Scale Setting for ${\alpha }_s$ Beyond Leading Order

Abstract

We present a general procedure for applying the scale-setting prescription of Brodsky, Lepage and Mackenzie to higher orders in the strong coupling constant $\alphas$. In particular, we show how to apply this prescription when the leading coefficient or coefficients in a series in $\alphas$ are anomalously small. We give a general method for computing an optimum scale numerically, within dimensional regularization, and in cases when the coefficients of a series are known. We find significant corrections to the scales for $R_{e^{+}{e}^{-}}$, $\Gamma (B\to X_{u}e\bar{\nu })$, $\Gamma (t\to bW)$, and the ratios of the quark pole to $\MSbar$ and lattice bare masses.

Lattice 2000 (Perturbation Theory), 5 pages, 7 figures, LaTeX

References in corpus (1)

• Disentangling running coupling and conformal effects in QCD

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