I=2pion scattering length with the Wilson fermion

The calculation of the $I=2\mathrm{}$ pion scattering length in quenched lattice QCD is reexamined. The calculation is carried out with the Wilson fermion action employing Lüscher’s finite size scaling method at $\beta =5.9,$ $6.1,$ and $6.3$ corresponding to the range of lattice spacing $a\simeq 0.12-0.07\mathrm{fm}.$ We obtain in the continuum limit $a_0{/m}_{\pi }=-2.09\left(35\right)\mathrm{}1/{\mathrm{GeV}}^2,$ which is consistent with the prediction of chiral perturbation theory $a_0{/m}_{\pi }=-2.265\left(51\right)1/{\mathrm{GeV}}^2.$