Decay Constants of Heavy Pseudoscalar Mesons: Reconciling QCD Sum Rules and Lattice QCD

TL;DR

This paper improves QCD sum rule techniques to accurately predict decay constants of heavy pseudoscalar mesons, achieving better agreement with lattice QCD results and providing a potential method to determine the b-quark mass.

Contribution

It introduces novel improvements in QCD sum rule methods that reconcile decay constant predictions with lattice QCD results, also enabling b-quark mass estimation.

Findings

Predicted $f_B$ and $f_{B_s}$ are consistent with lattice QCD.

Achieved precise decay constant values: $f_B=192.0$ MeV, $f_{B_s}=228.0$ MeV.

Provided an independent determination of the b-quark mass.

Abstract

Exploiting recently proposed novel improvements of the techniques used for extracting from QCD sum rules pivotal hadron characteristics, including their systematic errors, we succeed to achieve a conspicuous agreement of the predictions of QCD sum rules for the decay constants $f_B$ and $f_{B_s}$ of the heavy pseudoscalar mesons $B$ and $B_s,$ which before tended to be slightly too large, with corresponding results from lattice QCD. Adopting for the crucial $b$-quark $\bar{\rm MS}$ mass the value $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$ GeV, we get $f_B=(192.0\pm14.6)$ MeV and $f_{B_s}=(228.0\pm19.8)$ MeV; clearly, this may be also viewed as a determination of the $b$-quark mass from sufficiently precise decay constants.