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We demonstrate that Borel QCD sum rules for heavy-light currents entail avery strong correlation between the $b$-quark mass $m_b$ and the $B$-mesondecay constant $f_B,$ that is, $\delta f_B/f_B\approx-8\delta m_b/m_b.$ Bystarting from $f_B$ as input, this observation allows for an accurate sum-ruledetermination of $m_b.$ Employing precise lattice QCD results for $f_B$ in oursum-rule study based on the three-loop $O(\alpha_s^2)$ heavy-light correlationfunction implies $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$ GeV for the $b$-quark$\bar{\rm MS}$ mass.

Mass of the $b$ Quark from QCD Sum Rules for $f_{B_{(s)}}$