Scale-invariant total decay width Γ(H → \( b\overline{b} \)) using the novel method of characteristic operator

Abstract

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 n_f -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 α_s 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 α_s(Q_*) and effective b-quark \( \overline{\textrm{MS}} \)-mass \( {\overline{m}}_b\left({Q}_{\ast}\right) \) are determined by absorbing all non-conformal {β_i}-terms from the renormalization group equations for either α_s 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 ∆α_s(M_Z) = ±0.0009, ∆M_H = 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%.