Lattice QCD calculations of radiative transitions between
hadrons have in the past been limited to processes of hadrons stable under the
strong interaction. Recently developed methods for $1\to2$ transition matrix
elements in a finite volume now enable the determination of radiative decay
rates of strongly unstable particles. Our lattice QCD study focuses on the
process $\pi \pi \to \pi \gamma^{\ast}$, where the $\rho$ meson is present as
an enhancement in the cross-section. We use $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV and a lattice size of
approximately $3.6$ fm. The required $2$-point and $3$-point correlation
functions are constructed from a set of forward, sequential and stochastic
light quark propagators. In addition to determining the $\rho$ meson resonance
parameters via the Lüscher method, the scattering phase shift is used in
conjunction with the $1\to2$ transition matrix element formalism of Brice\~no,
Hansen and Walker-Loud \cite{Briceno:2014uqa} to compute the
$\pi\pi\to\pi\gamma^{\ast}$ amplitude at several values of the momentum
transfer and $\pi\pi$ invariant mass.