The πγ → ππ transition and the ρ radiative decay width from lattice QCD

We report a lattice QCD determination of the πγ → ππ transition amplitude for the P-wave, I = 1 two-pion final state, as a function of the photon virtuality and ππ invariant mass. The calculation was performed with 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV, on a 32³ × 96 lattice with L ≈ 3.6 fm. We construct the necessary correlation functions using a combination of smeared forward, sequential and stochastic propagators, and determine the finite-volume matrix elements for all ππ momenta up to |P^~| = ^√3²_L^π and all associated irreducible representations. In the mapping of the finite-volume to infinite-volume matrix elements using the Lellouch-Lüscher factor, we consider two different parametrizations of the ππ scattering phase shift. We fit the q² and s dependence of the infinite-volume transition amplitude in a model-independent way using series expansions, and compare multiple different truncations of this series. Through analytic continuation to the ρ resonance pole, we also determine the πγ → ρ resonant transition form factor and the ρ meson photocoupling, and obtain |Gρπγ| = 0.0802(32)(20).