Matching of heavy-light flavour currents between HQET at order 1/m and QCD: I. Strategy and tree-level study

We present a strategy how to match the full set of components of the heavy-light axial and vector currents in Heavy Quark Effective Theory (HQET), up to and including 1/mh-corrections, to QCD. While the ultimate goal is to apply these matching conditions non-perturbatively, in this study we first have implemented them at tree-level, in order to find good choices of the matching observables with small \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{O}\left( {{1 \left/ {{m_{\mathrm{h}}^2}} \right.}} \right) $\end{document} contributions. They can later be employed in the non-perturbative matching procedure which is a crucial part of precision HQET computations of semileptonic decay form factors in lattice QCD. [graphic not available: see fulltext]