Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit

The overlap hypercube fermion is a variant of a chirally symmetric lattice fermion, which is endowed with a higher level of locality than the standard overlap fermion. We apply this formulation in quenched QCD simulations with light quarks. In the p-regime we evaluate the masses of light pseudoscalar and vector mesons, as well as the pion decay constant and the renormalisation constant Z_A. In the epsilon-regime we present results for the leading Low Energy Constants of the chiral Lagrangian, Sigma and F_pi. To this end, we perform fits to predictions by chiral Random Matrix Theory and by different versions of quenched Chiral Perturbation Theory, referring to distinct correlation functions. These results, along with an evaluation of the topological susceptibility, are also compared to the outcome based on the standard overlap operator