Hadronic structures from lattice QCD

• Antragsteller: Privatdozent Dr. Arwed Schiller
• Fachliche Zuordnung: Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder
• Förderung: Förderung von 2013 bis 2015
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 234004873

The investigation of the structure of hadrons belong to the most challenging fundamental problems in physics. According to QCD the measured properties of hadrons (e.g., momentum or angular momentum) are determined by their constituents - the quarks and gluons. A prominent recent example is the gluon distribution inside protons - its detailed knowledge is essential to understand the precise production mechanism of the Higgs boson, which is searched for at LHC in CERN. In the last decades lattice QCD has been developed into one of the most promising tools to investigate the low energy hadronic structure. Improved algorithms and computer resources allow to handle more and more complex and physically “real'' problems. Certainly, the distributions of quarks and gluons belong to these problems. They have to be compared with the experimental data. Despite large successes there remain partly significant uncertainties or differences to the phenomenological results. In this application we plan to investigate the momentum and spin distributions of quarks and the momentum distributions and angular momentum of gluons inside hadrons. Especially, we want to calculate the first moments of quark and gluon distribution functions - the so-called momentum fractions. The spinfraction for quarks are related to the helicity dependent quark distribution functions. The gluon angular momentum is computed from the gluonic energy momentum tensor. The computation includes the light (u,d) 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 very difficult to perform numerically using standard techniques - it is one source for the still exisiting difference to experimental results. An alternative promising method to handle this case is the application of the so-called Feynman-Hellmann theorem to compute those flavor singlet matrix elements. First computations show that in applying this method the signal-to-noise-ratio is improved indeed considerably. This improvement is bought by additional simulations with extended actions. As the underlying actions we plan to use for the fermionic part the SLiNC action, as the gauge action we take the tree level improved Symanzik. Being singlet quantities quark and gluon momentum fractions mix under renormalisation. We will compute the corresponding mixing matrix up to one-loop order in diagrammatic lattice perturbation theory. This work will be a significant and necessary part of the nucleon structure studies of the QCDSF collaboration located at many universities and institutes like, e.g. DESY, Regensburg, Liverpool, Edinburgh, Adelaide, RIKEN, Mexico and Leipzig.

• DFG-Verfahren: Sachbeihilfen