Radiative decay of the resonant $K^{\ast }$ and the $\gamma K\to K\pi$ amplitude from lattice QCD

We present the first calculation in lattice QCD of the process $\gamma K\to K\pi$ in which the narrow $K^{\ast }$ vector resonance appears. Using a lattice on which the pion has a mass of 284 MeV, we determine the transition amplitude at 128 points in the $(Q^2,E_{K\pi })$ plane, and find suitable resonant scattering descriptions. We demonstrate the need to account for $S$–wave $K\pi$ elastic scattering when converting the finite-volume matrix elements computed in lattice QCD to the physically relevant infinite-volume matrix elements, even when we are primarily interested in the $P$–wave amplitude. Analytically continuing parameterizations of the $\gamma K\to K\pi$ amplitude to the $K^{\ast }$ resonance pole, we obtain the $K^{\ast +}\to K^{+}\gamma$ transition form-factor, and compare the $Q^2=0$ value to the corresponding value extracted from the experimental partial-decay width.