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Abstract

In this paper, we investigate the semileptonic decay $D \to a_0(1450)\ell \nu_{\ell}$ with $\ell=(e, \mu)$ using QCD light-cone sum rules. For the scalar meson $a_0(1450)$, we treat it as a $q\bar{q}$ state and construct two distributed distribution schemes based on the light-cone harmonic oscillator model, then present their moments $\langle\xi^{n}_{2;a_0}\rangle |_{\mu}$ and Gegenbauer moments $a_{n;a_0}(\mu)$ at $\mu_0=1~\mathrm{GeV}$ and $\mu_k= 1.4~\mathrm{GeV}$ for $n=(1,3,5)$. In the large recoil region, we obtain the transition form factors (TFFs): $f_+^{D\to a_0({\rm S1})}(0)=0.769_{-0.114}^{+0.103}$, $f_+^{D \to a_0 ({\rm S2})}(0)=0.738_{-0.108}^{+0.106}$ and $f_{-}^{D \to a_0}(0)=0.688_{-0.086}^{+0.081}$. A simplified $z(q^2, t)$-series expansion parametrization is used to extrapolate the TFFs to the full physical $q^2$-region. By taking $q^2=10^{-5} ~\mathrm{GeV}^2$, we calculate the angular distribution of the differential decay width ${d\Gamma}/{d\cos\theta}$ over the range $\cos\theta_{\ell}\in [-1,1]$. Subsequently, we obtained differential decay widths and branching ratios for $D^0 \to a_0(1450)^- \ell^+ \nu_{\ell}$ and $D^- \to a_0(1450)^0 \ell^- \bar{\nu}_{\ell}$, with the branching ratios being of order $10^{-6}$. Finally, we analyze the three angular observables for the semileptonic decay process $D^- \to a_0(1450)^0 \ell^- \bar{\nu}_{\ell}$ with $\ell=(e,\mu)$, the forward-backward asymmetry $\mathcal{A}_{\rm{FB}}$, lepton polarization asymmetry $\mathcal{A}_{\lambda_\ell}$ and the $q^2$-differential flat term $\mathcal{F}_{\mathrm{H}}$.