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

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 $D_s\to {\left[\pi \pi \right]}_{\mathrm{S}}e{\nu }_e$ 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 $D_s^{+}\to f_0(\to {\left[\pi \pi \right]}_{\mathrm{S}})e^{+}{\nu }_e$ decay obtained under the narrow width approximation is a litter bit lower than the data, the result obtained under the resonant Flatté model is in consistent with the data while shows a litter bit larger, indicating a sizable mixing $\sim 20°$ 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 $D_s\to {\left[\pi \pi \right]}_{\mathrm{S}}$ form factors with the isoscalar scalar dipion light-cone distribution amplitudes. Our calculation of $D_s\to {\left[\pi \pi \right]}_{\mathrm{S}}$ 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 Flatté model, revealing a bright prospect to study the four-body leptonic decays of heavy mesons with the dimeson light-cone distribution amplitudes.

Comments: 23 pages, 14 figures, 7 tables