Resonant π+γ →π+π0 Amplitude from Quantum Chromodynamics

We present the first ab initio calculation of a radiative transition of a hadronic resonance within quantum chromodynamics (QCD). We compute the amplitude for π π →π γ^⋆, as a function of the energy of the π π pair and the virtuality of the photon, in the kinematic regime where π π 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 →π γ^⋆ form factor.