QCD sum rules for parameters of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-meson distribution amplitudes
Muslem Rahimi, Marcel Wald
Abstract
We obtain new estimates for the parameters ${\ensuremath{\lambda}}_{E}^{2}$, ${\ensuremath{\lambda}}_{H}^{2}$ and their ratio $\mathcal{R}={\ensuremath{\lambda}}_{E}^{2}/{\ensuremath{\lambda}}_{H}^{2}$, 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 $\mathcal{R}=(0.1\ifmmode\pm\else\textpm\fi{}0.1)$ with ${\ensuremath{\lambda}}_{H}^{2}=(0.15\ifmmode\pm\else\textpm\fi{}0.05)\text{ }\text{ }{\mathrm{GeV}}^{2}$ and ${\ensuremath{\lambda}}_{E}^{2}=(0.01\ifmmode\pm\else\textpm\fi{}0.01)\text{ }\text{ }{\mathrm{GeV}}^{2}$.