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I=2 Pion Scattering Phase Shift with Wilson Fermions

We present a lattice QCD calculation of the scattering phase shift for the I=2 $S$-wave two-pion system using the finite size method proposed by Lüscher. We work in the quenched approximation employing the standard plaquette action at $β=5.9$ 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 4-point function evaluated for a set of relative spatial momenta. In order to change 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 $0 < p^2 < 0.3 {\rm GeV}^2$.