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Within the QCD light-cone sum rule (LCSR) approach, we investigate thetransition form factors of $D\rightarrow a_0(980)$ up to the twist-3 light-conedistribution amplitudes (LCDAs) of the scalar meson $a_0(980)$ in the two-quarkpicture. Using these form factors, we calculate the differential decay widthsand branching ratios of the $D\rightarrow a_0(980) e^+ \nu_e$ semileptonicdecays. We obtain ${\mathcal B}(D^0\rightarrow a_0^- (980) e^+\nu_e)=(4.08^{+1.37}_{-1.22})\times 10^{-4}$ and ${\mathcal B}(D^+\rightarrowa_0^0 (980) e^+ \nu_e)=(5.40^{+1.78}_{-1.59})\times 10^{-4}$. The results aresensitive to the $a_0(980)$ inner structure. These decays can be searched forat BESIII experiment, and any experimental observations will be useful toidentify internal quark contents of the $a_0(980)$ meson, which will shed lighton understanding theoretical models.

Study of $\mathbf{\boldsymbol{D \rightarrow a_0 (980) e^+ \nu_e}}$ decay in the light-cone sum rules approach