Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field.
Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field.
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DOI：
10.1103/physrevlett.121.022004
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发表时间：
2017-07
影响因子：
8.6
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
部分子准分布函数提供了一条用格点QCD从头计算部分子分布函数的途径。计算准PDF所面临的问题之一是非定域算子的重正化。通过引入一个辅助场，我们可以用一对局部算子来代替推广理论中的非局部算子。在晶格上，这与静态夸克理论密切相关。在这种方法中，我们将展示如何理解混合的模式，允许手征对称性破缺，并获得一个主公式的重正化的非局部运营商，取决于三个参数。我们提出了一种非微扰确定这些参数的方法，并使用微扰理论转换为修改的最小减法（MS[over <$]）方案。利用威尔逊扭曲质量费米子和非局域算符中威尔逊线的不同离散化，获得了两种晶格间距的重整化参数。使用这些参数，我们显示的核子矩阵元的重正化的效果与介子质量约370兆电子伏，并比较两个晶格间距的重正化结果。重整化矩阵元在不同的Wilson线离散和晶格间距之间是一致的。
Parton quasidistribution functions provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the modified minimal subtraction (MS[over ¯]) scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters, we show the effect of renormalization on nucleon matrix elements with a pion mass of approximately 370 MeV and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.