Simulations of lattice fermions with chiral symmetry in quantum chromodynamics
This thesis is dedicated to explore the feasibility of extraction of the low energy constants of the chiral Lagrangian in the epsilon--regime of quenched QCD. We apply two formulations of the Ginsparg-Wilson fermions, namely, the Neuberger operator and the hypercube overlap operator to compute the observables of interest. As a main result we present the comparison of the distributions of the leading individual eigenvalues of the Neuberger operator in QCD and the analytical predictions of chiral random matrix theory. We observe a good agreement as long as each side of the physical volume exceeds about 1.12 fm. At the same time the chiral condensate Sigma can also be estimated. It turns out that this bound for L is generic and sets the size of the physical volume where the axial correlator behaves according to chiral perturbation theory. This allows us to compute a value for the pion decay constant. The simulations also show that due to the high probability of the near-zero modes it is prohibitively difficult to sample the axial correlator in the neutral topological sector. In the higher sectors, however, we observe that the sensitivity of the analytical predictions for the axial correlator to extract Sigma is lost to a large extent. As an alternative procedure we only consider the contribution from the zero modes. Here we are able to obtain an estimate for the pion decay constant and alpha, where alpha is a low energy constant peculiar to quenching. We calculate the topological susceptibility, both for the Neuberger operator and for the overlap hypercube operator. It turns out that the result with the overlap hypercube operator is closer to the continuum limit. Also the locality properties are superior to those of the Neuberger fermions. As a theoretical development the Lüscher topology conserving gauge action is investigated. This enables us to sample the observables of interest in the epsilon--regime without recomputing the index.
School:Humboldt-Universität zu Berlin
Source Type:Master's Thesis
Keywords:lattice QCD Gitter epsilon Regime chiral perturbation theory regime random matrix
Date of Publication:11/01/2004