arXiv subjects

Zhi-Fei Wu

Publications and source records attributed to Zhi-Fei Wu.

8 recordsLinked to original sources

arXiv2026

Probability-based Estimates of the Uncalculated N$^5$LO QCD Contribution to the Hadronic $W$-Boson Decay Width

The perturbative QCD corrections to the hadronic decay width of the $W$ boson are currently known up to next-to-next-to-next-to-next-to-leading order ($\mathrm{N^4LO}$), whereas the exact $\mathrm{N^5LO}$ correction remains unavailable owing to its formidable computational complexity. In this work, we estimate the $\mathrm{N^5LO}$ contributions by adopting Bayesian analysis (BA). Before performing the estimation, the Principle of Maximum Conformality (PMC) is employed to improve the precision of the initial scale-dependent perturbative series. Through recursive application of the renormalization group equation, non-conformal terms are absorbed into the strong running coupling, yielding a scheme-independent, scale-invariant perturbative series with improved convergence. The PMC procedure determines an effective coupling $α_s(Q_*)$, with the PMC scale fixed as $Q_* = 100.102~\mathrm{GeV}$ at next-to-next-to-leading logarithmic accuracy. Based on the improved and more precise series, the $95.5\%$ BA credible interval yields an uncertainty of $Δδ_\mathrm{QCD}|_{\mathrm{PMC, BA}}^{\mathrm{N^5LO}} = \pm 1.0\times 10^{-5}$. The resulting hadronic branching ratio is $\mathcal{B}(W\to \text{hadrons})|_\mathrm{PMC} = (65.84\pm 1.54)\%$, which is consistent with experimental data within reasonable errors.

hep-ph↗

arXiv2026

A new method for estimating unknown one-order higher QCD corrections to the perturbative series using the linear regression through the origin

It is generally believed that the QCD theory is the fundamental theory for strong interactions. Due to the asymptotic freedom at the short distances, after proper factorization, one can predict the value of high-energy physical observable by using the perturbative QCD (pQCD). It has been demonstrated that by recursively using of renormalization group equation with the help of Principle of Maximum Conformality (PMC), one can eliminate conventional renormalization scheme-and-scale ambiguities existed in the initial fixed-order pQCD series. To extend the predictive power of pQCD, we are still facing the problem of how to reliably estimate the contributions from the unknown higher-order (UHO) terms. In this paper, using the PMC scheme-and-scale invariant series as the starting point, we suggest a novel method of using linear regression through the origin (LRTO) to fix the asymptotic form of the pQCD series, which subsequently predicts the reasonable magnitude of the one-order higher UHO-terms. As an explicit example, we apply the method to deal with the ratio $R_τ$, which has been calculated up to four-loop QCD corrections. Our results show that the LRTO method works well, demonstrating its reliability and significant predictive power for estimating the UHO-terms. Especially, we show that the scale-invariant and more convergent PMC series exhibits a much better predictive power with stability and reliability than the initial scale-dependent pQCD series.

hep-ph↗

arXiv2025

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

In this paper, a novel method via using the characteristic operator~(CO) ${\cal \hat{D}}_{n_γ, n_β}$ is proposed to extend the applicability of PMC, which is a theoretical generalization of previous PMC single-scale setting approach. 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 $α_s$ 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 $Γ(H\to b\bar{b})$ under the $\overline{\rm MS}$-scheme. Using the CO framework, its effective coupling $α_{s}(Q_{*})$ and effective $b$-quark $\overline{\rm MS}$-mass $\overline{m}_{b}(Q_{*})$ are determined by absorbing all non-conformal $\{β_{i}\}$-terms from the renormalization group equations for either $α_s$ or $\overline{m}_{b}$ 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, $Γ(H \to b\bar{b}) = 2.3819 _{-0.0231}^{+0.0230}$~MeV, whose errors are squared averages of the ones associated with $Δα_{s}(M_{Z}) = \pm 0.0009$, $ΔM_{H} = 0.11$~GeV, $Δ\overline{m}_{b}(\overline{m}_{b}) = \pm 0.007$~GeV, and the uncalculated N$^{5}$LO contributions $ΔΓ= \pm0.0001$~MeV predicted via Bayesian analysis with the degree-of-belief ${\rm DoB}=95.5\%$.

hep-ph↗

arXiv2024

Reanalysis of the top-quark pair production via the $e^+ e^-$ annihilation near the threshold region up to N$^3$LO QCD corrections

In this paper, we present an improved analysis of the top-quark pair production via the process $e^{+}e^{-}\to γ^{*}\to t\bar{t}$ near the threshold region up to next-to-next-to-next-to-leading order (N$^3$LO) QCD corrections. Near the threshold region, the top-quark velocity $v$ tends to zero, leading to Coulomb singularity. To achieve a reasonable prediction in the threshold region, we reconstruct the analytical expression for the Coulomb-terms up to N$^{3}$LO accuracy by using the PSLQ algorithm, whose numerical values agree well with the previous N$^3$LO-level calculations. It is found that the N$^{3}$LO series still has sizable renormalization scale dependence, and to improve the precision of the series, we apply the Principle of Maximum Conformality to eliminate such scale dependence. After that, the Coulomb part is resummed into a Sommerfeld-Gamow-Sakharov factor, which finally leads to a much more reasonable behavior near the threshold region.

hep-ph↗

arXiv2024

Precise determination of the top-quark on-shell mass $M_t$ via its scale-invariant perturbative relation to the top-quark $\overline{\rm MS}$ mass ${\overline m}_t({\overline m}_t)$

It has been shown that the principle of maximum conformality (PMC) provides a systematic way to solve conventional renormalization scheme and scale ambiguities. The scale-fixed predictions for physical observables using the PMC are independent of the choice of renormalization scheme -- a key requirement of renormalization group invariance. In the paper, we derive new degeneracy relations based on the renormalization group equations that involve both the usual $β$-function and the quark mass anomalous dimension $γ_m$-function, respectively. These new degeneracy relations lead to an improved PMC scale-setting procedures, such that the correct magnitudes of the strong coupling constant and the $\overline{\rm MS}$-running quark mass can be fixed simultaneously. By using the improved PMC scale-setting procedures, the renormalization scale dependence of the $\overline{\rm MS}$-on-shell quark mass relation can be eliminated systematically. Consequently, the top-quark on-shell (or $\overline{\rm MS}$) mass can be determined without conventional renormalization scale ambiguity. Taking the top-quark $\overline{\rm MS}$ mass ${\overline m}_t({\overline m}_t)=162.5^{+2.1}_{-1.5}$ GeV as the input, we obtain $M_t\simeq 172.41^{+2.21}_{-1.57}$ GeV. Here the uncertainties are combined errors with those also from $Δα_s(M_Z)$ and the approximate uncertainty stemming from the uncalculated five-loop terms predicted through the Padé approximation approach.

hep-ph↗

arXiv2023

Approximate N$^5$LO Higgs boson decay width $Γ(H\toγγ)$

The precision and predictive power of perturbative QCD (pQCD) prediction depends on both a precise, convergent fixed-order series and a reliable way of estimating the contributions of unknown higher-order (UHO) terms. It has been shown that by applying the Principal of Maximum Conformality (PMC), which applies the renormalization group equation recursively to set the effective magnitude of $α_s$ of the process, the remaining conformal coefficients will be well matched with the corresponding $α_s$ at each orders, leading to a scheme-and-scale invariant and convergent perturbative series. Thus different from conventional scheme-and-scale dependent fixed-order series, the PMC series will provide a more reliable platform for estimating UHO contributions. In this paper, by using the total decay width $Γ(H\toγγ)$ which has been calculated up to N$^4$LO QCD corrections, we derive its PMC series by using the PMC single-scale setting approach and estimate its unknown N$^5$LO contributions by using the Bayesian analysis. The Bayesian-based approach estimates the magnitude of the UHO contributions based on an optimized analysis of probability density distribution, and the predicted UHO contribution becomes more accurate when more loop terms have been known to tame the probability density function. Using the top-quark pole mass $M_t$=172.69 GeV and the Higgs mass $M_H$=125.25 GeV as inputs, we obtain $Γ(H\toγγ) =9.56504~{\rm keV}$ and the estimated N$^5$LO contribution to the total decay width is $ΔΓ_H=\pm1.65\times10^{-4}~{\rm keV}$ for the smallest credible interval of $95.5\%$ degree-of-belief.

hep-ph↗

arXiv2023

Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and Bayesian Analysis

In addition to the evaluation of high-order loop contributions, the precision and predictive power of perturbative QCD (pQCD) predictions depends on two important issues: (1) how to achieve a reliable, convergent fixed-order series, and (2) how to reliably estimate the contributions of unknown higher-order terms. The recursive use of renormalization group equation, together with the Principle of Maximum Conformality (PMC), eliminates the renormalization scheme-and-scale ambiguities of the conventional pQCD series. The result is a conformal, scale-invariant series of finite order which also satisfies all of the principles of the renormalization group. In this paper we propose a novel Bayesian-based approach to estimate the size of the unknown higher order contributions based on an optimized analysis of probability distributions. We show that by using the PMC conformal series, in combination with the Bayesian analysis, one can consistently achieve high degree of reliability estimates for the unknown high order terms. Thus the predictive power of pQCD can be greatly improved. We illustrate this procedure for two pQCD observables: $R_{e^+e^-}$ and $R_τ$, which are each known up to four loops in pQCD. Numerical analyses confirm that by using the scale-independent and more convergent PMC conformal series, one can achieve reliable Bayesian probability estimates for the unknown higher-order contributions.

hep-ph↗

arXiv2023

Precise perturbative predictions from fixed-order calculations

The intrinsic conformality is a general property of the renormalizable gauge theory, which ensures the scale-invariance of a fixed-order series at each perturbative order. Following the idea of intrinsic conformality, we suggest a novel single-scale setting approach under the principle of maximum conformality (PMC) with the purpose of removing the conventional renormalization scheme-and-scale ambiguities. We call this newly suggested single-scale procedure as the PMC$_{\infty}$-s approach, in which an overall effective $α_s$, and hence an overall effective scale is achieved by identifying the $\{β_0\}$-terms at each order. Its resultant conformal series is scale-invariant and satisfies all renormalization group requirements. The PMC$_{\infty}$-s approach is applicable to any perturbatively calculable observables, and its resultant perturbative series provides an accurate basis for estimating the contribution from the unknown higher-order (UHO) terms. Using the Higgs decays into two gluons up to five-loop QCD corrections as an example, we show how the PMC$_{\infty}$-s works, and we obtain $Γ_{\rm H}\big|_{\text{PMC}_{\infty}\text{-s}}^{\rm PAA} = 334.45^{+7.07}_{-7.03}~{\rm KeV}$ and $Γ_{\rm H}\big|_{\text{PMC}_{\infty}\text{-s}}^{\rm B.A.} = 334.45^{+6.34}_{-6.29}~{\rm KeV}$. Here the errors are squared averages of those mentioned in the body of the text. The Pad$\acute{e}$ approximation approach (PAA) and the Bayesian approach (B.A.) have been adopted to estimate the contributions from the UHO-terms. We also demonstrate that the PMC$_{\infty}$-s approach is equivalent to our previously suggested single-scale setting approach (PMCs), which also follows from the PMC but treats the $\{β_i\}$-terms from different point of view. Thus a proper using of the renormalization group equation can provide a solid way to solve the scale-setting problem.

hep-ph↗