格点上的超对称量子色动力学：汤川耦合与四次耦合的精细调节和抵消项
Supersymmetric QCD on the lattice: Fine-tuning and counterterms for the Yukawa and quartic couplings
AI总结：
本研究针对格点离散化的$\mathcal{N} = 1$超对称量子色动力学，通过微扰计算三点、四点格林函数，确定汤川与四次耦合的精细调节及抵消项系数，完成单圈格点SQCD作用量的精细调节，为数值模拟铺路。
摘要：
在本研究中，我们确定了在欧几里得格点上离散化的$\mathcal{N} = 1$超对称量子色动力学中参数的精细调节。我们关注的是汤川耦合（胶微子-夸克-标量夸克相互作用）和四次耦合（四标量夸克相互作用）的重整化。鉴于超对称在格点上被破坏，必须向离散化的拉格朗日量中添加非超对称抵消项，其系数必须经过适当精细调节，以便在连续极限下恢复超对称。为了推导重整化因子和抵消项系数，我们在单圈和格距最低阶上微扰计算了相关的三点格林函数（用于汤川耦合）和四点格林函数（用于四次耦合）。维数正规化和格点正规化均被用于实现修正最小减除方案。我们的格点公式对胶微子和夸克场采用威尔逊离散化，对胶子采用威尔逊规范作用量，对标量夸克场采用朴素离散化。本研究的一个主要困难在于标量夸克场的不同分量在量子层面上相互混合。因此，为了对耦合进行适当的精细调节，必须在重整化条件中考虑这些混合。所有格林函数和重整化因子都显式依赖于颜色数$N_c$、味道数$N_f$和规范参数$α$，这些量未作具体指定。本工作延续了先前对超对称量子色动力学的研究，并完成了格点上超对称量子色动力学作用量的单圈精细调节，为超对称量子色动力学的数值模拟铺平了道路。
英文摘要：
In this study, we determine the fine-tuning of parameters in $\mathcal{N} = 1$ Supersymmetric QCD, discretized on a Euclidean lattice. Our focus is on the renormalization of Yukawa (gluino-quark-squark interactions) and quartic (four-squark interactions) couplings. Given that SUSY is broken on the lattice, non-supersymmetric counterterms must be added to the discretized Lagrangian, with coefficients which must be appropriately fine-tuned in order to recover SUSY in the continuum limit. To deduce the renormalization factors and the coefficients of the counterterms, we compute the relevant three-point (for the Yukawa couplings) and four-point Green's functions (for the quartic couplings) perturbatively to one-loop and to the lowest order in lattice spacing. Both dimensional and lattice regularizations are used to implement the Modified Minimal Subtraction scheme. Our lattice formulation employs the Wilson discretization for gluino and quark fields, the Wilson gauge action for gluons, and naive discretization for squark fields. One main difficulty in this study lies in the fact that different components of squark fields mix among themselves at the quantum level. Consequently, for an appropriate fine-tuning of the couplings, these mixings must be taken into account in the renormalization conditions. All Green's functions and renormalization factors exhibit an explicit dependence on the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $α$, which are left unspecified. This work follows previous investigations on SQCD and finalizes the one-loop fine-tuning of the SQCD action on the lattice, paving the way for numerical simulations of SQCD.
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