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

Abstract

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 ${\lambda }_E^2=(0.01\pm 0.01){\text{GeV}}^2$.

Comments: 31 pages, 12 figures; corrected format, included source files, improved numerical analysis