We present a lattice QCD calculation of the scattering phase shift for the $I=2\mathrm{}S$-wave two-pion system using the finite size method proposed by Lüscher. We work in the quenched approximation employing the standard plaquette action at $\beta =5.9\mathrm{}$ 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 ${24}^3\times 60,$ ${32}^3\times 60,$ and ${48}^3\times 60$ lattices. The phase shift is successfully calculated over the momentum range $0<\mathrm{}{p}^2<0.3\mathrm{}{\mathrm{GeV}}^2.$

• Received 20 September 2002

DOI:https://doi.org/10.1103/PhysRevD.67.014502