QCD sum rules for parameters of the $B$-meson distribution amplitudes

We obtain new estimates for the parameters $\lambda_{E}^2$, $\lambda_H^2$ and their ratio $\mathcal{R} = \lambda_{E}^2/\lambda_H^2$, which appear in the second moments of the $B$-meson light-cone distribution amplitudes defined in the heavy-quark effective field theory. The computation is based on two-point QCD sum rules for the diagonal correlation function and includes all contributions up to mass dimension seven in the operator-product expansion. For the ratio we get $\mathcal{R} = (0.1 \pm 0.1)$ with $\lambda_H^2 = (0.15 \pm 0.05) \, \text{GeV}^2$ and $\lambda_E^2 = (0.01 \pm 0.01) \, \text{GeV}^2$.