle-II experiments.
