Bottom Quark Mass from ${\rm Y}$ Sum Rules to $\mathcal{O}({\alpha }_s^3)$

Abstract

We use the $\mathcal{O}({\alpha }_s^3)$ approximation of the heavy-quark vacuum polarization function in the threshold region to determine the bottom quark mass from nonrelativistic ${\rm Y}$ sum rules. We find very good stability and convergence of the perturbative series for the bottom quark mass in $\overline{\mathrm{MS}}$ renormalization scheme. Our final result is ${\overline{m}}_b({\overline{m}}_b)=4.169\pm 0.008_{th}\pm 0.002_{{\alpha }_s}\pm 0.002_{exp}$.

Comments: 23 pages, 6 figures, journal version