  In this talk I report on the results of a recent calculation of the \alpha_s
corrections to a three-point correlation function at the three-loop level in
QCD perturbation theory, which allows one to extract the matrix element of B^0
-\bar B^0 mixing with next-to-leading order accuracy. The evaluation of mixing
parameter at NLO allows for a consistent analysis of B^0 -\bar B^0 mixing since
the coefficient functions of the effective Hamiltonian for this process are
known with the necessary accuracy.
