Lattice perturbation theory and Renormalisation

强子的大多数性质信息都是由局域算符的强子矩阵元导出的，这些矩阵元可以在格点QCD框架下计算。要将晶格结果与连续统量联系起来，必须知道算子的重整化。我们专注于微扰重整化，并将这些结果与非微扰获得的重整化常数进行比较。我们计划在单圈格点微扰理论中导出具有多个协变导数的双夸克算符的重整化因子和改进系数。（具有单个协变导数的算子的结果已经发表。这将使我们能够计算极化和非极化核子结构函数的最低几阶矩。四夸克算符的重整化和改进将被研究。这些结果与以下方面有关，例如，在深度非弹性散射和重夸克的弱衰变中的高扭曲效应。技术将被开发，包括更高的循环贡献。一个新的重正化程序计划开发的第一时刻的广义部分子分布函数。

Information on most properties of hadrons is derived from hadronic matrix elements of local operators which can be calculated in the framework of lattice QCD. To relate the lattice results to continuum quantities the renormalisation of the operators must be known. We concentrate on the perturbative renormalisation and will compare those results with non-perturbatively obtained renormalisation constants. We plan to derive the renormalisation factors as well as the improvement coefficients for two-quark operators with more than one covariant derivative in one-loop lattice perturbation theory. (Results for operators with a single covariant derivative have already been published.) This will allow us to compute the lowest few moments of the polarised and unpolarised nucleon structure functions. The renormalisation and improvement of four-quark operators will be investigated. The results are relevant for, e.g., higher twist effects in deep inelastic scattering and weak decays of heavy quarks. Techniques will be developed to include higher-loop contributions. A new renormalisation program is planned to be developed for the first moments of generalised parton distribution functions.