A bstract The vacuum polarization tensor and the corresponding vacuum polarization function are the basis for calculations of numerous observables in lattice QCD. Examples are the hadronic contributions to lepton anomalous magnetic moments, the running of the electroweak and strong couplings and quark masses. Quantities which are derived from the vacuum polarization tensor often involve a summation of current correlators over all distances in position space leading thus to the appearance of short-distance terms. The mechanism of O a $$ mathcal{O}(a) $$ improvement in the presence of such short-distance terms is not directly covered by the usual arguments of on-shell improvement of the action and the operators for a given quantity. If such short-distance contributions appear, the property of O a $$ mathcal{O}(a) $$ improvement needs to be reconsidered. We discuss the effects of these short-distance terms on the vacuum polarization function for twisted mass lattice QCD and find that even in the presence of such terms automatic O a $$ mathcal{O}(a) $$ improvement is retained if the theory is tuned to maximal twist.
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机译：Bstract真空偏振张量和相应的真空偏振函数是计算晶格QCD中许多可观察者的基础。例子是Lepton异常磁性时刻的幂声贡献，电挖掘的运行和强耦合和夸克群众。源自真空偏振张量的量通常涉及当前态相关器的总和在位置空间中的所有距离上，从而导致短距离术语的出现。 O A $$ mathcal {o}（a）在存在此类短距离术语的情况下改善的机制不直接由行动和运营商的常规争论和给定数量的惯例。如果出现此类短距离贡献，则需要重新考虑O A $ Mathcal {O}（a）$$的属性。我们讨论了这些短距离术语对扭曲质量晶格QCD真空偏振函数的影响，并发现即使在存在这样的术语时，即使在这种术语存在时，可以自动o获得$$ mathcal {o}（a）$$改善理论被调整为最大扭曲。
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