Bottom Quark Mass from Υ Mesons

The bottom quark pole mass M b is determined using a sum rule which relates the masses and the electronic decay widths of the Υ mesons to large n moments of the vacuum polarization function calculated from nonrelativistic quantum chromodynamics. The complete set of next-to-next-to-leading order (i.e. O(α 2 s , α s v, v 2) where v is the bottom quark c.m. velocity) corrections is calculated and leads to a considerable reduction of theoretical uncertainties compared to a pure next-to-leading order analysis. However, the theoretical uncertainties remain much larger than the experimental ones. For a two parameter fit for M b , and the strong MS coupling α s , and using the scanning method to estimate theoretical uncertainties, the next-to-next-to-leading order analysis yields 4.74 GeV ≤ M b ≤ 4.87 GeV and 0.096 ≤ α s (M z) ≤ 0.124 if experimental uncertainties are included at the 95% confidence level and if two-loop running for α s is employed. M b and α s have a sizeable positive correlation. For the running MS bottom quark mass this leads to 4.09 GeV ≤ m b (M Υ(1S) /2) ≤ 4.32 GeV. If α s is taken as an input, the result for the bottom quark pole mass reads 4.78 GeV ≤ M b ≤ 4.98 GeV (4.08 GeV ≤ m b (M Υ(1S) /2) ≤ 4.28 GeV) for 0.114 < ∼ α s (M z) ≤ 0.122. The discrepancies between the results of three previous analyses on the same subject by Voloshin, Jamin and Pich, and Kühn et al. are clarified. A comprehensive review on the calculation of the heavy quark-antiquark pair production cross section through a vector current at next-to-next-to leading order in the nonrelativistic expansion is presented.