Low Energy Constants from the zero mode contribution to the pseudo-scalar correlator

We apply different types of overlap operators in quenched QCD simulations to compute the zero mode contribution to the pseudo-scalar correlator. In particular we use the conventional Neuberger Dirac operator and the overlap hypercube Dirac operator. Confronting our data with the analytical predictions by Chiral Perturbation Theory we evaluate the pion decay constant and the parameter \alpha of the quenched chiral Lagrangian.