在背景场理论框架下利用QCD求和规则表征$D_s^+$介子衰变常数及轻子衰变的性质
Characterize the properties of $D_s^+$-meson decay constant and leptonic decays by using QCD sum rules within background field theory framework
AI总结：
本研究在背景场理论框架下用QCD求和规则精确计算$D_s^+$介子衰变常数，通过两种约束方案得到与现有结果吻合的数值，并进一步计算轻子衰变分支比、提取CKM矩阵元$|V_{cs}|$。
AI中文摘要：
$D_s^+$介子的轻子衰变近年来受到了广泛关注。本研究在背景场理论框架下，采用QCD求和规则方法对衰变常数$f_{D_s^+}$进行了精确计算。计算过程中完整纳入了直至六维凝聚态的夸克传播子贡献。通过采用两种不同的约束方案，分别得到$f_{D_s^+}^{\text{(I)}} = 253.0_{-3.1}^{+3.3}\text{ MeV}$和$f_{D_s^+}^{\text{(II)}} = 251.8_{-1.3}^{+1.4}\text{ MeV}$，二者均与已有的理论和实验结果高度吻合。其中传统方案遵循标准的 Borel 窗口判据，导数方案则通过辅助函数降低了衰变常数对Borel参数的依赖。基于这些衰变常数并结合NLO电弱辐射修正，我们进一步计算了两种方案下三个轻子衰变道的分支比。结合粒子数据组（PDG）最新的$\text{B}(D_s^+ \to \text{μ}^+ \nu_μ)$分支比，我们从两种方案中分别提取出CKM矩阵元$|V_{cs}|^{\text{(I)}} = 0.967 \text{±} 0.012$和$|V_{cs}|^{\text{(II)}} = 0.970 \text{±} 0.005$。
英文摘要：
The leptonic decays of the $D_s^+$-meson have received considerable attention in recent years. In this work, we perform a precise calculation of the decay constant $f_{D_s^+}$ using the QCD sum rules method within the background field theory framework. In our calculation, we fully include the quark propagator contributions up to dimension-six condensates. By adopting two different constraint schemes, we obtain $f_{D_s^+}^{\text{(I)}} = 253.0_{-3.1}^{+3.3}\ \text{MeV}$ and $f_{D_s^+}^{\text{(II)}} = 251.8_{-1.3}^{+1.4}\ \text{MeV}$, respectively, both of which are in good agreement with existing theoretical and experimental results. The conventional scheme follows the standard Borel window criteria, while the derivative scheme reduces the dependence of the decay constant on the Borel parameter through an auxiliary function. Based on these decay constants and incorporating the NLO electroweak radiative corrections, we further calculate the branching fractions for the three leptonic decay channels for both schemes. Combined with the latest branching fraction $\mathcal{B}(D_s^+ \to μ^+ ν_μ)$ from the PDG, we extract the CKM matrix elements $|V_{cs}|^{\text{(I)}} = 0.967 \pm 0.012$ and $|V_{cs}|^{\text{(II)}} = 0.970 \pm 0.005$ from the two schemes, respectively.
