论文标题
$ b_s \ to ϕ \ ell^+ \ ell^ - $ $ $ $ $ $ $ $ $在PQCD分解方法中使用晶格QCD输入的方法
Study of $B_s\to ϕ\ell^+ \ell^-$ decays in the PQCD factorization approach with lattice QCD input
论文作者
论文摘要
在本文中，我们使用$ l^ - =（e^ - ，μ^ - ，τ^ - ）$系统地研究了半肌衰减$ b_s \ to ϕl^+ l^ - $，分别使用“ pqcd+ lattice rattice”分量方法。我们首先使用PQCD方法在低$ q^2 $区域中评估了所有相关的形式$ f_i（q^2）$，我们还以高$ q^2 $区域的价格采取了可用的晶状体QCD结果，以提高$ f_i（q^2）$的外推，以提高$ q^2 $ q^2 $ Q^2 $区域的外推到Endpoint $ Q^2_ $ q^2_}然后，我们计算了分支比率和许多其他物理观察结果：$ a_ {fb}^{l} $，$ f_l^ϕ $，$ s_ {3,4,7} $，$ a_ {5,6,8,9} $ p^{\ prime} _ {4,5,6,8} $。从我们的研究中，我们找到以下几点：（a）pqcd和“ pqcd+ lattice”预测$ {\ cal b}（b_s \ cal b_s \ to d of tos to nim^+μ^ - ）$的$ 7 \ times 10^$ lh，n.在仍然很大的错误中的总和规则预测； （b）我们定义并计算了分支比率$ r_D = {eμ} $和$ r_ϕ^{μτ} $的比率; (c) the PQCD and "PQCD+Lattice" predictions of the longitudinal polarization $F_L$, the CP averaged angular coefficients $S_{3,4,7} $ and the CP asymmetry angular coefficients $A_{5,6,8,9}$, agree with the LHCb measurements in all considered bins within the still large experimental errors; （d）对于当前仍然未知的观察物$ r_Dcartibles $ r_ϕ^{eμ}，r_x^{μτ}，a_ {fb}^{l}，p_ {1,2,3} $和$ p^{\ prime} _ {4,5,6,6,8} $ lhcb and belle-ii consection insurime stry量。
In this paper, we studied systematically the semileptonic decays $B_s \to ϕl^+ l^-$ 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 took the available lattice QCD results at the high-$q^2$ region as additional input to improve the extrapolation of $F_i(q^2)$ from the low-$q^2$ region to the endpoint $q^2_{max}$. We then calculated the branching ratios and many other physical observables: $A_{FB}^{l}$, $F_L^ϕ$, $S_{3,4,7}$, $A_{5,6,8,9}$ and the clean angular observables $P_{1,2,3} $ and $P^{\prime}_{4,5,6,8}$.From our studies, we find the following points: (a) the PQCD and "PQCD+Lattice" predictions of ${\cal B}( B_s \to ϕμ^+ μ^-)$ are about $7\times 10^{-7}$, which agree well with the LHCb measured values and the QCD sum rule prediction within still large errors; (b) we defined and calculated the ratios of the branching ratios $R_ϕ^{eμ}$ and $R_ϕ^{μτ}$; (c) the PQCD and "PQCD+Lattice" predictions of the longitudinal polarization $F_L$, the CP averaged angular coefficients $S_{3,4,7} $ and the CP asymmetry angular coefficients $A_{5,6,8,9}$, agree with the LHCb measurements in all considered bins within the still large experimental errors; and (d) for those currently still unknown observables $R_ϕ^{eμ}, R_ϕ^{μτ}, A_{FB}^{l}, P_{1,2,3}$ and $P^{\prime}_{4,5,6,8}$, we suggest LHCb and Belle-II Collaboration to measure them in their experiments.
