Accurate Bottom-Quark Mass from Borel QCD Sum Rules for the Decay Constants of $B$ and $B_s$ Mesons

We show that in the context of QCD sum rules a strong (anti-) correlation between the $b$-quark mass $m_b$ and the $B$-meson's decay constant $f_B$ emerges: $\delta f_B/f_B\approx -8 \delta m_b/m_b.$ This observation allows us to derive a precise value of $m_b$ from a Borel sum rule for the two-point correlator of heavy-light currents exploiting accurate $f_B$ results from lattice QCD as input: $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$ GeV.