Decay Constants of Beauty Mesons from QCD Sum Rules

TL;DR

This paper analyzes the decay constants of beauty mesons using QCD sum rules, highlighting discrepancies with lattice QCD results and the sensitivity of predictions to scale setting and quark mass inputs.

Contribution

It provides a detailed QCD sum rule analysis of beauty meson decay constants, revealing scale dependence and the impact of quark mass choices on predictions.

Findings

QCD sum rule predictions for $f_B$ are larger than lattice results at $ar{m}_b=4.18$ GeV.

Matching lattice results suggests a higher $b$-quark mass of 4.247 GeV.

Decay constants in the beauty sector are highly sensitive to renormalization scale.

Abstract

Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the $\overline{\rm MS}$ scheme $\overline{m}_b(\overline{m}_b)\approx4.18\;\mbox{GeV},$ the sum-rule result $f_B\approx210$-$220\;\mbox{MeV}$ for the $B$ meson decay constant is substantially larger than the recent lattice-QCD finding $f_B\approx190\;\mbox{MeV}.$ Requiring QCD sum rules to reproduce the lattice-QCD value of $f_B$ yields a significantly larger $b$-quark mass: $\overline{m}_b(\overline{m}_b)=4.247\;\mbox{GeV}.$ (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants $f_D,$ $f_{D_s},$ $f_{D^*}$ and $f_{D_s^*}$ are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants - and especially for the ratio $f_{B^*}/f_B$ - prove to be very sensitive to the specific scale setting.