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In this paper we revisit $D_s \to f_0$ form factors from the light-cone sumrules with the light meson light-cone distribution amplitudes. The mainmotivation 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 collaborationand the $D_s \to f_0$ form factor extracted under the intermediate resonantmodel. 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 widthapproximation is a litter bit lower than the data, the result obtained underthe resonant Flatt\'e model is in consistent with the data while shows a litterbit 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 independentprediction, we suggest to calculate $D_s \to \left[ \pi\pi \right]_{\rm S}$form factors with the isoscalar scalar dipion light-cone distributionamplitudes. Our calculation of $D_s \to \left[ \pi\pi \right]_{\rm S}$ formfactors is carried out at the leading twist level due to the finite knowledgeof dipion system, the result of differential width shows a moderate evolutionin contrast to that obtained from the narrow width approximation and theFlatt\'e model, revealing a bright prospect to study the four-body leptonicdecays of heavy mesons with the dimeson light-cone distribution amplitudes.

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