Footprint in fitting \(B\rightarrow D\) vector form factor and determination for D-meson leading-twist LCDA

In this paper, we fit the \(B\rightarrow D\) vector transition form factor (TFF) by using the data measured by BABAR and Belle Collaborations within Monte Carlo (MC) method. Meanwhile, the \(B\rightarrow D\) 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 \(B\rightarrow D\) TFF \(f_{+}^{BD}(q^2)\) at the large recoil region is \(f_{+}^{BD}(0)=0.648_{-0.063}^{+0.067}\), 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 \(B\rightarrow D\ell ^+\nu _{\ell }\), which lead to the results \({\mathcal {B}}(B^0\rightarrow D^-\ell ^+\nu _{\ell }) =(2.10_{-0.38}^{+0.44})\times 10^{-2}\) and \({\mathcal {B}}(B^+\rightarrow {\bar{D}}^0\ell ^+\nu _{\ell }) =(2.26_{-0.41}^{+0.48})\times 10^{-2}\). Finally, we predict the CKM matrix element with two scenarios \(|V_{cb}|_{\textrm{SR}}=41.55_{-4.50}^{+4.91}\times 10^{-3}\) and \(|V_{cb} |_{\textrm{MC}}=41.47_{-2.66}^{+2.55 }\times 10^{-3}\) from \(B^0\rightarrow D^-\ell ^+\nu _{\ell }\), \(|V_{cb}|_{\textrm{SR}}=40.54_{-3.80}^{+4.33}\times 10^{-3}\) and \(|V_{cb} |_{\textrm{MC}}=40.46_{-1.38}^{+1.40}\times 10^{-3}\) from \(B^+\rightarrow {\bar{D}}^0\ell ^+\nu _{\ell }\) which are in good agreement with theoretical and experimental predictions.