Empirical determination of the kaon distribution amplitude

Abstract

We propose a data-driven approach to extract the kaon leading-twist distribution amplitude (DA) from empirical information on the ratio of the neutral-to-charged kaon electromagnetic form factors, R K . Our study employs a two-parameter representation of the DA at ζ = 2 GeV , designed to capture the expected broadening and asymmetry of the distribution, as well as the soft endpoint behavior predicted by quantum chromodynamics (QCD). Our leading-order analysis of the latest experimental measurements of R K reveals that the extracted DA exhibits a somewhat significant skewness, with the first symmetric moment being approximately ⟨ 1 − 2 x ⟩ K = 0.082 ( 7 ) . On the other hand, the broadness and general shape of the produced distributions show a reasonable consistency with contemporary lattice and continuum QCD analyses. These findings highlight the importance of accurately determining the profile of the DA, especially the skewness and its relation to S U F ( 3 ) flavor symmetry breaking, as well as the inclusion of higher-order effects in the hard-scattering kernels for analyzing data at experimentally accessible scales.