Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator

Abstract

In this paper, a novel method via using the characteristic operator~(CO) ${\hat{\mathcal{D}}}_{n_{\gamma },n_{\beta }}$ is proposed to extend the applicability of PMC, which is a theoretical generalization of previous PMC single-scale setting approach. Using the CO formulism, we are able to facilitate the derivation of complex scenarios within a structured theoretical framework, leading to simpler procedures and more compact expressions. 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 ${\alpha }_s$ 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 $\Gamma (H\to b\bar{b})$ under the $\overline{\mathrm{MS}}$-scheme. Using the CO framework, its effective coupling ${\alpha }_s(Q_{\ast })$ and effective $b$-quark $\overline{\mathrm{MS}}$-mass ${\overline{m}}_b(Q_{\ast })$ are determined by absorbing all non-conformal $\{{\beta }_i\}$-terms from the renormalization group equations for either ${\alpha }_s$ or ${\overline{m}}_b$ simultaneously. The PMC scale is fixed up to N${}^3$LL-accuracy, $Q_{\ast }=55.2916$~GeV and a scale-invariant total decay width is obtained, $\Gamma (H\to b\bar{b})=2.3819_{-0.0231}^{+0.0230}$~MeV, whose errors are squared averages of the ones associated with $\Delta {\alpha }_s(M_Z)=\pm 0.0009$, $\Delta M_H=0.11$~GeV, $\Delta {\overline{m}}_b({\overline{m}}_b)=\pm 0.007$~GeV, and the uncalculated N${}^5$LO contributions $\Delta \Gamma =\pm 0.0001$~MeV predicted via Bayesian analysis with the degree-of-belief $\mathrm{DoB}=95.5\%$.

arXiv comment27 pages, 4 figures

References in corpus (61)

• Renormalons
• Five-Loop Running of the QCD coupling constant
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• Quark Mass Anomalous Dimension to alpha_s**4
• The five-loop beta function of Yang-Mills theory with fermions
• Naive nonabelianization and resummation of fermion bubble chains
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• Correlator of the quark scalar currents and Γ_{tot}(H --> hadrons) at O(α_s^3) in pQCD
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• Quark Mass and Field Anomalous Dimensions to $\mathcal{O}({\alpha }_s^5)$
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
• The Renormalization Scale-Setting Problem in QCD
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• Meaningful characterisation of perturbative theoretical uncertainties
• The large top quark mass expansion for Higgs boson decays into bottom quarks and into gluons
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• On Higgs decays to hadrons and the R-ratio at N^4LO
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Aspects of SU(N_c) Gauge Theories in the Limit of Small Number of Colors
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• Completing the hadronic Higgs boson decay at order ${\alpha }_s^4$
• An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Massless correlators of vector, scalar and tensor currents in position space at orders alpha_s^3 and alpha_s^4: explicit analytical results
• Complete QCD Corrections of Order O(α_s^3) to the Hadronic Higgs Decay
• Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy
• Exact Top Yukawa corrections to Higgs boson decay into bottom quarks
• Higgs Decay to Top Quarks at O(α_s^2)
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• $Gamma(H\to b\bar{b})$ to order $\alpha {\alpha }_s$
• Extending the Predictive Power of Perturbative QCD
• The Higgs boson inclusive decay channels $H\to b\bar{b}$ and $H\to gg$ up to four-loop level
• The order $O(\bar{\alpha }{\bar{\alpha }}_s)$ and $O({\bar{\alpha }}^2)$ corrections to the decay width of the neutral Higgs boson to the $\bar{b}b$ pair
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• Setting the Renormalization Scale in pQCD: Comparisons of the Principle of Maximum Conformality with the Sequential Extended Brodsky-Lepage-Mackenzie Approach
• The Generalized Scheme-Independent Crewther Relation in QCD
• Precise perturbative predictions from fixed-order calculations
• Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and Bayesian Analysis
• Renormalization group summation and analytic continuation from spacelike to timeline regions
• Novel Method to Reliably Determine the QCD Coupling from $R_{\mathrm{uds}}$ Measurements and its effects to Muon $g-2$ and $\alpha (M_Z^2)$ within the Tau-Charm Energy Region
• Analytic decay width of the Higgs boson to massive bottom quarks at order ${\alpha }_s^3$
• Gauge dependence of the perturbative QCD predictions under the momentum space subtraction scheme
• Analytic decay width of the Higgs boson to massive bottom quarks at next-to-next-to-leading order in QCD
• Reanalysis of the Higgs-boson decay $H\to gg$ up to ${\alpha }_s^6$-order level using the principle of maximum conformality
• Higher-order QCD corrections to $H\to b\bar{b}$ from rational approximants
• Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders
• The $\{\beta \}$-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order $O({\alpha }_s^4)$
• Reanalysis of the top-quark pair production via the $e^{+}{e}^{-}$ annihilation near the threshold region up to N${}^3$LO QCD corrections
• Precise determination of the top-quark on-shell mass $M_t$ via its scale-invariant perturbative relation to the top-quark $\overline{\mathrm{MS}}$ mass ${\overline{m}}_t({\overline{m}}_t)$
• Adler function, Bjorken polarized sum rule: confirmation of elements of the $\{\beta \}$-expansion and the diagrams
• Approximate N${}^5$LO Higgs boson decay width $\Gamma (H\to \gamma \gamma )$
• Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\mathrm{MS}}$-scheme running mass
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Renormalization-group improved Higgs to two gluons decay rate

Cited by in corpus (1)

• Higgs boson decay to massive bottom quarks at order ${\alpha }_s^4$ induced by top-quark Yukawa couplings