The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD

Abstract

The elastic I=1 p-wave ππ scattering amplitude is calculated together with the isovector timelike pion form factor using lattice QCD with Nf=2+1 dynamical quark flavors. Wilson clover ensembles generated by the Coordinated Lattice Simulations (CLS) initiative are employed at four lattice spacings down to a=0.05fm, several pion masses down to mπ=200MeV, and spatial volumes of extent L=3.1–5.5fm. The set of measurements on these ensembles, which is publicly available, enables an investigation of systematic errors due to the finite lattice spacing and spatial volume. The ππ scattering amplitude is fit on each ensemble by a Breit–Wigner resonance lineshape, while the form factor is described better by a thrice-subtracted dispersion relation than the Gounaris–Sakurai parametrization.