Bottom quark mass from {Upsilon} mesons
- Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0319 (United States)
The bottom quark pole mass M{sub b} is determined using a sum rule which relates the masses and the electronic decay widths of the {Upsilon} mesons to large {ital 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({alpha}{sub s}{sup 2},{alpha}{sub s}v,v{sup 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{sub b}, and the strong M{bar S} coupling {alpha}{sub s}, and using the scanning method to estimate theoretical uncertainties, the next-to-next-to-leading order analysis yields 4.74 GeV {le}M{sub b}{le}4.87 GeV and 0.096{le}{alpha}{sub s}(M{sub z}){le}0.124 if experimental uncertainties are included at the 95{percent} confidence level and if two-loop running for {alpha}{sub s} is employed. M{sub b} and {alpha}{sub s} have a sizable positive correlation. For the running M{bar S} bottom quark mass this leads to 4.09 GeV {le}m{sub b}(M{sub {Upsilon}(1S)}/2){le}4.32 GeV. If {alpha}{sub s} is taken as an input, the result for the bottom quark pole mass reads 4.78 GeV {le}M{sub b}{le}4.98 GeVthinsp[4.08 GeV {le}m{sub b}(M{sub {Upsilon}(1S)}/2){le}4.28 GeV] for 0.114{le}{alpha}{sub s}(M{sub z}){le}0.122. The discrepancies between the results of three previous analyses on the same subject by Voloshin, Jamin, and Pich and K{umlt u}hn {ital et al.} are clarified. A comprehensive review on the calculation of the heavy-quark{endash}antiquark pair production cross section through a vector current at next-to-next-to leading order in the nonrelativistic expansion is presented. {copyright} {ital 1998} {ital The American Physical Society}
- OSTI ID:
- 292733
- Journal Information:
- Physical Review, D, Vol. 59, Issue 1; Other Information: PBD: Jan 1999
- Country of Publication:
- United States
- Language:
- English
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