The bottom-quark mass from non-relativistic sum rules at NNNLO

We determine the mass of the bottom quark from high moments of the bottom production cross section in e+ e- annihilation, which are dominated by the threshold region. On the theory side next-to-next-to-next-to-leading order (NNNLO) calculations both for the resonances and the continuum cross section are used for the first time. We find mb,PS(2 GeV) = 4.532 +0.013 -0.039 GeV for the potential-subtracted mass and mb,MSbar(mb,MSbar) = 4.193 +0.022 -0.035 GeV for the MSbar bottom-quark mass.
37 pages, 5 figures. Minor change in charm-effect uncertainty, update of conversion uncertainty for MSbar mass, added clarifications and references