Scale setting for αs beyond leading order -: art. no. 034023

We present a general procedure for incorporating higher-order information into the scale-setting prescription of Brodsky, Lepage and Mackenzie. In particular, we show how to apply this prescription when the leading coefficient or coefficients in a series in the strong coupling alpha(s) are anomalously small and the original prescription can give an unphysical scale. 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 apply it to the heavy quark mass and energy renormalization in lattice NRQCD, and to a variety of known series. Among the latter, we find significant corrections to the scales for the ratio of e(+)e(-) to hadrons over muons, the ratio of the quark pole to (MS) over bar mass, the semileptonic B-meson decay width, and the top decay width. Scales for the latter two decay widths, expressed in terms of (MS) over bar masses, increase by factors of five and thirteen, respectively, substantially reducing the size of radiative corrections.