  The Principle of Maximal Conformality (PMC) provides a rigorous method for
eliminating renormalization scheme-and-scale ambiguities for perturbative QCD
predictions. The PMC uses the renormalization group equation to fix the
$\beta$-pattern of each order in an arbitrary pQCD approximant, and it then
determines the optimal renormalization scale by absorbing all $\{\beta_{i}\}$
terms into the running coupling at each order. The resulting coefficients of
the pQCD series match the scheme-independent conformal series with $\beta=0$.
As in QED, different renormalization scales appear at each order; we call this
the multi-scale approach. In this paper, we present a novel single-scale
approach for the PMC, in which a single effective scale is constructed to
eliminate all non-conformal $\beta$-terms up to a given order simultaneously.
The PMC single-scale approach inherits the main features of the multi-scale
approach; for example, its predictions are scheme-independent, and the pQCD
convergence is greatly improved due to the elimination of divergent renormalon
terms. As an application of the single-scale approach, we investigate the
$e^+e^-$ annihilation cross-section ratio $R_{e^+e^-}$ and the Higgs
decay-width $\Gamma(H \to b \bar{b})$, including four-loop QCD contributions.
The resulting predictions are nearly identical to the multi-scale predictions
for both the total and differential contributions. Thus in many cases, the PMC
single-scale approach PMC-s, which requires a simpler analysis, could be
adopted as a reliable substitution for the PMC multi-scale approach for setting
the renormalization scale for high-energy processes, particularly when one does
not need detailed information at each order. The elimination of the
renormalization scale uncertainty increases the precision of tests of the
Standard Model at the LHC.
