Flavor singlet physics with background fields from lattice QCD

在过去的几十年里，晶格量子色动力学已经发展成为研究低能强子结构的最有前途的工具之一。实验研究和理论研究之间的相互作用已经达到了很高的水平。改进的算法和计算机资源允许处理越来越复杂和基本的问题。其中我们提到了强子的自旋含量-它由价夸克、海夸克和胶子组成，到目前为止还没有一个令人满意的精度。在这个应用中，我们研究了以能量动量张量(EMT)编码的夸克和胶子的动量分布和强子中夸克的自旋含量的基本强子结构。计算既包括轻夸克，也包括奇异夸克。研究格子上的海夸克和胶子可观测性需要计算具有不连通的夸克线的矩阵元素，这是使用标准三点函数技术所面临的计算挑战。为了计算这些有趣的单重矩阵元素，我们将使用Feynman-Hellmann(FH)定理作为另一种有前途的方法，在FH定理中，基本上是在背景场中研究两点函数。由QCDSF合作完成的第一次计算，例如对核子的自旋含量的计算，表明信噪比确实有了很大的改善。这种概念改进的代价是用扩展的动作进行额外的模拟。作为EMT矩阵元素的晶格算子通常需要重新正规化，最好是非微扰的。同样，在这种情况下，由于低信噪比，使用标准技术的单重态算子的重整化因子很难甚至实际上不可能测量。作为可能的解决办法，我们也将利用跳频方法。第一次对局域算符的计算表明，这种新的方法可以非常成功地应用于这些类型的算符。除了上面讨论的自旋和动量分布所需的算符之外，我们还将在这个重正化程序中包括更多的局域算符，如伪标量、矢量或反对称张量流。作为我们计划的研究中费米子部分的基本作用，我们使用SLiNC作用，作为规范作用，我们采用树级改进的Symanzik。

In the last decades lattice quantum chromodynamics has been developed into one of the most promising tools to investigate the low energy hadronic structure. A very high level of the interaction between experimental and theoretical investigations has been reached. Improved algorithms and computer resources allow to handle more and more complex and fundamental problems. Among others we mention the spin content of the hadron - its composition from the valence quarks, sea quarks and gluons is not known up to now to a satisfactory precision.In this application we investigate fundamental hadronic structures as the momentum distributions of quarks and gluons encoded in the energy-momentum tensor (EMT) and the spin content of quarks in the hadron. The computation includes the light quarks as well as strange quarks. The investigation of sea quark and gluon observables on the lattice requires the calculation of matrix elements with disconnected quark lines what is computational challenging using the standard three-point function technique. In order to compute these flavor singlet matrix elements we will use as alternative promising method the Feynman-Hellmann (FH) theorem in which basically two-point functions are studied in background fields. First computations, e.g. for the spin content of the nucleon, done by the QCDSF collaboration show that the signal-to-noise ratio is improved indeed considerably. The price for this conceptual improvement is paid by additional simulations with extended actions.Lattice operators as the EMT matrix elements need to be renormalised in general, preferably nonperturbatively. Also in this case, the renormalisation factors for singlet operators using standard techniques are difficult or even practically impossible to measure due to low signal-to-noise ratios.As possible way-out we will we will exploit the FH approach as well. First calculations for local operators show that this novel approach can be applied very successfully to these types of operators.In addition to the operators needed for the spin and momentum distributions discussed above we will include in this renormalisation programme also further local operators, like the pseudoscalar, vector or antisymmetric tensor currents.As the underlying actions in our planned investigations we use for the fermionic part the SLiNC action, as the gauge action we take the tree level improved Symanzik.