Probing the equivalence of chiral LCSRs in $D \to πe ν_e$ decays and extraction of $|V_{cd}|$

Abstract

In the paper, we have carried out research on the $D\toπ$ decay process. We employ two different currents to study the $D\toπ$ 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 $\mathcal{B}(D^0\to π^-e^+ν_e)_{\text{I}} = 0.31_{-0.05}^{+0.05}$, $\mathcal{B}(D^+\to π^0e^+ν_e)_{\text{I}} = 0.39_{-0.06}^{+0.06}$, $\mathcal{B}(D^0\to π^-e^+ν_e)_{\text{II}} = 0.27_{-0.03}^{+0.05}$, $\mathcal{B}(D^+\to π^0e^+ν_e)_{\text{II}} = 0.34_{-0.04}^{+0.06}$, 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.

Figures (6)

• Figure 1: The pion twist-2 LCDA at initial scale $\mu_0 = 1$ GeV. For comparison, we also include results from truncated form, LQCD RQCD:2019osh, DS model (BD and RL schemes) Chang:2013pq, and AdS/QCD model Ahmady:2018muv.
• Figure 2: The pion twist-3 LCDAs $\phi_{3;\pi}^p(x,\mu_0)$ and $\phi_{3;\pi}^\sigma(x,\mu_0)$ at initial scale $\mu_0$ that adopted in the Scheme-II. As a comparison, the truncated from, QCDSR-I Ball:1998je and QCDSR-II Braun:1989iv are also present here.
• Figure 3: The $D\to \pi$ TFF $f_+^{D\pi}(0)$ at large recoil point. As a comparison, we also present other experimental and theoretical predictions.
• Figure 4: The TFF $f_{+}^{D\pi}(q^2)$ versus $q^2$ in the whole physical region for Schemes I and II. As a comparison, we also give other experimental and theoretical predictions for comparison.
• Figure 5: The differential decay widths for $D \to \pi e\nu_e$ for schemes I and II. The result of the Belle Belle:2006idb, BESIII BESIII:2015tql, BaBar BaBar:2014xzf, and CLEO CLEO:2009svp Collaborations and the LQCD FermilabLattice:2004ncdFermilabLattice:2022gkuDiVita:2010mlb prediction are presented as a comparison.