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Radiative decay of the resonant $K^*$ and the $γK \to K π$ amplitude from lattice QCD

We present the first calculation in lattice QCD of the process $γK \to Kπ$ in which the narrow $K^*$ 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 $(Q^2, E_{Kπ})$ plane, and find suitable resonant scattering descriptions. We demonstrate the need to account for $S$--wave $Kπ$ 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 $γK \to Kπ$ amplitude to the $K^*$ resonance pole, we obtain the $K^{*+} \to K^+ γ$ transition form-factor, and compare the $Q^2=0$ value to the corresponding value extracted from the experimental partial-decay width.