$B^0$-$\bar{B}^0$ mixing with Fermilab heavy quarks

Abstract

We discuss the matching procedure for heavy-light 4-quark operators using the Fermilab method for heavy quarks and staggered fermions for light quarks. These ingredients enable us to construct the continuum-limit operator needed to determine the oscillation frequency of neutral B mesons. The matching is then carried out at the one-loop level. We also present an updated preliminary result for the ratio ξ , based on calculations using the MILC Collaboration's ensembles of lattice gauge fields.

The Brown Muck of $B^0$ and $B^0_s$ Mixing: Beyond the Standard Model

“…These error estimates are made by way of comparison with our collaboration's previous SM B mixing studies [80,81], where results for errors on the mixing parameter β …”

“…Table 9.2: Systematic error budget for the hadronic mixing matrix element, O (N ) . Previous column entries are derived from previous FNAL-MILC calculations for SM B mixing [80,81].…”

“…The relative size of these effects can be estimated by considering the ratio of lattice spacings, a ≈ 0.09 fm (the finest lattice used in [80,81]) and a ≈ 0.06 fm, giving an improvement factor of ∼ terms in the chiral fit functions, as described in Sec. 8.3, finite volume errors will be incorporated in the bootstrap errors obtained from the chiral and continuum extrapolation.…”