Probing the equivalence of chiral LCSRs in $D \to \pi e \nu_e$ decays and extraction of $|V_{cd}|$

Abstract

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.