We compute the $I=2$ $\pi \pi$ scattering length at pion masses of $m_{\pi }\sim 294$, 348, and 484 MeV in fully-dynamical lattice QCD using Lüscher’s finite-volume method. The calculation is performed with domain-wall valence-quark propagators on asqtad-improved MILC configurations with staggered sea quarks at a single lattice spacing, $b\sim 0.125\mathrm{fm}$. Chiral perturbation theory is used to perform the extrapolation of the scattering length from lattice quark masses down to the physical value, and we find $m_{\pi }{a}_2=-0.0426\pm 0.0006\pm 0.0003\pm 0.0018$, in good agreement with experiment. The $I=2$ $\pi \pi$ scattering phase shift is calculated to be $\delta =-43\pm 10\pm 5°$ at $|\mathbf{p}|\sim 544\mathrm{MeV}$ for $m_{\pi }\sim 484\mathrm{MeV}$.

• Received 1 July 2005

DOI:https://doi.org/10.1103/PhysRevD.73.054503