  We present the first QCD spectral sum rules analysis of the SU(3) breaking
parameter \xi and an improved estimate of the renormalization group invariant
(RGI) bag constant \hat{B}_{B_q} both entering into the B^0_{d,s} -
\bar{B}^0_{d,s} mass-differences. The averages of the results from the Laplace
and moment sum rules to order \alpha_s are f_B\sqrt{\hat B_B} \simeq (247 \pm
59) MeV and \xi \equiv f_{B_s} \sqrt{\hat B_{B_s}} / f_{B} \sqrt{\hat B_{B}}
\simeq (1.18\pm 0.03), in units where f_\pi=130.7 MeV. Combined with the
experimental data on the mass-differences \Delta M_{d,s}, one obtains the
constraint on the CKM weak mixing angle |V_{ts}/V_{td}|^2 > 20.0 (1.1).
Alternatively, using the weak mixing angle from the analysis of the unitarity
triangle and the data on \Delta M_d, one predicts \Delta M_s=18.6 (2.2) ps^{-1}
in agreement with the present experimental lower bound and within the reach of
Tevatron 2.
