1S and $\overline{MS}$ Bottom Quark Masses from $\Upsilon$ Sum Rules

The bottom quark $1S$ mass, $M_b^{1S}$, is determined using sum rules which relate the masses and the electronic decay widths of the $\Upsilon$ mesons to moments of the vacuum polarization function. The $1S$ mass is defined as half the perturbative mass of a fictitious ${}^3S_1$ bottom-antibottom quark bound state, and is free of the ambiguity of order $\Lambda_{QCD}$ which plagues the pole mass definition. Compared to an earlier analysis by the same author, which had been carried out in the pole mass scheme, the $1S$ mass scheme leads to a much better behaved perturbative series of the moments, smaller uncertainties in the mass extraction and to a reduced correlation of the mass and the strong coupling. We arrive at $M_b^{1S}=4.71\pm 0.03$ GeV taking m_b(\bar m_b)$ can be reduced if the three-loop corrections to the relation of pole and $\bar{MS}$ mass are known and if the error in the strong coupling is decreased.