New Determination of the Pole Mass of thebQuark Using Lattice QCD

Abstract

Recent results from lattice QCD simulations provide a realistic picture, based upon first principles, of $\Upsilon$ physics. We combine these results with the experimentally measured mass of the $\Upsilon$ meson to obtain an accurate and reliable value for the $b$ quark's pole mass. We use two different methods, each of which yields a mass consistent with $M_b=5.0\mathrm{}\left(2\right)\mathrm{}$ GeV. This corresponds to a bare mass of $M_b^0=4.0\mathrm{}\left(1\right)\mathrm{}$ GeV in our lattice theory and an $\overline{\mathrm{MS}}$ mass of $M_b^{\overline{\mathrm{MS}}}\left(M_b\right)=4.0\mathrm{}\left(1\right)\mathrm{}$ GeV ($\overline{\mathrm{MS}}$ denotes the modified minimal-subtraction scheme). We discuss the implications of this result for the $c$-quark mass.