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arXiv 2102.00858hep-lat
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QCD中规范不变重整化方案对费米子双线性和能量动量张量的应用

Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor

M. Costa, I. Karpasitis, G. Panagopoulos, H. Panagopoulos, T. Pafitis, A. Skouroupathis, G. Spanoudes

备注：
22 pages, 9 figures, 3 tables
发表信息：
Phys. Rev. D 103, 094509 (2021)
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摘要：

我们考虑规范不变，质量无关的处方重整化复合算子，正则化的晶格上，在坐标空间（X-空间）重整化方案的精神。处方只涉及格林函数的产品规范不变的运营商，位于不同的时空点，在某种程度上，以避免潜在的接触奇点。这样的格林函数可以在数值模拟中以非微扰的方式计算，而不需要固定规范：因此，这种“中间”方案的重整化可以以完全非微扰的方式进行。在$\overline{\rm MS}$格式中表示重整化算子需要计算相应的转换因子。后者只能在微扰理论中计算，这是由$\overline{\rm MS}$的本质决定的;然而，由于以下属性，计算大大简化：i）在没有算子混合的情况下，它们只涉及无质量的两点函数;这些量可以计算到非常高的微扰阶。ii）它们是规范不变的;因此，它们可以在方便的规范中计算。iii）在可能发生算子混合的情况下，只有规范不变算子将出现在混合模式中：与涉及与规范变量算子（其可能包含鬼场）混合的其他方案不同，本方案中的混合矩阵大大减少。尽管如此，一些三点函数的计算可能无法完全避免。我们通过计算QCD中$\barψΓψ$形式的费米子双线性算符的转换因子，将这一过程简化到最低阶。我们还采用规范不变的计划在胶子和夸克的能量动量张量算符之间的混合的研究：我们计算到一个循环的转换因子的非微扰混合矩阵的$\overline{\rm MS}$计划。

英文摘要：

We consider a gauge-invariant, mass-independent prescription for renormalizing composite operators, regularized on the lattice, in the spirit of the coordinate space (X-space) renormalization scheme. The prescription involves only Green's functions of products of gauge-invariant operators, situated at distinct space-time points, in a way as to avoid potential contact singularities. Such Green's functions can be computed nonperturbatively in numerical simulations, with no need to fix a gauge: thus, renormalization to this "intermediate" scheme can be carried out in a completely nonperturbative manner. Expressing renormalized operators in the $\overline{\rm MS}$ scheme requires the calculation of corresponding conversion factors. The latter can only be computed in perturbation theory, by the very nature of the $\overline{\rm MS}$; however, the computations are greatly simplified by virtue of the following attributes: i) In the absense of operator mixing, they involve only massless, two-point functions; such quantities are calculable to very high perturbative order. ii) They are gauge invariant; thus, they may be computed in a convenient gauge. iii) Where operator mixing may occur, only gauge-invariant operators will appear in the mixing pattern: Unlike other schemes, involving mixing with gauge-variant operators (which may contain ghost fields), the mixing matrices in the present scheme are greatly reduced. Still, computation of some three-point functions may not be altogether avoidable. We exemplify the procedure by computing, to lowest order, the conversion factors for fermion bilinear operators of the form $\barψΓψ$ in QCD. We also employ the gauge-invariant scheme in the study of mixing between gluon and quark energy-momentum tensor operators: We compute to one loop the conversion factors relating the nonperturbative mixing matrix to the $\overline{\rm MS}$ scheme.

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