The resonant $π^+γ\toπ^+π^0$ 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 $ππ\to πγ^\star$, 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 $m_π\approx 400$~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 $ρ\to πγ^\star$ form factor.

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