Anatomy of f₀(980) via the signal $ππ$ state in semileptonic Dₛ decays

The nature of light scalar mesons remains an unsolved puzzle in hadron physics, complicated by their large widths and controversial partonic structure. We propose to resolve this problem in a comprehensive study of isoscalar two-pion state ([ππ]S), the signal channel of f₀(980), through its light-cone distribution amplitudes ($2π$DAs). A key finding is that charge parity forces the twist-3 $2π$DAs to be asymmetric in the momentum fractions of the quark and antiquark. This property stands in stark contrast to the symmetric twist-3 distribution amplitudes of a conventional f₀(980) meson, as derived from QCD sum rules in the narrow-width approximation. We calculate the Dₛ → [ππ]S transition form factors and discover a significant cancellation between the twist-2 and twist-3 contributions. This leads to a QCD prediction for the Dₛ⁺ → [ππ]S e⁺ νₑ decay width that is significantly smaller than the experimental measurement. Our results indicate that the lowest Fock state is not the dominant configuration of the isoscalar two-pion state produced in charm decays, in contrast to the case in B decays. Future precision measurements can constrain the high-twist $2π$DAs associated with multi-particle Fock states, offering a new path to elucidate the structure of the light scalar mesons.