Fixing the parameters of Lattice HQET including 1/mB terms

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