  The pi+pi+ s-wave scattering phase-shift is determined below the inelastic
threshold using Lattice QCD. Calculations were performed at a pion mass of
m_pi~390 MeV with an anisotropic n_f=2+1 clover fermion discretization in four
lattice volumes, with spatial extent L~2.0, 2.5, 3.0 and 3.9 fm, and with a
lattice spacing of b_s~0.123 fm in the spatial direction and b_t b_s/3.5 in the
time direction. The phase-shift is determined from the energy-eigenvalues of
pi+pi+ systems with both zero and non-zero total momentum in the lattice volume
using Luscher's method. Our calculations are precise enough to allow for a
determination of the threshold scattering parameters, the scattering length a,
the effective range r, and the shape-parameter P, in this channel and to
examine the prediction of two-flavor chiral perturbation theory: m_pi^2 a r =
3+O(m_pi^2/Lambda_chi^2). Chiral perturbation theory is used, with the Lattice
QCD results as input, to predict the scattering phase-shift (and threshold
parameters) at the physical pion mass. Our results are consistent with
determinations from the Roy equations and with the existing experimental phase
shift data.
