We present an update on our lattice QCD calculation of the radiative process $\pi \pi \to \pi \gamma^{}$, which is enhanced by the presence of the $\rho$ resonance. The calculations were performed with 2+1 clover fermions at $m_\pi \approx 320$ MeV and $L$ approx $3.6$ fm, and we have now analyzed the data from the full set of gauge configurations. Using the results of our recent high-precision calculation of the pi pi scattering phase shift on the same ensemble together with the $1 \to 2$ transition matrix element formalism of Brice\~no, Hansen and Walker-Loud, we compute the $\pi \pi \to \pi \gamma^{}$ amplitude at several interesting values of $q^2$ and $\pi \pi$ invariant mass near the $\rho$ resonance.

Hadron Structure