On one-loop corrections to matching conditions of Lattice HQET including $1/m_{B}$ terms

HQET is an effective theory for QCD with $N _{f}$ light quarks and a massive valence quark if the mass of the latter is much bigger than $\Lambda _{QCD}$. As any effective theory, HQET is predictive only when a set of parameters has been determined through a process called matching. The non-perturbative matching procedure including 1/mb terms, developped by the ALPHA collaboration, consists of 19 carefully chosen observables which are precisely computable in lattice QCD as well as in lattice HQET. The matching conditions are then a set of 19 equations which relate the QCD and HQET values of these observables. We present a study of one-loop corrections to two generic matching observables involving correlation function with an insertion of the $A_{0}$ operator. Our results enable us to quantify the quality of the relevant observables in view of the envisaged nonperturbative implementation of this matching procedure.