Light-cone sum rules analysis of the semi-leptonic $D_s^{+}\to f_0(980)(\to {\pi }^{+}{\pi }^{-})e^{+}{\nu }_e$ decay incorporating $f_0(980)$ mixing state twist-2 distribution amplitudes

Abstract

The isospin-singlet scalar meson $f_0(980)$ is hypothesized to consist of two energy eigenstates, forming a mixture of $\frac{1}{\sqrt{2}}(\bar{u}u+\bar{d}d)$ and $\bar{s}s$. Building on this framework, we apply the QCD sum rules approach in the background field theory to compute the $f_0(980)$ decay constant, yielding $f_{f_0}({\mu }_0=1\text{GeV})=0.386\pm 0.009\text{GeV}$. Subsequently, we derive the first two $\xi$-moments of the leading-twist light-cone distribution amplitude ${\varphi }_{2;f_0}$. Using QCD light-cone sum rules, we then calculate the $D_s^{+}\to f_0(980)$ transition form factor (TFF) $f_{+}(q^2)$, obtaining $f_{+}(0)=0.516_{-0.024}^{+0.027}$ at the large-recoil point. We extend $f_{+}(q^2)$ to the full physical region via a simplified series expansion parameterization, enabling calculations of the differential decay widths and the branching fraction $\mathcal{B}(D_s^{+}\to f_0(980)(\to {\pi }^{+}{\pi }^{-})e^{+}{\nu }_e)=(1.783_{-0.189}^{+0.227})\times 10^{-3}$. Our theoretical predictions align well with the latest BESIII Collaboration measurements within reasonable errors.

Comments: 15 pages, 5 figures