Exploring the hadronic structure using the Feynman-Hellmann theorem

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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.