New Determination of the Pole Mass of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi></mml:math>Quark Using Lattice QCD

Abstract

Recent results from lattice QCD simulations provide a realistic picture, based upon first principles, of $\ensuremath{\Upsilon}$ physics. We combine these results with the experimentally measured mass of the $\ensuremath{\Upsilon}$ 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 ${M}_{b}=5.0(2)$ GeV. This corresponds to a bare mass of ${M}_{b}^{0}=4.0(1)$ GeV in our lattice theory and an $\stackrel{-}{\mathrm{MS}}$ mass of ${M}_{b}^{\stackrel{-}{\mathrm{MS}}}({M}_{b})=4.0(1)$ GeV ($\stackrel{-}{\mathrm{MS}}$ denotes the modified minimal-subtraction scheme). We discuss the implications of this result for the $c$-quark mass.