The resonant π+γ → π+π⁰ amplitude from Quantum Chromodynamics

Abstract

We present the first ab initio calculation of a radiative transition of a hadronic resonance within Quantum Chromodynamics (QCD). We compute the amplitude for ππ → πγ* , as a function of the energy of the ππ pair and the virtuality of the photon, in the kinematic regime where ππ couples strongly to the unstable ρ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to m_π ≈ 400 MeV. We obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the ρ pole and identify from its residue the ρ → πγ* form-factor.