Computing the eta and eta Mesons in Lattice QCD

It has been known for a long time that the large experimental singlet-octet mass gap in the pseudoscalar meson mass spectrum originates from the anomaly of the axial vector current, i.e. from nonperturbative effects and the nontrivial topological structure of the QCD vacuum. In the N_colour -> infinity limit of the theory, this connection elucidates in the famous Witten-Veneziano relation between the eta-mass and the topological susceptibility of the quenched QCD vacuum.While lattice QCD has by now produced impressive high precision results on the flavour nonsinglet hadron spectrum, the determination of the pseudoscalar singlet mesons from direct correlator studies is markedly lagging behind, due to the computational complexity in handling observables that include OZI-rule violating diagrams, like the eta propagator. In this article, we report on some recent progress in dealing with the numerical bottleneck problem.