Scattering length from BS wave function inside the interaction range

Abstract

We evaluate $I=2$ two-pion scattering length through the scattering amplitude obtained by the Bethe-Salpeter wave function inside the interaction range. The scattering length is computed with $m_\pi = 0.52-0.86$ GeV in the quenched lattice QCD. Furthermore, the half-off-shell amplitude is calculated, from which the effective range is extracted. Our results are compared with those by the conventional finite size method and by chiral perturbation theory to confirm consistency.