Prospects for the measurement of the $b$-quark mass at the ILC

This note presents an analysis of the potential of future high-energy electron-positron colliders to measure the $b$-quark mass. We perform a full-simulation study of the measurement of the ratio of the three-jet rates in events with $bbar{b}(g)$ and $qbar{q}(g)$ production, $R_{3}^{bl}$, and assess the dominant uncertainties, including theory and experimental systematic uncertainties. We find that the ILC Higgs factory stage, with an integrated luminosity of 2 ab$^{-1}$ at $sqrt{s}=$ 250 GeV can measure the $b-$quark $bar{MS}$ mass at a scale of 250 GeV ($m_b(250~$GeV$)$) with a precision of 1 GeV. From this result we extrapolate the potential of the GigaZ run running at $sqrt{s}= m_Z$. We expect $m_b(m_Z)$ can be determined with an 0.12 GeV uncertainty, exceeding the precision of the LEP and SLD measurements by a factor $sim$3.