格点上的超对称QCD：四次耦合的精细调节与抵消项
Supersymmetric QCD on the lattice: Fine-tuning and counterterms for the quartic couplings
AI总结：
本文针对 $N=1$ SQCD格点作用量，利用单圈连续与格点微扰论计算四次耦合抵消项的重整化与精细调节条件。
摘要：
在本工作中，我们计算了出现在 $N=1$ 超对称QCD（SQCD）格点作用量中的抵消项的重整化。特别地，我们通过连续介质和格点微扰论，在单圈层级详细研究了四次耦合的精细调节。对于格点版本的SQCD，我们对胶子场使用Wilson规范作用量，对费米子场（夸克、胶微子）使用Wilson费米子作用量；对于标夸克场，我们使用朴素离散化。在格点上，标夸克场的不同分量彼此混合，并且在量子层级总共出现十个四次项。因此，重整化条件必须考虑这些效应，以便适当地精细调节所有四次耦合。我们关于格林函数和重整化因子的所有结果都显式解析地依赖于颜色数 $N_c$、味数 $N_f$ 和规范参数 $α$，这些量均保持未指定。文中还给出了特定情形 $N_f=1$ 的结果，在该情形中对称性只允许五个线性独立的四次项。对于格林函数的计算，我们同时考虑单粒子可约和单粒子不可约费曼图。了解这些重整化因子对于将来自非微扰研究的数值结果与“物理”可观测量联系起来是必要的。
英文摘要：
In this work we calculate the renormalization of counterterms which arise in the lattice action of $N = 1$ Supersymmetric QCD (SQCD). In particular, the fine-tunings for quartic couplings are studied in detail through both continuum and lattice perturbation theory at one-loop level. For the lattice version of SQCD we make use of the Wilson gauge action for gluon fields and the Wilson fermion action for fermion fields (quarks, gluinos); for squark fields we use naïve discretization. On the lattice, different components of squark fields mix among themselves and a total of ten quartic terms arise at the quantum level. Consequently, the renormalization conditions must take into account these effects in order to appropriately fine-tune all quartic couplings. All our results for Green's functions and renormalization factors exhibit an explicit analytic dependence on the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $α$, which are left unspecified. Results for the specific case $N_f=1$ are also presented, where the symmetries allow only five linearly independent quartic terms. For the calculation of the Green's functions, we consider both one-particle reducible and one-particle irreducible Feynman diagrams. Knowledge of these renormalization factors is necessary in order to relate numerical results, coming from nonperturbative studies, to ``physical'' observables.
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