  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 $\lambda_E^2 = (0.01 \pm
0.01) \, \text{GeV}^2$ and $\lambda_H^2 = (0.11 \pm 0.02) \, \text{GeV}^2$.
