Eur. Phys. J. C (2025) 85: 552
https://doi.org/10.1140/epjc/s10052-025-14275-x

Regular Article - Theoretical Physics

Footprint in fitting $B\to D$ vector form factor and determination for D-meson leading-twist LCDA

¹ Department of Physics, Guizhou Minzu University, 550025, Guiyang, People’s Republic of China
² School of Science, Chongqing University of Posts and Telecommunications, 400065, Chongqing, People’s Republic of China
³ Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing, People’s Republic of China

^a fuhb@gzmu.edu.cn

Received: 7 January 2025
Accepted: 4 May 2025
Published online: 19 May 2025

Abstract

In this paper, we fit the $B\to D$ vector transition form factor (TFF) by using the data measured by BABAR and Belle Collaborations within Monte Carlo (MC) method. Meanwhile, the $B\to D$ TFF is also calculated by using the QCD light-cone sum rules approach (LCSRs) within right-handed chiral current correlation function. In the TFF, D-meson leading-twist light-cone distribution amplitude (LCDA) is the most important non-perturbative input parameter, the precise behavior of which is mainly determined by the parameter $B_{2;D}$ in the light-cone harmonic oscillator model. Through fitting the TFF, we determine the value $B_{2;D}=0.445$. Then, we present the curve of D-meson leading-twist LCDA in comparison with other theoretical approaches. Subsequently, the $B\to D$ TFF $f_{+}^{\mathit{BD}}(q^2)$ at the large recoil region is $f_{+}^{\mathit{BD}}(0)=0.{648}_{-0.063}^{+0.067}$, which is compared in detail with theoretical estimates and experimental measurements. Furthermore, we calculated the decay width and branching fractions of the Cabibbo-favored semileptonic decays $B\to D{\ell }^{+}{\nu }_{\ell }$, which lead to the results $\mathcal{B}(B^0\to D^{-}{\ell }^{+}{\nu }_{\ell })=(2.{10}_{-0.38}^{+0.44})\times {10}^{-2}$ and $\mathcal{B}(B^{+}\to {\overline{D}}^0{\ell }^{+}{\nu }_{\ell })=(2.{26}_{-0.41}^{+0.48})\times {10}^{-2}$. Finally, we predict the CKM matrix element with two scenarios $|V_{\mathit{cb}}{|}_{\text{SR}}=41.{55}_{-4.50}^{+4.91}\times {10}^{-3}$ and $|V_{\mathit{cb}}{|}_{\text{MC}}=41.{47}_{-2.66}^{+2.55}\times {10}^{-3}$ from $B^0\to D^{-}{\ell }^{+}{\nu }_{\ell }$, $|V_{\mathit{cb}}{|}_{\text{SR}}=40.{54}_{-3.80}^{+4.33}\times {10}^{-3}$ and $|V_{\mathit{cb}}{|}_{\text{MC}}=40.{46}_{-1.38}^{+1.40}\times {10}^{-3}$ from $B^{+}\to {\overline{D}}^0{\ell }^{+}{\nu }_{\ell }$ which are in good agreement with theoretical and experimental predictions.