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 $\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e{)}_{\text{I}}=0.31_{-0.05}^{+0.05}$, $\mathcal{B}(D^{+}\to {\pi }^0{e}^{+}{\nu }_e{)}_{\text{I}}=0.39_{-0.06}^{+0.06}$, $\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e{)}_{\text{II}}=0.27_{-0.03}^{+0.05}$, $\mathcal{B}(D^{+}\to {\pi }^0{e}^{+}{\nu }_e{)}_{\text{II}}=0.34_{-0.04}^{+0.06}$, 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.

Comments: 11 pages, 6 figures, accepted for publication in Nucl.Phys.A