ππ → πγ* amplitude and the resonant ρ → πγ* transition from lattice QCD

We present a determination of the P-wave pi pi -> pi gamma* transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-Luscher formalism. We determine the amplitude for a range of discrete values of the pi pi energy and virtuality of the photon and observe the expected dynamical enhancement due to the. resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the rho pole extract the rho -> pi gamma* transition form factor. This calculation, at m(pi) approximate to 400 MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.