HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation

Abstract

We determine non-perturbatively the parameters of the lattice HQET Lagrangian and those of the time component of the heavy-light axial-vector current in the quenched approximation. The HQET expansion includes terms of order 1/m b . Our results allow to compute, for example, the heavy-light spectrum and B-meson decay constants in the static approximation and to order 1/m b in HQET. The determination of the parameters is separated into universal and non-universal parts. The universal results can be used to determine the parameters for various discretizations. The computation reported in this paper uses the plaquette gauge action and the "HYP1/2" action for the b-quark described by HQET. The parameters of the current also depend on the light-quark action, for which we choose non-perturbatively O(a)-improved Wilson fermions.

Non-perturbative tests of continuum HQET through small-volume two-flavour QCD

“…3 The worrying behaviour of perturbation theory for C PS/V may also be read off from the data points in figure 4, where in fact no signs of an asymptotic convergence with the loop order in C PS/V from about the b-quark mass scale on of any of the curves through the points can be stated. This is even more so for 6) in the right panel of figure 4, as a direct effective finite-volume estimates of f B /f B * involving C PS/V , too, where Γ PS /Γ V cancels the ratio of meson masses in Y PS/V . The growing deviations of the data points from the polynomial fits in 1/z towards the charm quark scale for this quantity are inherited from the corresponding behaviour of the higher-order terms in Γ PS /Γ V (see previous paragraph).…”

“…We note that eq. (B.8) can be established to order O(1/m) at the non-perturbative level [6,9] by a matching calculation of QCD and lattice HQET in a small physical volume. This procedure is free of renormalon ambiguities due to the non-perturbative determination of the matching coefficients.…”

“…Here we focus on the Heavy Quark Effective Theory (HQET) [1][2][3][4] which provides a natural framework to study heavy-light mesons through a systematic expansion in the inverse heavy quark mass, 1/m h . A non-perturbative implementation of HQET on the lattice [5], including the nextto-leading order in the 1/m h -expansion, has been tested and applied successfully for the quenched case in the past [6][7][8]. It requires to solve a set of matching relations between quantities in continuum QCD and lattice HQET in a small physical volume.…”

“…which is a key ingredient to the finite-volume matching part of the ALPHA Collaboration's B-physics programme based on HQET non-perturbatively renormalized and matched to QCD at O(1/m h ) [5][6][7][8][9][10][11][12], lies very well within the applicability domain of HQET. This is, for instance, also in line with the onset of the linear behaviour reported in the treelevel study [13] of the 1/z-dependence of the HQET parameters contributing to the full set of heavy-light flavour currents in HQET at O(1/m h ).…”

“…of [6]. Besides its obvious dependence on z and a/L, δ (0) Ω also depends on the kinematical setup of the Schrödinger functional, inherited from the observable itself.…”