B^0_{d,s} - \bar{B}^0_{d,s} mass-differences from QCD spectral sum rules

Abstract

We present the first QCD spectral sum rules analysis of the SU(3) breaking parameter ξand 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 α_s are f_B\sqrt{\hat B_B} \simeq (247 \pm 59) MeV and ξ\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_π=130.7 MeV. Combined with the experimental data on the mass-differences ΔM_{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 ΔM_d, one predicts ΔM_s=18.6 (2.2) ps^{-1} in agreement with the present experimental lower bound and within the reach of Tevatron 2.