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

Accurate determinations of the MS 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). Furthermore, such resummation techniques improve the agreement between the values of the MS b-quark mass extracted from the various moments of R(s) = σ (e+e− → hadrons) /σpt [σpt = 4πα 2/(3s)], obviating the need to choose an optimum moment for determining mb (mb). Resummation techniques are also shown to reduce renormalization-scale dependence in the relation between b-quark MS and pole mass and in the relation between the pole and 1S mass.