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

TL;DR

This study uses lattice QCD to analyze the radiative decay of the $K^*$ resonance and the $ ext{γ}K o K ext{π}$ amplitude, highlighting the importance of elastic scattering effects and providing a first-principles calculation of the transition form factor.

Contribution

First lattice QCD calculation of the $ ext{γ}K o K ext{π}$ process including the $K^*$ resonance, accounting for elastic scattering in the finite-volume to infinite-volume transition.

Findings

Determined the transition amplitude at 128 kinematic points.

Showed the necessity of including $S$--wave elastic scattering effects.

Extracted the $K^{*+} o K^+ ext{γ}$ form factor and compared with experimental data.

Abstract

We present the first calculation in lattice QCD of the process $\gamma K \to K\pi$ 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 $(Q^2, E_{K\pi})$ 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 $K^*$ resonance pole, we obtain the $K^{*+} \to K^+ \gamma$ transition form-factor, and compare the $Q^2=0$ value to the corresponding value extracted from the experimental partial-decay width.