Parameters of heavy quark effective theory from N f = 2 lattice QCD

Abstract

We report on a non-perturbative determination of the parameters of the lattice Heavy Quark Effective Theory (HQET) Lagrangian and of the time component of the heavy-light axial-vector current with N f = 2 flavors of massless dynamical quarks. The effective theory is considered at the 1/m h order, and the heavy mass m h covers a range from slightly above the charm to beyond the beauty region. These HQET parameters are needed to compute, for example, the b-quark mass, the heavy-light spectrum and decay constants in the static approximation and to order 1/m h in HQET. The determination of the parameters is done non-perturbatively. The computation reported in this paper uses the plaquette gauge action and two different static actions for the heavy quark described by HQET. For the light-quark action we choose non-perturbatively O(a)-improved Wilson fermions.

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

“…It requires to solve a set of matching relations between quantities in continuum QCD and lattice HQET in a small physical volume. In twoflavour QCD, the resulting non-perturbative set of HQET parameters [9] was recently used to extract phenomenologically relevant parameters such as the b-quark mass, the B-meson decay constant and hyperfine splittings from large-volume simulations [10][11][12]. At present there are efforts to extend the matching strategy to include the vector meson channel [13,14] in order to compute f B * and form factors of semi-leptonic B (s) → π (K) transitions.…”

“…Additional details can be found in appendices B and C of reference [9]. Working in a finite (and small) volume, all matrix elements and energies become effective quantities which intrinsically depend on the scale L 1 .…”

“…the renormalization factor of which, Z P (µ, g 2 0 ), has been determined non-perturbatively in the SF scheme at scale µ = 1/L 1 during the production runs reported in [9]. Since they have not been quoted in that reference we list them together with further details in table 4.…”

“…We use the "HQET[L 1 ]" lattices with T = L = L 1 as specified in table C.1 and C.2 of ref. [9]. For completeness we list some additional details in table 5 that were not published there.…”

“…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 ).…”