Exploring the hadronic structure using the Feynman-Hellmann theorem

强子结构的研究属于粒子物理学的基础领域。因此，QCD的晶格形式起着至关重要的作用。它已经达到了可以与实验甚至预测进行现实比较的水平。确定可观测量的基础是计算矩阵元素，即状态间算子的期望值。特别是，对于物理点附近的大晶格，这是相当复杂的，并且受到大误差的影响。本项目采用费曼-赫尔曼（FH）方法计算相应的观测值。它使用两点函数，不容易出现这些问题。但是，需要修改传播器和/或操作。最初的计算表明，它可以成功地用于相关数量，如重子内部夸克的自旋分数或形状因子。在这个提议中，我们想将FH方法应用于三个实验基本量：1。大动量传递中的强子形式因子：这些可观察到的已经和将要在JLab测量，实验家的兴趣非常高！通过我们的方法，我们可以达到以前不可能达到的动量区域。强子中夸克的动量分数：属于基本结构量。它们是通过能量动量张量的期望值来计算的。为了减小晶格的影响，我们建议使用一个改进的版本。矩阵元素本身将通过一个改进的传播器用跳频计算。强子结构函数：它们是粒子物理学中最基本的量之一。我们使用一种创新的方法来直接计算它们——大多数以前的计算只涉及最初的几个时刻。在这个方案中，结构函数由正向康普顿散射振幅确定。在晶格上，这实际上只有用FH方法才能实现，这在可行性研究中已经得到了令人信服的证明。我们的目标是（非）极化结构函数，特别是在小x和大x区域，在那里人们遇到了显着的现象学空白。此外，我们研究了更高捻度的贡献。我们考虑非单重态和单重态结构函数。我们计算的基础是不同晶格尺寸、夸克质量和晶格间距的大量配置，这些配置允许进行所需的外推。

The investigation of the hadronic structure belongs to the fundamental areas in particle physics. Thereby the lattice formulation of the QCD plays an essential role. It has reached a level which makes possible a realistic comparison with experiment and even forecasts.The basis of the determination of the observables is the calculation of matrix elements, ie the expectation values of operators between states. Especially, for large lattices near the physical point this is rather complicated and afflicted with large errors. In this project the Feynman-Hellmann (FH) method is applied to compute the corresponding observables. It uses two-point functions which are not so prone to those problems. However, one needs modified propagators and/or actions. First calculations showed that it can be used sucessfully for relevant quantities like the spin fraction of quarks inside baryons or form factors. In this proposal we want to apply the FH method to three experimentally essential quantities:1. Hadronic form factors at large momentum transfer: these observableshave been and will measures at JLab, the interest of the experimentalists is very high! With our approach wie could reach momentum regions whic was not possible before.2. Momentum fraction of quarks in hadrons: they belong to the basic structural quantities. They are calculated via the expectation value of the energy-momentum-tensor. We propose to use an improved version of it in order to diminish des influence of the lattice. The matrix element itself will be computed with FH via a modified propagator.3. Hadronic structure functions: they are among the most fundamental quantities in particle physics. We use an innovative approach to compute them directly - most previous calculations concerned the first few moments only. In this proposal the structure functions are determined via the forward Compton scattering amplitude. On the lattice this is possible practically only with the FH method, which has been demonstrated convincingly in a feasibility study. Our targets are (un)polarized structure functions especially also in the region of small and large x where one encountered significant phenomenological gaps. Additionally, we investigate the higher twist contribtions. We consider nonsinglet and singlet structure functions.Basis of our computations is the large number of configurations for different lattice sizes, quark masses and lattice spacings whic allow for the needed extrapolations.