Empirical determination of the kaon distribution amplitude

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, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi mathvariant="script">R</a:mi> <a:mi>K</a:mi> </a:msub> </a:math> . Our study employs a two-parameter representation of the DA at <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>ζ</d:mi> <d:mo>=</d:mo> <d:mn>2</d:mn> <d:mtext> </d:mtext> <d:mtext> </d:mtext> <d:mi>GeV</d:mi> </d:math> , 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi mathvariant="script">R</f:mi> <f:mi>K</f:mi> </f:msub> </f:math> reveals that the extracted DA exhibits a somewhat significant skewness, with the first symmetric moment being approximately <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo stretchy="false">⟨</i:mo> <i:mn>1</i:mn> <i:mo>−</i:mo> <i:mn>2</i:mn> <i:mi>x</i:mi> <i:msub> <i:mo stretchy="false">⟩</i:mo> <i:mi>K</i:mi> </i:msub> <i:mo>=</i:mo> <i:mn>0.082</i:mn> <i:mo stretchy="false">(</i:mo> <i:mn>7</i:mn> <i:mo stretchy="false">)</i:mo> </i:math> . 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 <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>S</o:mi> <o:msub> <o:mi>U</o:mi> <o:mi>F</o:mi> </o:msub> <o:mo stretchy="false">(</o:mo> <o:mn>3</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> flavor symmetry breaking, as well as the inclusion of higher-order effects in the hard-scattering kernels for analyzing data at experimentally accessible scales.