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

We report a lattice QCD determination of the pi gamma -> pi pi transition amplitude for the P-wave, I = 1 two-pion final state, as a function of the photon virtuality and pi pi invariant mass. The calculation was performed with 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV, on a 32(3) x 96 lattice with L approximate to 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 pi pi momenta up to vertical bar(P) over right arrow vertical bar = root 3 2 pi/L and all associated irreducible representations. In the mapping of the finite-volume to infinite-volume matrix elements using the Lellouch-Luscher factor, we consider two different parametrizations of the pi pi scattering phase shift. We fit the q(2) 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 rho resonance pole, we also determine the pi gamma -> rho resonant transition form factor and the rho meson photocoupling, and obtain vertical bar G(rho pi gamma)vertical bar = 0.0802(32) (20).