Reviving the energy-dependent partonic structure of $f_0(980)$ via two-pion distribution amplitudes

Abstract

We present a novel framework for analyzing four-body semileptonic weak decays, performing the first high-twist analysis of the $D_s \to \left[ \pi\pi \right]_{\rm S}$ form factors using light-cone distribution amplitudes for the isoscalar two-pion state ($2\pi$DAs). It is motivated by persistent tensions between phenomenological cascade analyses and QCD-based interpretations of the partonic structure of $f_0$ meson. Our study reveals that the twist-3 $2\pi$DAs incorporate an asymmetry in the partial-wave expansion, a feature absent in single $f_0$ distribution amplitudes, that drives a substantial cancellation between twist-2 and twist-3 contributions to the form factors. As a result, the predicted decay rate falls significantly below the experimental value. These findings indicate that the isoscalar two-pion system near the charm scale is not primarily a $q{\bar q}$ state, reviving the energy-dependent partonic structures of light scalar mesons by highlighting a fundamental limitation of the single-meson LCDA approach in describing such complex systems.