Flavor thresholds and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi></mml:math>in the modified minimal-subtraction scheme

Abstract

A discussion of the modified minimal-subtraction ($\stackrel{-}{\mathrm{MS}}$) prescription in QCD is presented. Effects of flavor thresholds on ${\ensuremath{\alpha}}_{s}(\ensuremath{\mu})$ and ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$ are examined. Two parametrization options are described. In the first approach, distinct mass scales ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}^{({N}_{F})}$ associated with ${N}_{F}$, the effective number of flavors, are introduced. In the second scheme, a standard ${N}_{F}$-independent ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$ is adopted but the functional form of $\ensuremath{\alpha}(\ensuremath{\mu})$ is slightly modified.