Scale-invariant total decay width Γ(H → b b ¯ $$ b\overline{b} $$ ) using the novel method of characteristic operator - Jiang Yan; Xing-Gang Wu; Jian-Ming Shen; Xu-Dong Huang; Zhi-Fei Wu (Journal of High Energy Physics)
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) D ̂ n γ , n β $$ {\hat{D}}_{n_{γ },{n}_{β }} $$ 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 b ¯ $$ b\overline{b} $$ ) under the MS ¯ $$ \overline{MS} $$ -scheme. Using the CO framework, its effective coupling α s (Q *) and effective b-quark MS ¯ $$ \overline{MS} $$ -mass m ¯ b Q ∗ $$ {\overline{m}}_b\left(Q_{*}\right) $$ are determined by absorbing all non-conformal {β i }-terms from the renormalization group equations for either α s or m ¯ b $$ {\overline{m}}_b $$ simultaneously. The PMC scale is fixed up to N3LL-accuracy, Q * = 55.2916 GeV and a scale-invariant total decay width is obtained, Γ H → b b ¯ = 2.3819 − 0.0231 + 0.0230 $$ Γ \left(H→ b\overline{b}\right)={2.3819}_{-0.0231}^{+0.0230} $$ MeV, whose errors are squared averages of the ones associated with ∆α s (M Z ) = ±0.0009, ∆M H = 0.11 GeV, Δ m ¯ b m ¯ b $$ Δ {\overline{m}}_b\left({\overline{m}}_b\right) $$ = ±0.007 GeV, and the uncalculated N5LO contributions ∆Γ = ±0.0001 MeV predicted via Bayesian analysis with the degree-of-belief DoB = 95.5%.