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

TL;DR

This paper revisits the theoretical uncertainties in $B^0$-$ar{B}^0$ mixing within the Standard Model, highlighting how improved lattice calculations and chiral extrapolation methods significantly alter key ratio estimates.

Contribution

It introduces a modified chiral extrapolation method that incorporates logarithmic terms, leading to a substantial revision of the ratio $\xi$ used in mixing analyses.

Findings

Revised $\xi$ ratio from 1.15±0.05 to 1.32±0.10

Significant shift due to improved chiral extrapolation

Enhanced understanding of theoretical uncertainties in 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 $B^0_s$-$\bar{B}^0_s$ 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 $\xi$, from the conventional $1.15\pm0.05$ to $\xi=1.32\pm0.10$.