Constraining inverse moment of $B$-meson distribution amplitude using Lattice QCD data

We constrain the inverse moment of the $B$-meson light-cone distribution amplitude (LCDA), $\lambda_B$ in heavy quark effective theory, using form factor estimates from Lattice QCD collaboration. The estimation of the parameter $\lambda_B$ has, until now, relied solely on QCD sum rule methods and deals with significant uncertainty. In this work, we express the form factors for the $B \to K$ channel, calculated within the light-cone sum rule (LCSR) approach, in terms of the $B$-meson LCDAs. By incorporating recent Lattice results from the HPQCD collaboration for the $B \to K$ form factors at zero momentum transfer ($q^2$ = 0), we impose constraints on this parameter. Consequently, we achieve a twofold reduction in uncertainty compared to the QCD sum rule estimate, yielding $\lambda_B=338\pm 68$ MeV, when the $B$-meson LCDAs are expressed in the Exponential model. Additionally, we compare the form factor predictions, using the constrained $\lambda_B$ value, with the earlier analyses for other channels as well, such as $B\to \pi$ and $B \to D$.