  We compute perturbative matching coefficients to the Heavy Quark Effective
Theory representation for the QCD effective local $\Delta B=2$ Hamiltonian that
determines the mass difference in $B^0-\bar{B}^0$ system of states. We report
on the results at NNLO in the strong coupling constant for matching
coefficients of two physical operators in HQET. Our results provide the firm
confirmation that the recent NLO sum rules analysis of the bag parameter $B_q$
is stable with regard of inclusion of higher order radiative corrections. As a
by-product of our calculation we give a fully analytical solution for the one
loop QCD-to-HQET matching problem: we present the explicit formulas for the
renormalization of four quark operators of the full bases in both QCD and HQET
and the expressions for matching coefficients in a closed form.
