Matching of heavy-light flavour currents between HQET at order 1/m and QCD: I. Strategy and tree-level study

Abstract

We present a strategy how to match the full set of components of the heavylight axial and vector currents in Heavy Quark Effective Theory (HQET), up to and including 1/m h-corrections, to QCD. While the ultimate goal is to apply these matching conditions non-perturbatively, in this study we first have implemented them at tree-level, in order to find good choices of the matching observables with small O(1/m 2 h) contributions. They can later be employed in the non-perturbative matching procedure which is a crucial part of precision HQET computations of semileptonic decay form factors in lattice QCD.

Non-perturbative Heavy Quark Effective Theory: An application to semi-leptonic B-decays

“…Following [5,6,7,8], we fix the 19 parameters in the HQET expansion of the action and vector/axial currents through matching equations, which we write in the form…”

“…These have been studied at tree-level in [8] for a particular class of matching conditions. Note that at tree-level and in the continuum limit, the L-dependence of dimensionless observables Φ i appears only in the combination z = Lm h .…”

“…The correlation functions are illustrated in [1], where it is also explained how they relate to quantum mechanical Hilbert space matrix elements. In order to determine the parameters ω i , 1 ≤ i ≤ 19, the above correlation functions as well as some related to the axial current are combined to 19 observables [8,18]. First of all, ratios are formed such that the renormalization of the boundary quark fields drops out.…”

“…We now illustrate a few results of the tree-level computation [8] of the HQET parameters for the vector currents that are needed for the semi-leptonic B-decays.…”

“…Due to the block structure of ϕ and because of additional simplifications, which occur at tree-level, and with the choice of twist angles according to the strategy of [8], one can determine the parameters one after the other from the matching equations (18). A main motivation of the tree-level study in [8] was to investigate the effect of higher-order corrections (in 1/m h ) in the system of matching equations and to test the choice of observables.…”