A TWO-LOOP APPLICATION OF THE THRESHOLD EXPANSION: THE BOTTOM QUARK MASS FROM bb̄ PRODUCTION

between the two-point function of the bottom vector current and the inclusive bottom quark cross section mediated by a virtual photon, which is valid up to a small correction from bb̄ radiation from light quarks. The left hand side can be computed in perturbation theory; the right hand side from data. The parameters of the lowest Υ(nS) resonances are well-measured, but the continuum cross section above the threshold is not. Hence the experimental error of the right hand side decreases with increasing n, because higher moments weight lower s. When the integral over s is saturated by the threshold region, the bottom quarks are non-relativistic, and 2mb/ √ n and mb/n appear as new momentum scales in the problem, related to the typical momentum mbv and Talk presented at RADCOR98, Barcelona, September, 1998. The numerical result of this version supersedes the version printed in the proceedings volume, which was affected by a program error.