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We evaluate scattering amplitudes at on-shell and half off-shell for $I=2$S-wave two-pion system using the Bethe-Salpeter wave function inside theinteraction range in the quenched QCD. The scattering length and effectiverange are extracted from these scattering amplitudes. Quark mass dependence ofthem is investigated with the pion mass ranged in $0.52$--$0.86$~GeV. Weexamine consistency between a result by the conventional finite volume methodand our estimate, as well as the phenomenological value.

Quark mass dependence of on-shell and half off-shell scattering amplitudes from Bethe-Salpeter wave function inside the interaction range