  We compute the perturbative corrections to the HQET sum rules for the matrix
element of the \Delta B=2 operator that determines the mass shift of $B^0$,
$\bar{B}^0$ states. Technically, we obtain analytically the non-factorizable
contributions at order $\alpha_s$ to the bag parameter that first appear at the
three-loop level. Together with the known non-perturbative corrections due to
vacuum condensates and $1/m_b$ corrections, the full next-to-leading order
result is now available. We present a numerical value for the renormalization
group invariant bag parameter that is phenomenologically relevant and discuss
comparison with recent lattice determinations.
