Heavy-strange meson decay constants in the continuum limit of quenched QCD

Abstract

We improve a previous quenched result for heavy-light pseudoscalar meson decay constants with the light quark taken to be the strange quark. A finer lattice resolution (a ≈ 0.05 fm) in the continuum limit extrapolation of the data computed in the static approximation is included. We also give further details concerning the techniques used in order to keep the statistical and systematic errors at large lattice sizes L/a under control. Our final result, obtained by combining these data with determinations of the decay constant for pseudoscalar mesons around the D s , follows nicely the qualitative expectation of the 1/m-expansion with a (relative) 1/m-term of about −0.5 GeV/m PS. At the physical b-quark mass we obtain F Bs = 193(6) MeV, where all errors apart from the quenched approximation are included.

NeutralB-meson mixing from unquenched lattice QCD with domain-wall light quarks and staticbquarks

“…Thus our observations are consistent with the scaling behavior expected from power counting. We can also compare our power-counting estimates with the findings of the ALPHA Collaboration, who performed a study of f B s at several lattice spacings using static b-quarks with similar link smearings in the quenched approximation [76]. Although ALPHA observes a violation of Oða 2 Þ scaling behavior at inverse lattice spacings below a À1 % 2:5 GeV, the difference between the predicted value for f B s at a % 0:11 fm given Oða 2 Þ scaling and the value of f B s that they obtain in the continuum limit using data within the scaling region is only about 25%, which is again close to our power-counting estimate.…”

A proposal for B-physics on current lattices

“…Due to present day computer limitations, it is not possible, however, to work directly with the heaviest quarks (as the b-quark) propagating on the simulated lattice. Various strategies, more or less inspired to the heavy quark effective theory (HQET) [7][8][9][10][11][12], have been devised to circumvent this intrinsic difficulty, which go from non-perturbative matching of HQET onto QCD [13][14][15][16][17][18] to finite size scaling methods with relativistic heavy quark(s) [19][20][21][22]. Relativistic heavy-quark actions designed (highly tuned) to have reduced cutoff effects [23][24][25][26] have also been employed for this purpose.…”

HQET at order 1/m: III. Decay constants in the quenched approximation

“…This shortcoming has now been cured by exploiting (i) a method based on solving a GEVP to reduce the systematic errors on bare matrix elements coming from the contribution of excited states to correlation functions and (ii) all-to-all propagators to improve the statistical precision. For example, at the finest lattice resolution considered, we have obtained a result for the bare static decay constant (HYP2 action), which is three times more precise than the result in [35] at β = 6.45 where ten times more configurations were analyzed in the Schrödinger Functional setup.…”

“…Although our direct computation of f Bs in HQET avoids any interpolation (or extrapolation) in the heavy mass, we show in figure 4 a comparison of our HQET result with an interpolation between previous results for f Ds [35] and the static value. As the decay constant itself does not have a well defined infinite mass limit, in the figure we plot the quantity r (red circle in figure 4) and the non-perturbative result in [35] for the decay constant around the charm JHEP12(2010)039 quark mass (blue triangles in figure 4). The static limit of this quantity is r 3/2 0 Φ RGI 1 , which we have also non-perturbatively computed here (purple square in figure 4).…”