几何发散单圈格点Feynman积分的一般性质
General properties of logarithmically divergent one-loop lattice Feynman integrals
摘要：
证明了代数发散单圈格点Feynman积分的一般形式I（p，a）= f（p）log（aM）+g（p，M），直到格点间距a -> 0时积分项为零.这里p表示外动量的总和，M是一个任意的质量尺度。f（p）被证明是普适的，并且与相应连续统积分中的类似量一致（正则化，例如，通过动量截止）。这对于格点量子色动力学β函数的普适性和重整化晶格算符在一圈处的反常维数是必不可少的。这里给出的结果和参数是arXiv：0709.0781中给出的结果和参数的简化版本。这个论证的一个值得注意的特点是，它不涉及外动量的泰勒展开，因此与该展开相关的红外发散不会出现。
英文摘要：
We prove that logarithmically divergent one-loop lattice Feynman integrals have the general form I(p,a) = f(p)log(aM)+g(p,M) up to terms which vanish for lattice spacing a -> 0. Here p denotes collectively the external momenta and M is an arbitrary mass scale. The f(p) is shown to be universal and to coincide with the analogous quantity in the corresponding continuum integral (regularized, e.g., by momentum cut-off). This is essential for universality of the lattice QCD beta-function and anomalous dimensions of renormalized lattice operators at one loop. The result and argument presented here are simplified versions of ones given in arXiv:0709.0781. A noteworthy feature of the argument here is that it does not involve Taylor expansion in external momenta, hence infra-red divergences associated with that expansion do not arise.
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