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

Abstract

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 $B_s^0$-${\bar{B}}_s^0$ 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 $1.15\pm 0.05$ to $\xi =1.32\pm 0.10$.

Comments: 10 pp., 4 figs; text on some other papers clarified, reference added