Improvement of Renormalization-Scale Uncertainties Within Empirical Determinations of the b-Quark Mass

Accurate determinations of the b-quark mass mb(mb) from σ(e+e-→hadrons) experimental data currently contain three comparable sources of uncertainty; the experimental uncertainty from moments of this cross-section, the uncertainty associated with αs(Mz), and the theoretical uncertainty associated with the renormalization scale. Through resummation of all logarithmic terms explicitly determined in the perturbative series by the renormalization-group (RG) equation, it is shown that the renormalization-scale dependence is virtually eliminated as a source of theoretical uncertainty in mb(mb). This resummation also reduces the estimated effect of higher-loop perturbative contributions, further reducing the theoretical uncertainties in mb(mb). Furthermore, such resummation techniques improve the agreement between the values of the b-quark mass extracted from the various moments of R(s) = σ(e+e-→hadrons)/σpt [σpt = 4πα2/(3s)], obviating the need to choose an optimum moment for determining mb(mb). Based on this analysis, the resulting value of the b-mass is mb(mb) = 4.207 GeV ± 40 MeV, where the dominant uncertainty now arises from the experimental moments. Resummation techniques are also shown to reduce renormalization-scale dependence in the relation between b-quark and pole mass and in the relation between the pole and 1S mass.