Computation of $\bar{\Lambda }$ and ${\lambda }_1$ with Lattice QCD

Abstract

We pursue a new method, based on lattice QCD, for determining the quantities $\bar{\Lambda }$, ${\lambda }_1$, and ${\lambda }_2$ of heavy-quark effective theory. We combine Monte Carlo data for the meson mass spectrum with perturbative calculations of the short-distance behavior, to extract $\bar{\Lambda }$ and ${\lambda }_1$ from a formula from HQET. Taking into account uncertainties from fitting the mass dependence and from taking the continuum limit, we find $\bar{\Lambda }=0.68{+0.02}_{-0.12}\text{GeV}$ and ${\lambda }_1=-(0.45\pm 0.12){\text{GeV}}^2$ in the quenched approximation.

Comments: 7 pp, 4 figs (in v2 Fig. 4 now shows Ref. 13, as advertised); in v3 error in BLM scale is corrected