I = 2 π π S -wave scattering phase shift from lattice QCD

The π+ π+ s-wave scattering phase shift is determined below the inelastic threshold using lattice QCD. Calculations were performed at a pion mass of m π∼ 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 π+ π+ systems with both zero and nonzero total momentum in the lattice volume using Lüscher’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 π 2 a r= 3+ O (m π 2/Λ χ 2). Chiral perturbation theory is used, with the lattice QCD results as …