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We consider the effects of a non-vanishing strange-quark mass in the determination of the full basis of dimension six matrix elements for $B_{s}$ mixing, in particular we get for the ratio of the $V-A$ Bag parameter in the $B_s$ and $B_d$ system: $\overline{B}^s_{Q_1} / \overline{B}^d_{Q_1} = 0.987^{+0.007}_{-0.009}$.
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