According to the renormalization group invariance, any physical observable should be invariant under different renormalization schemes and scales. Nevertheless, a fixed-order pQCD approximant cannot inherently satisfy this requirement, giving rise to the conventional scheme-and-scale ambiguities. The principle of maximum conformality (PMC) offers a process-independent approach to address these two types of ambiguities. In practice, it is necessary to handle the nf -terms in the pQCD series with caution to obtain accurate PMC predictions. In this paper, a novel method via using the characteristic operator (CO) \( {\hat{D}}_{n_{\gamma },{n}_{\beta }} \) is proposed to extend the applicability of PMC, which is a theoretical generalization of previous PMC single-scale setting approach. The CO framework not only streamlines derivations for complex scenarios, yielding simplified procedures and more compact expressions, but also achieves a scheme-and-scale invariant pQCD series by fixing the correct effective magnitude of αs and the running mass simultaneously. Both are well matched with the expansion coefficients of the series, leading to the wanted scheme-and-scale invariant conformal series. As an example, we show the achievement of scale-invariant N4LO total decay width Γ(H → \( b\overline{b} \) ) under the \( \overline{\textrm{MS}} \) -scheme. Using the CO framework, its effective coupling αs(Q*) and effective b-quark \( \overline{\textrm{MS}} \) -mass \( {\overline{m}}_b\left({Q}_{\ast}\right) \) are determined by absorbing all non-conformal {βi}-terms from the renormalization group equations for either αs or \( {\overline{m}}_b \) simultaneously. The PMC scale is fixed up to N3LL-accuracy, Q* = 55.2916 GeV and a scale-invariant total decay width is obtained, \( \Gamma \left(H\to b\overline{b}\right)={2.3819}_{-0.0231}^{+0.0230} \) MeV, whose errors are squared averages of the ones associated with ∆αs(MZ) = ±0.0009, ∆MH = 0.11 GeV, \( \Delta {\overline{m}}_b\left({\overline{m}}_b\right) \) = ±0.007 GeV, and the uncalculated N5LO contributions ∆Γ = ±0.0001 MeV predicted via Bayesian analysis with the degree-of-belief DoB = 95.5%.
