$D_s \to f_0$ form factors and the $D_s^+ \to \left[ \pi\pi \right]_{\rm S} e^+ \nu_e$ decay from light-cone sum rules

TL;DR

This paper calculates $D_s o f_0$ form factors using light-cone sum rules to better understand the decay $D_s^+ o [\pi\pi]_S e^+ u_e$, comparing models with experimental data and proposing a model-independent approach.

Contribution

It introduces a calculation of $D_s o [\pi\pi]_S$ form factors using isoscalar scalar dipion light-cone distribution amplitudes, advancing the theoretical understanding of these decays.

Findings

The differential decay width under the narrow width approximation is slightly below experimental data.

The Flatté model results are consistent with data but slightly larger, indicating a 20-degree mixing angle.

The model-independent prediction shows moderate evolution, promising for future studies of four-body heavy meson decays.

Abstract

In this paper we revisit $D_s \to f_0$ form factors from the light-cone sum rules with the light meson light-cone distribution amplitudes. The main motivation of this study is the differential decay width of $D_s \to \left[\pi\pi \right]_{\rm S} e \nu_e$ measured recently by BESIII collaboration and the $D_s \to f_0$ form factor extracted under the intermediate resonant model. Our result of the differential width of $D_s^+ \to f_0 (\to \left[ \pi\pi \right]_{\rm S}) e^+ \nu_e$ decay obtained under the narrow width approximation is a litter bit lower than the data, the result obtained under the resonant Flatt\'e model is in consistent with the data while shows a litter bit larger, indicating a sizable mixing $\sim 20\degree$ between ${\bar s}s$ and ${\bar u}u+{\bar d}d$ of $f_0$. In order to obtain a model independent prediction, we suggest to calculate $D_s \to \left[ \pi\pi \right]_{\rm S}$ form factors with the isoscalar scalar dipion light-cone distribution amplitudes. Our calculation of $D_s \to \left[ \pi\pi \right]_{\rm S}$ form factors is carried out at the leading twist level due to the finite knowledge of dipion system, the result of differential width shows a moderate evolution in contrast to that obtained from the narrow width approximation and the Flatt\'e model, revealing a bright prospect to study the four-body leptonic decays of heavy mesons with the dimeson light-cone distribution amplitudes.