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

Abstract

We report on the computation of the B s meson decay constant in Heavy Quark Effective Theory on the lattice. The next to leading order corrections in the HQET expansion are included non-perturbatively. We estimate higher order contributions to be very small. The results are extrapolated to the continuum limit, the main systematic error affecting the computation is therefore the quenched approximation used here. The Generalized Eigenvalue Problem and the use of all-to-all propagators are important technical ingredients of our approach that allow to keep statistical and systematic errors under control. We also report on the decay constant f B s of the first radially excited state in the B s sector, computed in the static limit

Excited state Effects in Nucleon Matrix Element Calculations

“…We have also used a generalized eigenvalue (GEV) approach as first suggested in [18] and further developed and refined in Refs. [19,20,21]. We considered two variational basis: in the first, two interpolating fields are considered, namely the standard one…”

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

“…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.…”

“…Furthermore and analogously, we define the following QCD observables, suppressing again their dependence on M , L and θ: 8) where Y PS and Y V are the finite-volume heavy-light pseudoscalar and vector decay constant, respectively. As L → ∞, they become proportional to the physical heavy-light pseudoscalar…”

“…Along the lines of ref. [32] one can express the lowest-order HQET approximation of the QCD matrix element of A 0 , in slight adaption of our notation introduced before, as 8) such that at leading order in the inverse heavy quark mass, 1/m h , the conversion function C PS defines a RGI-mass scaling function that contains the full (logarithmic) mass dependence, whereas the non-perturbative matrix element in the static effective theory, X RGI , becomes a pure mass independent number. Here, the renormalization scale µ of the static current is identified with µ = m * , where m * is implicitly defined by the solution of m * = m(m * ), m being the renormalized (running) heavy quark mass.…”

“…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 ).…”