The $\pi\pi\to\pi\gamma^\star$ amplitude and the resonant   $\rho\to\pi\gamma^\star$ transition from lattice QCD
  We present a determination of the $P$-wave $\pi\pi\to\pi\gamma^\star$ 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-L\"uscher 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 $\rho$ 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 $\rho\to \pi \gamma^\star$ transition form factor. This calculation, at $m_\pi\approx 400$ MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD. 
Ra\'ul A. Brice\~no, Jozef J. Dudek, Robert G. Edwards, Christian J.   Shultz, Christopher E. Thomas, David J. Wilson
hep-ph hep-lat