论文标题
通过扰动理论透过QCD保形窗口
Looking through the QCD Conformal Window with Perturbation Theory
论文作者
论文摘要
我们使用扰动理论研究QCD的共形窗口，从扰动上的上边缘开始，并尽可能地向下朝着强耦合方案迈进。我们这样做是通过利用$ \ Overline {\ rm MS} $ $β$功能的可用五循环计算，并为普通的扰动系列以及Banks-Zaks Conformal Expantion提供了Borel重新定义技术。还使用了大$ n_f $结果。我们认为，$ \ Overline {\ rm MS} $ $β$ - 功能的扰动系列很可能是渐近的，并且不可重新定位，但是Borel重新定义技术可以改善普通的扰动理论。我们发现有大量证据表明，$ n_f = 12 $的QCD在IR中流向保形场理论。尽管证据较弱，但我们发现$ n_f = 11 $也可能位于保形窗口内。我们还计算固定点上质量异常$γ$的值，并将其与可用的晶格结果进行比较。共形窗口可能会扩展到$ n_f $的较低值，但是我们的方法以$ n_f <11 $分解，我们期望非扰动效果变得重要。在委内兹亚诺限制中进行了类似的分析。
We study the conformal window of QCD using perturbation theory, starting from the perturbative upper edge and going down as much as we can towards the strongly coupled regime. We do so by exploiting the available five-loop computation of the $\overline{\rm MS}$ $β$-function and employing Borel resummation techniques both for the ordinary perturbative series and for the Banks-Zaks conformal expansion. Large-$n_f$ results are also used. We argue that the perturbative series for the $\overline{\rm MS}$ $β$-function is most likely asymptotic and non-Borel resummable, yet Borel resummation techniques allow to improve on ordinary perturbation theory. We find substantial evidence that QCD with $n_f=12$ flavours flows in the IR to a conformal field theory. Though the evidence is weaker, we find indications that also $n_f=11$ might sit within the conformal window. We also compute the value of the mass anomalous dimension $γ$ at the fixed point and compare it with the available lattice results. The conformal window might extend for lower values of $n_f$, but our methods break down for $n_f<11$, where we expect that non-perturbative effects become important. A similar analysis is performed in the Veneziano limit.
