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We present the first ab initio calculation of a radiative transition of ahadronic resonance within quantum chromodynamics (QCD). We compute theamplitude for $\pi\pi \to \pi\gamma^\star$, as a function of the energy of the$\pi\pi$ pair and the virtuality of the photon, in the kinematic regime where$\pi\pi$ couples strongly to the unstable $\rho$ resonance. This exploratorycalculation is performed using a lattice discretization of QCD with quarkmasses corresponding to $m_\pi \approx 400$~MeV. We obtain a description of theenergy dependence of the transition amplitude, constrained at 48 kinematicpoints, that we can analytically continue to the $\rho$ pole and identify fromits residue the $\rho \to \pi\gamma^\star$ form factor.

The resonant $\pi^+\gamma\to\pi^+\pi^0$ amplitude from Quantum Chromodynamics