Lattice perturbation theory and Renormalisation

强子的大部分性质信息是由局部算符的强子矩阵元素导出的，这些局部算符可以在晶格QCD的框架下计算得到。为了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重整化常数进行比较。我们计划在单环晶格微扰理论中推导具有一个以上协变导数的双夸克算子的重整化因子和改进系数。（关于单个协变导数算子的结果已经发表。）这将使我们能够计算出极化和非极化核子结构函数的最小矩。研究了四夸克算子的重整化和改进。这些结果与诸如深非弹性散射和重夸克弱衰变中的高扭转效应有关。将发展包括高循环贡献在内的技术。计划为广义部子分布函数的一阶矩开发一个新的重整化程序。

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.