Pion-pion scattering amplitudes and timelike pion form factor from Nf=2+1 Lattice QCD

Abstract

We study isovector pion-pion scattering and extract the electromagnetic pion form factor in the timelike region from Nf = 2 + 1 Lattice QCD ensembles at a single lattice spacing and two pion masses mπ = 200MeV and mπ = 280MeV, generated through the Coordinated Lattice Simulations (CLS) effort. The spectrum of QCD in a finite box is extracted from temporal correlation functions of suitably chosen single-meson and two-pion interpolating operators. The required correlation functions are efficiently computed using the stochastic LapH method, facilitating the present analysis in large spatial volumes with the bigger of the two spatial extents roughly L ~ 4.1 fm. We discuss how the calculation of two-point correlation functions involving the renormalized O(a)-improved isovector vector current can be achieved in the stochastic LapH framework. The finite-volume two-pion spectrum is mapped to the infinite-volume pion-pion scattering amplitude using the Lüscher method, and we extract the Breit-Wigner parameters of the lowest-lying vector resonance, the p meson. We implement the variant of the Lellouch-Lüscher method first suggested by Meyer, which enables the extraction of the energy dependence of the electromagnetic pion form factor at a number of discrete points in the timelike region. This form factor shows an enhancement around the mass of the p and dominates the QCD contribution to the anomalous magnetic moment of the muon through hadronic vacuum polarization at low energies, and is hence of phenomenological interest. In the isospin-symmetric setup employed by us, we observe deviations of the extracted form factor from the Gounaris-Sakurai parametrization, but an assessment of cutoff effects and the pion-mass dependence is needed before firm conclusion can be drawn.