I=2 $\pi\pi$ Scattering Phase Shift with two Flavors of $O(a)$ Improved Dynamical Quarks

We present a lattice QCD calculation of phase shift including the chiral and continuum extrapolations in two-flavor QCD. The calculation is carried out for I=2 S-wave $\pi\pi$ scattering. The phase shift is evaluated for two momentum systems, the center of mass and laboratory systems, by using the finite volume method proposed by L\"uscher in the center of mass system and its extension to general systems by Rummukainen and Gottlieb. The measurements are made at three different bare couplings $\beta = 1.80$, 1.95 and 2.10 using a renormalization group improved gauge and a tadpole improved clover fermion action, and employing a set of configurations generated for hadron spectroscopy in our previous work. The illustrative values we obtain for the phase shift in the continuum limit are $\delta$(deg.) $= - 3.50(64)$, $ - 9.5(30)$ and $ - 16.9(64)$ for $\sqrt{s}({\rm GeV})$ $=0.4$, $ 0.6$ and $ 0.8$, which are consistent with experiment.