几何发散单圈格点Feynman积分的结构
Structure of logarithmically divergent one-loop lattice Feynman integrals
摘要：
对于代数发散的单圈格点Feynman积分I（p，a），在较弱的一般条件下，我们证明了如下所期望的和关键的结构结果：I（p，a）= f（p）log（aM）+g（p）+h（p，M）直到格点间距a -> 0时为零的项.这里，p表示外动量的总和，M是一个可以任意选择的质量标度。f（p）和h（p，M）被证明是普适的，并且当连续统积分被动量截断或维数正则化时，它们与相应连续统积分中的类似量一致.非普适项g（p）被证明是p中与f（p）同阶的齐次多项式。这种结构是必不可少的一致性重整化晶格和QCD在一个循环的连续配方。
英文摘要：
For logarithmically divergent one-loop lattice Feynman integrals I(p,a), subject to mild general conditions, we prove the following expected and crucial structural result: I(p,a) = f(p)log(aM)+g(p)+h(p,M) up to terms which vanish for lattice spacing a -> 0. Here p denotes collectively the external momenta and M is a mass scale which may be chosen arbitrarily. The f(p) and h(p,M) are shown to be universal and coincide with analogous quantities in the corresponding continuum integral when the latter is regularized either by momentum cut-off or dimensional regularization. The non-universal term g(p) is shown to be a homogeneous polynomial in p of the same degree as f(p). This structure is essential for consistency between renormalized lattice and continuum formulations of QCD at one loop.
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