With the ongoing experimental interest in exploring the excited hadron spectrum, evaluations of the matrix elements describing the formation and decay of such states via radiative processes provide us with an important connection between theory and experiment. In particular, determinations obtained via the lattice allow for a direct comparison of QCD expectation with experimental observation. Here we present the first light-quark determination of the $\rho \to \pi \gamma$ transition form factor from lattice QCD using dynamical quarks. Using the PACS-CS $2+1$ flavor QCD ensembles we are able to obtain results across a range of masses, to the near physical value of $m_{\pi }=156\mathrm{MeV}$. An important aspect of our approach is the use of variational methods to isolate the desired QCD eigenstate. For low-lying states, such techniques facilitate the removal of excited state contributions. In principle, the method enables one to consider arbitrary eigenstates. We find our results are in accord with the nonrelativistic quark model for heavy masses. In moving towards the light-quark regime we observe an interesting quark mass dependence, contrary to the quark model expectation. Comparison of our light-quark result with experimental determinations highlights a significant discrepancy suggesting that disconnected sea-quark loop contributions may play a significant role in fully describing this process.

• Received 13 May 2015

DOI:https://doi.org/10.1103/PhysRevD.92.034513