1SandMS¯bottom quark masses fromΥsum 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 ${\rm Y}$ mesons to moments of the vacuum polarization function. The $1S$ mass is defined as half the perturbative mass of a fictitious ${}^3{S}_1$ bottom-quark–bottom-antiquark bound state, and is free of the ambiguity of order ${\Lambda }_{\mathrm{QCD}}$ 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 a reduced correlation of the mass and the strong coupling. We arrive at $M_b^{1S}=4.71\mathrm{}\pm 0.03$ GeV, taking ${\alpha }_s{(M}_Z)=0.118\mathrm{}\pm 0.004$ as an input. From that we determine the $\overline{\mathrm{MS}}$ mass as $m_b\left(m_b\right)=4.20\mathrm{}\pm 0.06$ GeV. The error in $m_b\left(m_b\right)$ can be reduced if the three-loop corrections to the relation of pole and $\overline{\mathrm{MS}}$ mass are known and if the error in the strong coupling is decreased.