[Formula Presented] pion scattering phase shift with Wilson fermions

Abstract

We present a lattice QCD calculation of the scattering phase shift for the (Formula presented)-wave two-pion system using the finite size method proposed by Lüscher. We work in the quenched approximation employing the standard plaquette action at (Formula presented) for gluons and the Wilson fermion action for quarks. The phase shift is extracted from the energy eigenvalues of the two-pion system, which are obtained by a diagonalization of the pion four-point function evaluated for a set of relative spatial momenta. In order to change the momentum of the two-pion system, calculations are carried out on (Formula presented) (Formula presented) and (Formula presented) lattices. The phase shift is successfully calculated over the momentum range (Formula presented) © 2003 The American Physical Society.