1SandMS¯bottom quark masses fromΥ

The bottom quark 1S mass, $M_b^{1S}$, is determined using sum rules whichrelate the masses and the electronic decay widths of the $\Upsilon$ mesons tomoments of the vacuum polarization function. The 1S mass is defined as half theperturbative mass of a fictitious ${}^3S_1$ bottom-antibottom quark boundstate, and is free of the ambiguity of order $\Lambda_{QCD}$ which plagues thepole mass definition. Compared to an earlier analysis by the same author, whichhad been carried out in the pole mass scheme, the 1S mass scheme leads to amuch better behaved perturbative series of the moments, smaller uncertaintiesin the mass extraction and to a reduced correlation of the mass and the strongcoupling. We arrive at $M_b^{1S}=4.71\pm 0.03$ GeV taking$\alpha_s(M_Z)=0.118\pm 0.004$ as an input. From that we determine the$\bar{MS}$ mass as $\bar m_b(\bar m_b) = 4.20 \pm 0.06$ GeV. The error in $\barm_b(\bar m_b)$ can be reduced if the three-loop corrections to the relation ofpole and $\bar{MS}$ mass are known and if the error in the strong coupling isdecreased.Comment: 20 pages, latex; numbers in Tabs. 2,3,4 corrected, a reference and a comment on the fitting procedure added, typos in Eqs. 2 and 23 eliminate