Reviving the energy-dependent partonic structure of f 0 ( 980 ) via two-pion distribution amplitudes

We present a novel framework for analyzing four-body semileptonic weak decays, performing the first high-twist analysis of the D s → [ π π ] S form factors using light cone distribution amplitudes for the isoscalar two-pion state ( 2 π DAs ). It is motivated by persistent tensions between phenomenological cascade analyses and QCD-based interpretations of the partonic structure of the f 0 meson. Our study reveals that the twist-three 2 π 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-two and twist-three 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 q ¯ state, reviving the energy-dependent partonic structures of light scalar mesons by highlighting a fundamental limitation of the single-meson light cone distribution amplitude approach in describing such complex systems.