Improved determination of b quark mass from spectroscopy

Using recently evaluated contributions (including a novel one calculated here), we present updated values for the pole mass and $\bar{MS}$ mass of the $b$ quark: $m_b=5022\pm58$ MeV, for the pole mass, and $\bar{m}_b(\bar{m}_b)=4286\pm36$ MeV for the $\bar{MS}$ one. These values are accurate including, respectively, $O(\alpha_s^5\log\alpha_s)$ and $O(\alpha_s^3)$ corrections and, in both cases, leading orders in the ratio $m_c^2/m_b^2$.