In the paper, we have carried out research on the $D\to\pi$ decay process. We employ two different currents to study the $D\to\pi$ transition form factors (TFFs) by using the light-cone sum rule within the framework of chiral current approach. Firstly, we follow the right-handed and left-handed currents for the correlators to present the expression of the vector form factors upto next-leading-order and leading-order accuracy, respectively. Here the twist-2 and twist-3 light-cone distribution amplitudes are constructed by the light-cone harmonic oscillator model. After exploring the TFFs into the whole physical $q^2$-region with the simplified $z$-series expansion, we obtain the branching fractions $\mathcal{ B}(D^0\to \pi^-e^+\nu_e)_{ \text{ I}} = 0.31_{ -0.05}^{ +0.05}$, $\mathcal{ B}(D^+\to \pi^0e^+\nu_e)_{ \text{ I}} = 0.39_{ -0.06}^{ +0.06}$, $\mathcal{ B}(D^0\to \pi^-e^+\nu_e)_{ \text{ II}} = 0.27_{ -0.03}^{ +0.05}$, $\mathcal{ B}(D^+\to \pi^0e^+\nu_e)_{ \text{ II}} = 0.34_{ -0.04}^{ +0.06}$, and extract the CKM matrix element $|V_{ cd}|_{ \text{ I}} = ( 0.21^{ +0.02}_{ -0.02} )\times 10^{ -2}$ as well as $|V_{ cd}|_{ \text{ II}} = ( 0.23^{ +0.02}_{ -0.02}) \times 10^{ -2}$. To verify the credibility of our calculations, these results are further compared with existing findings in the literature, showing good agreement within uncertainties.
Categories: hep-ph