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

M. R. Ahmady; V. Elias; A. Squires; T. G. Steele; Ailin Zhang

doi:10.1142/S0218301306004065

paper

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

arXiv:hep-ph/0401036 · doi:10.1142/S0218301306004065

Abstract

Accurate determinations of the MS-bar b-quark mass $m_{b} (m_{b})$ from $σ (e^{+} e^{-} \to hadrons)$ experimental data currently contain three comparable sources of uncertainty; the experimental uncertainty from moments of this cross-section, the uncertainty associated with $α_{s} (M_{z})$ , 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 $m_{b} (m_{b})$ . This resummation also reduces the estimated effect of higher-loop perturbative contributions, further reducing the theoretical uncertainties in $m_{b} (m_{b})$ . Furthermore, such resummation techniques improve the agreement between the values of the MS-bar b-quark mass extracted from the various moments of $R (s) = σ (e^{+} e^{-} \to hadrons) / σ_{pt}$ [ $σ_{pt} = 4 π α^{2} / (3 s)$ ], obviating the need to choose an optimummoment for determining $m_{b} (m_{b})$ . Resummation techniques are also shown to reduce renormalization-scale dependence in the relation between b-quark MS-bar and pole mass and in the relation between the pole and $1 S$ mass.

19 pages, latex2e, 6 eps figures contained in latex file. Errors corrected in equations (20)--(22)

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

Abstract

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