Flavor singlet physics with background fields from lattice QCD

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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.