  The study of the CKM matrix elements with increasing precision requires a
reliable evaluation of hadronic matrix elements of axial and vector currents
which can be done with Lattice QCD. The tiniest entry, |V_{ub}|, can be
estimated independently from B to tau nu and B to pi l nu decays. The ALPHA
collaboration has undertaken the effort to evaluate non-perturbatively the
decay constant f_B and the f^+(q) form factor for q^2 close to q_{max}^2
entering these determinations. Since for the b quark m_b >> a^{-1} for
available lattice sizes, an effective description of the b quark is necessary.
HQET provides an example of the latter. As any effective theory, HQET is
predictive only when a set of parameters have been determined through a process
called matching. The non-perturbative matching procedure applied by the ALPHA
collaboration consists of 19 matching conditions needed to fix all the relevant
parameters at order 1/m_B of the HQET action and the axial and vector currents.
We present a study of one-loop corrections to two representative matching
conditions. Our results enable us to quantify the quality of the observables
used in the matching procedure.
