A one-loop study of matching conditions for static-light flavor currents

Abstract

Heavy Quark Effective Theory (HQET) computations of semi-leptonic decays, e.g. B → πlν, require the knowledge of the parameters in the effective theory for all components of the heavy-light flavor currents. So far non-perturbative matching conditions have been employed only for the time component of the axial current. Here we perform a check of matching conditions for the time component of the vector current and the spatial component of the axial vector current up to one-loop order of perturbation theory and to lowest order of the 1/m-expansion. We find that the proposed observables have small higher order terms in the 1/m-series and are thus excellent candidates for a nonperturbative matching procedure.

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

“…The parameters depending on three angles (such as c V k, 3 ) show a stronger influence by the θ-choices and sizable effects of higher-order corrections in 1/z, which often do not decrease substantially (or not at all) in the "EX" case; thus, these effects appear to be a genuine property of them. Figure 4 also compares two alternative ways to determine ln Z stat V 0 , either based on two-or threepoint functions [8,18]. Owing to the visibly flatter 1/zdependence, the latter is obviously to be preferred, and ln Z HQET V 0 and ln Z HQET A behave similarly.…”

“…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.…”

“…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.…”

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

“…In particular, we investigate a considerable set of observables at varied kinematics, which in the spirit of the general non-perturbative matching strategy mentioned above are usually employed to define suitable matching relations. Complementary to perturbative studies [13,14,16], this yields non-perturbative insights into their heavy quark mass asymptotics and provides criteria for which of them are to be preferred within the matching strategy of [5], such as impact of mass-dependent cutoff effects in the continuum limit extrapolations, numerical accuracy and magnitude of higher-order corrections in 1/m h .…”

Numerical Stochastic Perturbation Theory and the Gradient Flow

“…In order to make these determinations more effective, however, perturbation theory needs to be pushed beyond the 1-loop order, which is in most cases technically involved. Although codes have been developed for the automation of such calculations [9], the inclusion of the gradient flow and the need for high order contributions complicate things further, rendering these computations rather challenging. For this reason we rely on Numerical Stochastic Perturbation Theory (NSPT) (see [10] for an introduction).…”