Scale-invariant total decay width Γ(H → $$ b\overline{b} $$) using the novel method of characteristic operator
Year: 2025
Type: article
Abstract: A bstract 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) $$ {\hat{D}}_{n_{\gamma },{n}_{\beta }} $$ 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 N 4 LO total decay width Γ( H → $$ b\overline{b} $$ b b ¯ ) under the $$ \overline{\textrm{MS}} $$ MS ¯ -scheme. Using the CO framework, its effective coupling α s ( Q * ) and effective b -quark $$ \overline{\textrm{MS}} $$ MS ¯ -mass $$ {\overline{m}}_b\left({Q}_{\ast}\right) $$ m ¯ b Q ∗ are determined by absorbing all non-conformal { β i }-terms from the renormalization group equations for either α s or $$ {\overline{m}}_b $$ m ¯ b simultaneously. The PMC scale is fixed up to N 3 LL-accuracy, Q * = 55 . 2916 GeV and a scale-invariant total decay width is obtained, $$ \Gamma \left(H\to b\overline{b}\right)={2.3819}_{-0.0231}^{+0.0230} $$ Γ H → b b ¯ = 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 .
Source: Journal of High Energy Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Awards: G3062115224, G4337271518, G4763861809
OpenAlex ID: W4409790674