The bottom $\bar{\rm MS}$ quark mass from sum rules at next-to-next-to-leading order

Abstract

We determine the bottom $\bar{\rm MS}$ quark mass $\bar{m}_b$ and the quark mass in the potential subtraction scheme from moments of the $b\bar{b}$ production cross section and from the mass of the Upsilon 1S state at next-to-next-to-leading order in a reorganized perturbative expansion that sums Coulomb exchange to all orders. We find $\bar{m}_b(\bar{m}_b)=(4.25\pm 0.08) $GeV and $m_{b,\rm PS}(2 {GeV})=(4.59\pm 0.08) $GeV for the potential-subtracted mass at the scale 2 GeV, adopting a conservative error estimate.