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

Abstract

We present a model-independent framework for analyzing four-body semileptonic decays, performing the first high-twist analysis of the $D_s \to \left[ ππ\right]_{\rm S}$ form factors using isoscalar two-pion light-cone distribution amplitudes($2π$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 $2π$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.

Figures (3)

• Figure 1: Illustrative diagrams of the color transparency mechanism in $B_s \to f_0 e^+ \nu_e$ decay.
• Figure 2: Twist-2 (up) and twist-3 (low) isoscalar $2\pi$DAs at the scale $\mu=1.3 \, {\rm GeV}$, by taking momentum fraction $\zeta=0.5$.
• Figure 3: The differential width $d\Gamma/dq^2$ of $D_{(s)} \to \left[ \pi\pi \right]_{\rm S} e^+ \nu_e$ (left) and $D_s \to \left[ f_0 \to \pi\pi \right] e^+\nu_e$ decays (right).