论文标题
QCD尖源异常尺寸：当前状态
QCD cusp anomalous dimension: current status
论文作者
论文摘要
审查了HQET场异常维度和QCD尖端异常维度及其特性的计算结果。 HQET字段异常尺寸$γ_H$最多已知4个循环。尖端异常尺寸$γ（φ）$最多已知3个回路，其小角度和大角度渐近线 - 最多4个循环。有一些（但不是全部）4个循环的颜色结构，并具有完整的$φ$依赖性。一些简单的贡献在较高的循环中已知。对于$γ（φ）$（轻度尖源异常尺寸）和$φ^2 $术语的$φ\ to \ infty $渐近型，小$ $φ$扩展（bremsstrahlung函数），$ \ mathcal {n} = 4 $ sym semplofion = 4 $ sym semplocy均等于QCD QCD sofders jcd sofders jcd satfors jccd saste fors qccd。关于$γ（φ）$的结构，有一个有趣的猜想，最多可容纳3个回路。在4个循环时，它可以容纳某些颜色结构，并为其他颜色结构分解。如果将其与$φ$相关的高度非平地功能相关的情况，它并不是偶然的；但是，尚不理解这种猜想及其失败的原因。欧几里得角$ ϕ \toπ$处的尖尖异常尺寸与由于保形对称性而引起的静态夸克 - 易夸克势；在QCD中，这种关系被与$β$函数成比例的异常项打破。 还提出了一些新的结果。使用$γ_H$的最新4循环结果，在这里，我们在4循环的shell重新归一化常数$ z_q^{\ text {os}} $中获得了某些术语的分析表达式，这些术语以前仅在数值上以数值为单位所知。我们还向5循环时向$γ_H$，$γ（φ）$的$γ_H$，$γ（φ）$提出了2个新贡献，并在4个回路时向Quark-Antiquark电位。
Calculation results for the HQET field anomalous dimension and the QCD cusp anomalous dimension, as well as their properties, are reviewed. The HQET field anomalous dimension $γ_h$ is known up to 4 loops. The cusp anomalous dimension $Γ(φ)$ is known up to 3 loops, and its small-angle and large-angle asymptotics -- up to 4 loops. Some (but not all) color structures at 4 loops are known with the full $φ$ dependence. Some simple contributions are known at higher loops. For the $φ\to\infty$ asymptotics of $Γ(φ)$ (the light-like cusp anomalous dimension) and the $φ^2$ term of the small-$φ$ expansion (the Bremsstrahlung function), the $\mathcal{N}=4$ SYM results are equal to the highest-weight parts of the QCD results. There is an interesting conjecture about the structure of $Γ(φ)$ which holds up to 3 loops; at 4 loops it holds for some color structures and breaks down for other ones. In cases when it holds it related highly non-trivial functions of $φ$, and it cannot be accidental; however, the reasons of this conjecture and its failures are not understood. The cusp anomalous dimension at Euclidean angle $ϕ\toπ$ is related to the static quark-antiquark potential due to conformal symmetry; in QCD this relation is broken by an anomalous term proportional to the $β$ function. Some new results are also presented. Using the recent 4-loop result for $γ_h$, here we obtain analytical expressions for some terms in the 4-loop on-shell renormalization constant of the massive quark field $Z_Q^{\text{os}}$ which were previously known only numerically. We also present 2 new contribution to $γ_h$, $Γ(φ)$ at 5 loops and to the quark-antiquark potential at 4 loops.
