OPE, Heavy-Quark Mass, and Heavy-Meson Decay Constants from QCD Sum Rules

TL;DR

This paper uses QCD sum rules to accurately determine heavy-meson decay constants, highlighting the importance of using the MS-bar mass scheme over the pole mass for better convergence and more reliable results.

Contribution

It introduces a novel method employing Borel-dependent dual thresholds to improve the extraction of heavy-meson decay constants from QCD sum rules.

Findings

Decay constants are larger when using MS-bar mass scheme.

Reorganization of perturbative expansion improves convergence.

Controlled uncertainties in decay constants are achieved.

Abstract

We present a sum-rule extraction of the decay constants of heavy-light mesons from the two-point correlator of pseudoscalar currents. To this end, we compare the perturbative expansions for the correlator and the decay constant performed in terms of either the pole mass or the running MS-bar mass of the heavy quark. The perturbative expansion expressed in terms of the pole mass exhibits no sign of convergence whereas reorganizing this very expansion in terms of the MS-bar mass yields a rather clear hierarchy of the perturbative contributions. Accordingly, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those extracted from its MS-bar-mass counterpart. Then, making use of the OPE in terms of the MS-bar mass we derive the decay constants of heavy mesons with emphasis on acquiring control over the uncertainties in the decay constants, related both to the input QCD parameters and to the limited accuracy of the method of sum rules. Gaining this control has become possible due to the application of our novel procedure for extracting hadron observables based on dual thresholds which depend on the Borel parameter.