How reliable are the HQET-sum rule predictions?

Abstract

We test the internal consistencies and the reliability of the existing estimates of the decay constant $f_B$ in the static limit, the meson-quark mass gap $\bar \Lambda$ and the kinetic energy $K$ of a heavy quark obtained from the heavy quark effective theory (HQET)-sum rules. Finite energy local duality sum rules (FESR) have also been used to fix $approximatively$ the value of the continuum energy and to study the correlations among these different parameters. Then, we deduce to two-loop accuracy: $\bl=(0.65\pm 0.05)$ GeV, $K=-(0.5 \pm 0.2)$GeV^2$, implying the value of the pole mass in HQET: $M_b= (4.61 \pm 0.05)$ GeV. By combining the results from the sum rules in HQET and in the full theory, we obtain $f_B^\infty=(1.98 \pm 0.31)f_\pi$ and the quadratic mass dependence of the pseudoscalar decay constant: $f_P\sqrt{M_P}=(0.33 \pm 0.06)$GeV$^{3/2}\als^{1/\beta_1}2}\als^{1/\beta_1 1-2\als/3\pi-1.1/M_Q +0.7/M_Q^2 .$