论文标题
集成相关函数中的对数增强的离散错误
Log-enhanced discretization errors in integrated correlation functions
论文作者
论文摘要
集成的时板相关函数$ g（t）$带重量$ k（t）$出现，例如，在矩的方法中，在MUON G-2的确定或确定平滑的光谱功能中，从重夸克相关器确定$α_s$。 对于伪量表相关器的（领先）归一化矩$ r_4 $，我们的结果是非扰动的结果，降低至$ a = 10^{ - 2} $ fm，对于大众，$ m $，$ m $，是Quenched近似值中符合符号的顺序。在小晶格间距中观察到$ r_4 $的显着弯曲，这是$ a^2 $的函数。 从集成数的Symanzik扩展开始，我们得出了自由理论中小晶格间距的积分的渐近收敛性，并证明积分的短距离部分会导致$ \ log（a）$ - 增强的离散错误时，当$ g（t）k（t）k（t）k（t）k（t）\ sim \，t $ for小$ t $ $ t $。在交互理论中，出现函数$ k（aλ）$。 对于$ r_4 $ - case，我们修改可观察到的可观察到以提高短距离行为，并证明它会导致非常平稳的连续限制。然后可以提取强耦合和$λ$ - 参数。通常，尤其是对于$ g-2 $，整体的短距离部分应由扰动理论确定。然后可以通过晶格计算的受控连续限量获得（主导的）休息。
Integrated time-slice correlation functions $G(t)$ with weights $K(t)$ appear, e.g., in the moments method to determine $α_s$ from heavy quark correlators, in the muon g-2 determination or in the determination of smoothed spectral functions. For the (leading-order-)normalised moment $R_4$ of the pseudo-scalar correlator we have non-perturbative results down to $a=10^{-2}$ fm and for masses, $m$, of the order of the charm mass in the quenched approximation. A significant bending of $R_4$ as a function of $a^2$ is observed at small lattice spacings. Starting from the Symanzik expansion of the integrand we derive the asymptotic convergence of the integral at small lattice spacing in the free theory and prove that the short distance part of the integral leads to $\log(a)$-enhanced discretisation errors when $G(t)K(t) \sim\, t $ for small $t$. In the interacting theory an unknown, function $K(aΛ)$ appears. For the $R_4$-case, we modify the observable to improve the short distance behavior and demonstrate that it results in a very smooth continuum limit. The strong coupling and the $Λ$-parameter can then be extracted. In general, and in particular for $g-2$, the short distance part of the integral should be determined by perturbation theory. The (dominating) rest can then be obtained by the controlled continuum limit of the lattice computation.
