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QSSR estimate of the $B_B$ parameter at next-to-leading order

We compute the leading $α_s$ corrections to the two-point correlator of the $O_{ΔB=2}$ operator which controls the $B^0 \bar B^0$ mixing. Using this result within the QCD spectral sum rules approach and some phenomenologically reasonable assumptions in the parametrization of the spectral function, we conclude that the vacuum saturation values $B_B\simeq B_{B^*}\simeq 1$ are satisfied within 15\%.