Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector—defined, e.g., in the Taylor scheme—remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci–Ferrari model. The latter is the simplest deformation of the Faddeev–Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with ab-initio lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.

中文翻译：

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具有小扩展参数的红外 QCD 窗口

朗道规范中 QCD 相关函数的晶格模拟已经建立了两个值得注意的事实。首先，规范扇区中的耦合常数（例如，在泰勒方案中定义）在所有尺度上都保持有限和适中，这表明某种微扰描述应该对红外动量有效。其次，胶子传播子在动量消失时达到一个有限的非零值，对应于胶子屏蔽质量。我们回顾了最近旨在通过微扰 Curci-Ferrari 模型描述朗道规范 QCD 的长距离特性的研究。后者是朗道规范中 Faddeev-Popov Lagrangian 的最简单变形，包括树级胶子筛选质量。到目前为止，有 有力的证据表明，这种方法成功地描述了红外 QCD 动力学的许多方面。特别是，以一环和二环阶计算了几个相关函数，并与从头算起晶格模拟。一个循环计算的典型误差约为百分之十，而在两个循环中下降到百分之几。我们回顾了淬火近似和动力夸克存在下的这种计算。在后一种情况下，手性对称性的自发破坏需要超越耦合扩展，但仍然可以用小参数的受控近似方案来描述。我们还回顾了非零温度和化学势方法的应用。