Ds→f0(980) form factors and the Ds+→(f0(980)→)ππSI=0e+νe decay from light-cone sum rules

Abstract

In this paper we revisit $D_s\to f_0(980)$ form factors from the light-cone sum rules based on the $\overline{q}q$ picture of $f_0(980)$. The main motivation of this study is the decay width of $D_s^{+}\to {\left[\pi ,\pi \right]}_S^{\text{I}=0}{e}^{+}{\nu }_e$ measured recently by BESIII collaboration and the $D_s\to f_0(980)$ form factor extracted under the resonant model, here the subscript S and superscript $\text{I}=0$ indicate the S-wave isoscalar dipion system. Our result of the differential width of $D_s^{+}\to f_0(980)(\to {\left[\pi ,\pi \right]}_S^{\text{I}=0})e^{+}{\nu }_e$ decay obtained under the narrow width approximation is lower than the data, the result obtained under the resonant Flatté model is consistent with the data, indicating a sizable mixing $\sim {20}^{\circ }$ between $\overline{s}s$ and $\overline{u}u+\overline{d}d$ of $f_0$. In order to get a model independent prediction, we suggest to calculate $D_s\to {\left[\pi ,\pi \right]}^{\text{I}=0}$ form factors with the isoscalar dipion light-cone distribution amplitudes. Our calculation of $D_s\to {\left[\pi ,\pi \right]}^{\text{I}=0}$ form factors is carried out at leading twist level due to the finite knowledge of dipion system, the differential width shows a moderate evolution in contrast to that obtained from the narrow width approximation and the Flatté model. Since the $D_s\to f_0(980)$ form factors is dominated by the twist three contribution, further measurements on four-body semileptonic charm decays would help us to study the dimeson light-cone distribution amplitudes, especially for the subleading twist one.