Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach
Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach
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DOI：
10.1103/physrevd.101.074509
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发表时间：
2020-02
影响因子：
5
通讯作者：
J. Green;K. Jansen;F. Steffens
中科院分区：
文献类型：
--
作者：
J. Green;K. Jansen;F. Steffens
利用格点QCD研究了强子的部分子分布函数和横动量依赖的部分子分布函数。非定域性使得很难理解这些算子的重整化和改进。在以前的工作中，我们表明，通过在格点上引入辅助场，可以理解为在扩展理论中的两个局部算子的乘积的轴上威尔逊线算子。在本文中，我们提供了详细的微扰理论中的因子的计算转换从我们的晶格合适的重整化方案的MS-酒吧计划。扩展我们的工作，我们研究了西曼齐克改进的扩展理论，以了解模式的离散化效果线性的晶格间距，$a $，这是目前即使晶格费米子行动完全保留手征对称性。这为PDF晶格计算的最终O（a）$改进提供了前景。我们还推广我们的方法适用于威尔逊线沿着晶格对角线和分段直链接路径。
Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the renormalization and improvement of these operators using standard methods. In previous work, we showed that by introducing an auxiliary field on the lattice, one can understand an on-axis Wilson-line operator as the product of two local operators in an extended theory. In this paper, we provide details about the calculation in perturbation theory of the factor for conversion from our lattice-suitable renormalization scheme to the MS-bar scheme. Extending our work, we study Symanzik improvement of the extended theory to understand the pattern of discretization effects linear in the lattice spacing, $a$, which are present even if the lattice fermion action exactly preserves chiral symmetry. This provides a prospect for an eventual $O(a)$ improvement of lattice calculations of PDFs. We also generalize our approach to apply to Wilson lines along lattice diagonals and to piecewise-straight link paths.