Quark mass dependence of $\gamma^{*}\pi\to\pi\pi$

Abstract

Usually the simulation of scattering processes in lattice QCD is carried out at unphysically high values of the quark masses. Hence, a method to extrapolate data obtained in lattice calculations to physical masses is needed to allow for comparison between theory and experiment. To obtain a sound extrapolation, dispersion relations and chiral perturbation theory can be invoked. While a simple combined approach known as the inverse amplitude method allows for a successful extrapolation of $\pi\pi\to\pi\pi$ data, a more complicated framework is needed for inelastic processes such as $\gamma^{*}\pi\to\pi\pi$. By employing a well-established dispersive description, the extrapolation can be performed for $\gamma^{*}\pi\to\pi\pi$ both for on-shell as well as virtual photons, the decay $\gamma^*\rightarrow\pi\pi\pi$ is also within the range of applicability. This particular process is interesting due to both its contribution to the anomalous magnetic moment of the muon and its connection to the axial anomaly.