Properties ofBmesons in lattice QCD

Abstract

The results of an extensive study of B-meson properties in quenched lattice QCD are presented. The studies are carried out in the static quark limit where the b-quark is taken to be infinitely massive. Our computations rely on a multistate smearing method introduced previously, with smearing functions generated from a relativistic lattice quark model. Systematic errors arising from excited state contamination, finite volume effects, and the chiral extrapolation for the light quarks are estimated. We obtain continuum results for the mass splitting M Bs − M Bu = 86 ± 12(stat) +7 −9 (syst) MeV, the ratio of decay constants f Bs /f Bu = 1.22 ± 0.04(stat) ± 0.02(syst). For the B-meson decay constant we separately exhibit the sizable uncertainties in the extrapolation to the continuum limit (a → 0) and higher order perturbative matching. We obtain f B = 188 ± 23(stat) ± 15(syst) +26 −0 (extrap) ± 14(pert) MeV.

Weak decays beyond leading logarithms

“…The most recent results are somewhat lower than quoted a few years ago. Based on a review by (Sachrajda, 1994), the recent extensive study by (Duncan et al, 1995) and the analyses in (Bernard et al, 1994), (Draper and McNeile, 1994) we conclude that F B d = (180 ± 40) MeV. This together with the earlier result of the European Collaboration (Abada et al, 1992) …”

“…Provided x d /x s has been accurately measured a determination of R t within ±10% should be possible. Indeed the most recent lattice results (Duncan et al, 1995), (Baxter et al, 1994) give F Bs /F B d = 1.22 ± 0.04. A similar result F Bs /F B d = 1.16 ± 0.05 has been obtained using QCD sum rules (Narison, 1994).…”

The heavy hadron spectrum

“…Note that if we take m Q a to ∞ in this calculation aE 0 will become V c /2 where V c is the unphysical self-energy part of the heavy quark potential discussed earlier. Again agreement between perturbation theory (Morningstar (1994), Duncan et al (1995)) and potential model results (Bali and Schilling (1992)) is reasonable given that aE 0 starts at O(α s ) and is only known to this order. The effect of tadpole-improvement is easy to work out in this case.…”

“…Again, the smearing does not affect the values of masses obtained, but a good smearing can reduce the errors. In fact potential-model type wavefunctions (much broader than for heavyonium) do work reasonably well (Duncan et al (1995), Ali Khan et al (1996)), used as a source for the heavy quark, as do gauge-invariant smearings typical of light hadron calculations (UKQCD (1996b)). The light anti-quark for the meson is taken to have a delta function source.…”

“…A lot of effort has been put into this for mesons in the static case (Duncan et al (1995), Draper et al (1995)) to ameliorate the noise problems. Again, the smearing does not affect the values of masses obtained, but a good smearing can reduce the errors.…”