Mass of the bottom quark from Upsilon(1S) at NNNLO: An update

We update our perturbative determination of MS mass m_b(m_b), by including the recently obtained four-loop coefficient in the relation between the pole and MS mass. First the renormalon subtracted (RS or RS') mass is determined from the known mass of the Y(1S) meson, where we use the renormalon residue N_m obtained from the asymptotic behavior of the coefficient of the 3-loop static singlet potential. MS mass is then obtained using the 4-loop renormalon-free relation between the RS (RS') and MS mass. We argue that the effects of the charm quark mass are accounted for by effectively using N_f = 3 in the mass relations. The extracted value is m_b(m_b) = 4222(40) MeV, where the uncertainty is dominated by the renormalization scale dependence.