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Lattice QCD calculations of radiative transitions between hadrons have in thepast been limited to processes of hadrons stable under the strong interaction.Recently developed methods for $1\to2$ transition matrix elements in a finitevolume now enable the determination of radiative decay rates of stronglyunstable particles. Our lattice QCD study focuses on the process $\pi \pi \to\pi \gamma^{*}$, where the $\rho$ meson is present as an enhancement in thecross-section. We use $2+1$ flavors of clover fermions at a pion mass ofapproximately $320$ MeV and a lattice size of approximately $3.6$ fm. Therequired $2$-point and $3$-point correlation functions are constructed from aset of forward, sequential and stochastic light quark propagators. In additionto determining the $\rho$ meson resonance parameters via the L\"uscher method,the scattering phase shift is used in conjunction with the $1\to2$ transitionmatrix element formalism of Brice\~no, Hansen and Walker-Loud to compute the$\pi\pi\to\pi\gamma^{*}$ amplitude at several values of the momentum transferand $\pi\pi$ invariant mass.

A study of the radiative transition $\pi \pi \to \pi \gamma^{*}$ with lattice QCD