The rho radiative decay width from lattice QCD

Pion photoproduction constitutes a prototype process, which allows for the study of the electro-weak decay of a QCD-unstable state, the $\rho$ resonance. It is also the most straightforward process to investigate such ( resonant ) transition matrix elements in lattice QCD. We performed a lattice calculation of the process $\pi\pi \to \rho \to \pi\gamma$, at presently the lightest pion mass of 317 MeV and in a large box of size (3.6 fm)$^3$. In addition to outlining the method for our calculation, we give account of our analysis of systematic uncertainties, with focus on parametrization dependence of the $P-$wave phase shift and the analytic continuation of our lattice data to the $\rho$ resonance pole to extract the coupling $|G_{\rho \pi \gamma} | = 0.0802\,(38)$.