论文标题
在红外线中运行耦合有限和单调的PQCD：它们何时反映了空间类似物的全体形态特性？
pQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables?
论文作者
论文摘要
We investigate a large class of perturbative QCD (pQCD) renormalization schemes whose beta functions $β(a)$ are meromorphic functions of the running coupling and give finite positive value of the coupling $a(Q^2)$ in the infrared regime ("freezing"), $a(Q^2) \to a_0$ for $Q^2 \to 0$.这样的耦合自动在平方动量$ q^2 $（$ \ equiv -q^2 $）的正轴上没有奇异性。重新归一化组方程（RGE）的显式集成导致耦合的隐式（倒置）解决方案，形式为$ \ ln（q^2/q^2 _ {\ rm in} in}）= {\ cal H}（a）$。对该解决方案的分析导致我们采用代数算法，以搜索$ a（q^2）$的landau奇异性在复杂的$ q^2 $平面的第一张Riemann纸上，即电杆和分支点（包括杆子和分支点（带有剪切））。我们提出了使用这种算法的特定代表性示例，并将发现的Landau奇异性与RGE在整个第一个Riemann纸中的二维数值整合后看到的landau奇异性进行了比较，在整个第一个Riemann纸中，后者的方法在数值上是要求的，并且可能并不总是精确。具体示例表明，提出的代数方法对于找出运行的PQCD耦合是否具有Landau奇异性以及（如果是），那么这些奇异性是有用的。
We investigate a large class of perturbative QCD (pQCD) renormalization schemes whose beta functions $β(a)$ are meromorphic functions of the running coupling and give finite positive value of the coupling $a(Q^2)$ in the infrared regime ("freezing"), $a(Q^2) \to a_0$ for $Q^2 \to 0$. Such couplings automatically have no singularities on the positive axis of the squared momenta $Q^2$ ($ \equiv -q^2$). Explicit integration of the renormalization group equation (RGE) leads to the implicit (inverted) solution for the coupling, of the form $\ln (Q^2/Q^2_{\rm in}) = {\cal H}(a)$. An analysis of this solution leads us to an algebraic algorithm for the search of the Landau singularities of $a(Q^2)$ on the first Riemann sheet of the complex $Q^2$-plane, i.e., poles and branching points (with cuts) outside the negative semiaxis. We present specific representative examples of the use of such algorithm, and compare the found Landau singularities with those seen after the 2-dimensional numerical integration of the RGE in the entire first Riemann sheet, where the latter approach is numerically demanding and may not always be precise. The specific examples suggest that the presented algebraic approach is useful to find out whether the running pQCD coupling has Landau singularities and, if yes, where precisely these singularities are.
