I = 1 and I = 2 π–π scattering phase shifts from Nf = 2 + 1 lattice QCD

The I=1p-wave and I=2s-wave elastic π–π   scattering amplitudes are calculated from a first-principles lattice QCD simulation using a single ensemble of gauge field configurations with Nf=2+1Nf=2+1 dynamical flavors of anisotropic clover-improved Wilson fermions. This ensemble has a large spatial volume V=(3.7 fm)3V=(3.7 fm)3, pion mass mπ=230 MeVmπ=230 MeV, and spatial lattice spacing as=0.11 fmas=0.11 fm. Calculation of the necessary temporal correlation matrices is efficiently performed using the stochastic LapH method, while the large volume enables an improved energy resolution compared to previous work. For this single ensemble we obtain mρ/mπ=3.350(24)mρ/mπ=3.350(24), gρππ=5.99(26)gρππ=5.99(26), and a clear signal for the I=2s-wave. The success of the stochastic LapH method in this proof-of-principle large-volume calculation paves the way for quantitative study of the lattice spacing effects and quark mass dependence of scattering amplitudes using state-of-the-art ensembles.