  We compute perturbative corrections to matching coefficients of QCD to HQET
for the matrix element of the $\Delta B=2$ operator that determines the mass
difference in $B^0-\bar{B}^0$ system of states. This involves the technical
point of choosing the operator basis in HQET, separating physical operators
from evanescent ones. We obtain an analytical result for some of the two-loop
corrections at order $\alpha_s^2$.
