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 $\xi$, needed to relate the oscillation frequency of $B^0_s$-$\bar{ B}^0_s$ mixing to the poorly known CKM element $V_{ td}$. 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 $\xi$, from the conventional $1.15\pm0.05$ to $\xi=1.32\pm0.10$.
Categories: hep-ph hep-lat