标题： QCD运行耦合常数是否具有因果解析结构？ 显示英文标题

标题： Can the QCD running coupling have a causal analyticity structure?

摘要： 求解QCD重正化群方程在二环和三环阶次下，我们得到了耦合常数作为尺度函数的显式表达式，该表达式用Lambert W函数表示。 我们研究了复平面上的“Landau奇点”的性质，并表明微扰冻结在某些情况下可能导致与因果性一致的解析结构。 我们分析了旨在消除“Landau奇点”的解析微扰理论（APT）方法，并表明在二环情况下，它可以通过Lambert W函数唯一地定义，并且根据第一个和第二个β函数系数β_0和β_1的值，它要么与微扰冻结一致（当β_1 < -β_0^2时），其红外极限为-β_0/β_1，要么导致非微扰的红外耦合，其极限为1/β_0（当β_1 > -β_0^2时）。 存在一种因果微扰耦合的可能性，这与如果增加味数（N_f）则QCD中存在纯微扰的Banks-Zaks相并具有红外固定点的想法是一致的。 因果性条件意味着微扰相在N_f \geq 10时实现。 显示英文摘要

摘要： Solving the QCD renormalization group equation at the 2-loop and 3-loop orders we obtain explicit expressions for the coupling as a function of the scale in terms of the Lambert W function. We study the nature of the ``Landau singularities'' in the complex Q^2 plane and show that perturbative freezing can lead, in certain cases, to an analyticity structure that is consistent with causality. We analyze the Analytic Perturbation Theory (APT) approach which is intended to remove the ``Landau singularities'', and show that at 2-loops it is uniquely defined in terms of the Lambert W function, and that, depending on the value of the first two beta function coefficients beta_0 and beta_1, it is either consistent with perturbative freezing (for beta_1 < -beta_0^2) with an infrared limit of -beta_0/beta_1 or leads to a non-perturbative infrared coupling with a limit of 1/beta_0 (for beta_1 > -beta_0^2). The possibility of a causal perturbative coupling is in accordance with the idea that a purely perturbative Banks-Zaks phase with an infrared fixed-point exists in QCD if the number of flavours (N_f) is increased. The causality condition implies that the perturbative phase is realized for N_f \geq 10.