论文标题
从相对论Quarkonium Sum规则的$α_s$的精确确定
Precise determination of $α_s$ from relativistic quarkonium sum rules
论文作者
论文摘要
我们从魅力和下Quark矢量的矩和魅力伪标准相关器的无量音比率确定了强的$α_s（m_z）$，称为$ r_q^{x，n} \ equiv（m_q^{x，n}）^\ frac {1} {n}/（m_q^{x，x，n+1}）^\ frac {1} {1} {1} {n+1} $，带有$ x = v，p $，以及$ 0 $ m_c^{p，0} $。在我们使用的数量中，质量依赖性非常弱，仅以对数输入，从$ \ Mathcal {o}（α_s^2）$开始。我们仔细研究了所有不确定性的来源，特别注意截断错误，并确保通过选择重新归一化量表变化来维持逐阶收敛。在计算矩比的实验不确定性时，正确考虑了各个力矩之间的相关性。此外，在对实验矢量电流矩的扰动贡献中，$α_s（m_z）$作为免费参数保存，以使我们提取强耦合的提取是公正的，仅基于实验数据。 $α_s$从矢量相关器中最精确的提取来自魅力夸克矩$ r_c^{v，2} $的比例，并读取$α_s（m_z）= 0.1168 \ pm 0.0019 $，因为我们最近在同伴信中讨论了。从底部矩，使用比率$ r_b^{v，2} $，我们找到$α_s（m_z）= 0.1186 \ pm0.0048 $。我们来自晶格伪量表魅力相关器的结果与先前确定的核心值一致，但由于我们对扰动误差的研究更加保守，因此具有更大的不确定性。平均从各种晶格输入获得的结果$ n = 0 $时刻，我们找到$α_s（m_z）= 0.1177 \ pm0.0020 $。将魅力相关器的实验和晶格信息组合到单个拟合度中，我们获得了$α_s（M_z）= 0.1170 \ pm 0.0014 $，这是本文的主要结果。
We determine the strong coupling $α_s(m_Z)$ from dimensionless ratios of roots of moments of the charm- and bottom-quark vector and charm pseudo-scalar correlators, dubbed $R_q^{X,n}\equiv(M_q^{X,n})^\frac{1}{n}/(M_q^{X,n+1})^\frac{1}{n+1}$, with $X=V,P$, as well as from the $0$-th moment of the charm pseudo-scalar correlator, $M_c^{P,0}$. In the quantities we use, the mass dependence is very weak, entering only logarithmically, starting at $\mathcal{O}(α_s^2)$. We carefully study all sources of uncertainties, paying special attention to truncation errors, and making sure that order-by-order convergence is maintained by our choice of renormalization scale variation. In the computation of the experimental uncertainty for the moment ratios, the correlations among individual moments are properly taken into account. Additionally, in the perturbative contributions to experimental vector-current moments, $α_s(m_Z)$ is kept as a free parameter such that our extraction of the strong coupling is unbiased and based only on experimental data. The most precise extraction of $α_s$ from vector correlators comes from the ratio of the charm-quark moments $R_c^{V,2}$ and reads $α_s(m_Z)=0.1168\pm 0.0019$, as we have recently discussed in a companion letter. From bottom moments, using the ratio $R_b^{V,2}$, we find $α_s(m_Z)=0.1186\pm0.0048$. Our results from the lattice pseudo-scalar charm correlator agree with the central values of previous determinations, but have larger uncertainties due to our more conservative study of the perturbative error. Averaging the results obtained from various lattice inputs for the $n=0$ moment we find $α_s(m_Z)=0.1177\pm0.0020$. Combining experimental and lattice information on charm correlators into a single fit we obtain $α_s(m_Z)=0.1170\pm 0.0014$, which is the main result of this article.
