Calculation of theBBparameter in the static limit

Abstract

We calculate the B B parameter, relevant for B 0 -B 0 mixing, from a lattice gauge theory simulation at β = 6.0. The bottom quarks are simulated in the static theory, the light quarks with Wilson fermions. Improved smearing functions produced by a variational technique, most, are used to reduce statistical errors and minimize excited-state contamination of the groundstate signal. We obtain B B (4.33 GeV) = 0.98−18 (systematic) which corresponds to B B = 1.40−26 (systematic) for the oneloop renormalization-scheme-independent parameter. The systematic errors include the uncertainty due to alternative (less favored) treatments of the perturbatively-calculated mixing coefficients; this uncertainty is at least as large as residual differences between Wilson-static and clover-static results. Our result agrees with extrapolations of results from relativistic (Wilson) heavy quark simulations.

Leptonic Decays of Heavy Quarks on the Lattice

“…In view of this issue, we wish to test the consistency of results from different groups, by listing in table 9 the values for B B (m b ) from refs. 100,162,163 , which were obtained by applying methods (M 1 ), (M 2 ) and (M 3 ) for uniform choices of input parameters. Indeed it turns out that method (M 2 ) systematically produces lower values of B B (m b ).…”

“…Attempts in this direction have been reported in the context of the B parameter B K 84,85 . Lattice results for the B parameter B B have been published recently using the static approximation 100,162,163 and also propagating heavy quarks 114,164,165 . Earlier attempts are discussed in refs.…”

Width difference in the Bs0-Bs0 system from lattice HQET

“…[4], UKQCD coll. [12], Christensen et al [13] and also by JLQCD coll. in NRQCD when their results are extrapolated to the infinite mass limit [14].…”

Status of lattice calculations of B-meson decays and mixing

“…In particular, the continuum limit has not been taken in any study so far. It turns out, though, that results for B-parameters and ξ are broadly consistent, regardless of whether NRQCD [39,40,26], relativistic heavy quarks [34,38,41] or the static approximation [42][43][44][45] …”

“…For the B-parameters B 0B0 , and the ratio ξ, there are not so many results available, and only one recent calculation uses dynamical quarks [26]. It is then clear that MILC [28] CPPACS [27] JLQCD [31] FNAL [30] MILC [29] Rome-II [22] ALPHA [17] UKQCD [34] UKQCD [33] APE [32] CPPACS [37] JLQCD [36] GLOK [35] MILC [28] CPPACS [27] JLQCD [31] FNAL [30] MILC [29] Rome-II [22] UKQCD [34] UKQCD [33] APE [38] JLQCD [26] JLQCD [40] JLQCD [39] SPQR [38,41] UKQCD [34] G+M [44,45] UKQCD [42,45] Kentucky [43] Fig. 2.…”