Improved Determination of the B Quark Mass from Spectroscopy

Using recently evaluated contributions (including a novel one calculated here), we present updated values for the pole mass and M S mass of the b quark: m b = 5022 ± 58 MeV, for the pole mass, and ¯ m b (¯ m b) = 4286±36 MeV for the M S one. These values are accurate including, respectively, O(α 5 s log αs) and O(α 3 s) corrections and, in both cases, leading orders in the ratio m 2 c /m 2 b. One of the sources of information for the quark masses is quarkonium spectroscopy. By evaluating the ¯ bb potential including relativistic and radiative corrections, as well as leading nonperturbative effects, and using this in a perturbative expansion, it has been possible to find values of the pole quark masses with increasing accuracy; [2,3,4] in this note we will go up to fourth and leading fifth order, in the approximation of neglecting " light " (u, d, s) quark masses and to leading order (actually, O(α s m 2 c /m 2 b)) in the c quark mass. The connection with the MS mass has been known for some time to one and two loops [5] : very recently, a three loop evaluation has been completed. Coupling this with the pole mass evaluations, we now have an order α 3 s result for the MS mass. We review here briefly this.