Remark on the Theoretical Uncertainty in $B^0$-$\bar{B}^0$ Mixing

We re-examine the theoretical uncertainty in the Standard Model expression for $B^0$-$\bar{B}^0$ mixing. We focus on lattice calculations of the ratio $ξ$, needed to relate the oscillation frequency of $B^0_s$-$\bar{B}^0_s$ mixing to $V_{td}$. We replace the usual linear chiral extrapolation with one that includes the logarithm that appears in chiral perturbation theory. We find a significant shift in the ratio $ξ$, from the conventional $1.15\pm0.05$ to $ξ=1.32\pm0.10$.

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