arXiv subjects

Sheng-Quan Wang

Publications and source records attributed to Sheng-Quan Wang.

At least 19 recordsLinked to original sources

arXiv2026

Analysis of $H \to J/ψ+γ$ up to Next-to-Next-to-Leading Order QCD Corrections

The rare exclusive decay of the Higgs boson $H \to J/ψ+ γ$ is an important channel for measuring the Yukawa coupling of the charm quark. In this article, we analyze the process by employing the Principle of Maximum Conformality (PMC) up to the next-to-next-to-leading order (NNLO) in QCD. Conventional scale setting leads to theoretical predictions affected by errors dominated by renormalization scale uncertainty. The PMC provides a systematic method to eliminate this renormalization scale uncertainty by resumming non-conformal $β$ contributions into the QCD running coupling via renormalization group equation (RGE). We obtain a PMC scale result of $Q_\star = 3.29\ \text{GeV}$, which reflects the low virtuality of the underlying QCD dynamics for the $H \to J/ψ+ γ$ process. In fact, this is an order of magnitude smaller than the guessed scale using the conventional method, i.e., $μ_r = m_H/2$. By removing non-conformal $\{β_i\}$-terms from the perturbative QCD (pQCD) series, the PMC eliminates renormalization scale uncertainty. Comparing results, we find that the PMC NLO QCD correction term is significantly enhanced, while the PMC NNLO QCD correction is suppressed. This indicates improved convergence of the pQCD series up to NNLO. Finally, we determine the decay width $Γ(H \to J/ψ+ γ) = 14.183^{+0.249}_{-0.347} \pm 0.022$ eV, where the first error arises from the factorization scale $μ_Λ\in [1, 2]\ \text{GeV}$, and the second error from estimating unknown higher-order terms using the Pade approximant approach. The corresponding branching fraction is $\mathcal{B}(H \to J/ψ+ γ) = 3.485_{-0.161}^{+0.152} \times 10^{-6}$.

hep-ph↗

arXiv2026

NNLO QCD Corrections to $D$-Wave Spin-Singlet Heavy Quarkonia Decay $η_{Q2}\toγγ$ via the Principle of Maximum Conformality

In this paper, we perform a comprehensive study of the decay process $η_{Q2}\toγγ$ for $D$-wave spin-singlet heavy quarkonia up to next-to-next-to-leading-order (NNLO) QCD corrections within the nonrelativistic QCD effective theory. Following its factorization formalism, the total decay width is decomposed into perturbatively calculable short-distance coefficients (SDCs) and nonperturbative $D$-wave long-distance matrix elements (LDMEs). The original NNLO series of SDCs suffers from sizable renormalization and factorization scale uncertainties. To eliminate such inherent scale ambiguities, we adopt the Principle of Maximum Conformality (PMC). We show that recursively applying the renormalization group equations for the running of $α_s$ and $D$-wave LDMEs within the PMC framework yields an effective strong coupling $α_s(Q_\ast)$ consistent with the expansion coefficients, resulting in a scale-invariant perturbative series. The determined PMC scales are $Q_\ast=1.483$ GeV for $η_{c2}$ and $Q_\ast=4.246$ GeV for $η_{b2}$. By removing divergent renormalon contributions, the PMC naturally improves the convergence of the perturbative series for SDCs. Our PMC predictions for the total decay widths are $Γ_{η_{c2}\toγγ}^{\rm PMC} = 3.322^{+0.899}_{-0.828}\ \text{eV}$ and $Γ_{η_{b2}\toγγ}^{\rm PMC} = 0.0188^{+0.0014}_{-0.0013}\ \text{eV}$. The uncertainties arise from variations of the charm and bottom quark masses $Δm_c=\pm 0.07$ GeV, $Δm_b=\pm 0.06$ GeV, as well as systematic errors from uncalculated higher-order corrections. The corresponding branching ratios are $\text{Br}(η_{c2}\toγγ) = \big(7.463^{+2.020}_{-1.860}\big)\times 10^{-6}$ and $\text{Br}(η_{b2}\toγγ) = \big(6.460^{+0.481}_{-0.447}\big)\times 10^{-7}$.

hep-ph↗

arXiv2026

Non-perturbaitve effects for the isoscalar light vector $ω$-meson in charmed meson semileptonic decays

Motivated by the renewed attention from the recent BESIII experiment on the semileptonic decay $D\to V \ellν_{\ell}$, we investigate semileptonic decay $D^+\to ω\ell^+ν_{\ell}$ within the framework of QCD light-cone sum rule in this work. By constructing correlation function with right-handed chiral current, the transverse twist-2 light-cone distribution amplitudes (LCDA) $ϕ^{\perp}_{2;ω}(x,μ)$ dominates the contribution in TFFs. We study the properties of twist-2 LCDA $ϕ^{\perp}_{2;ω}(x,μ)$ through light-cone harmonic oscillator model. Applying it to the TFFs, we obtained $A_1(0)$, $A_2(0)$, $V(0)$, and $A_0(0)$ at large recoil point. Two TFF ratios are $r_V=1.40^{+0.21}_{-0.19}$ and $r_2=1.01^{+0.17}_{-0.16}$. After extrapolating those TFFs to the whole physical $q^2$ region by using the simplified $z(q^2,t)$ series expansion, the ratio of longitudinal and transverse decay widths is $Γ_{\rm{L}}/Γ_{\rm{T}}=0.987^{+0.107}_{-0.121}$. Then, we get branching fraction $\mathcal{B}(D^+\to ωe^+ν_e)=(1.848^{+0.365}_{-0.330})\times 10^{-3}$ and $\mathcal{B}(D^+\to ωμ^+ν_μ)=(1.782^{+0.334}_{-0.303})\times 10^{-3}$, which is in good agreement with BESIII and CLEO Collaborations. Taking into account the secondary decay $ω\to π^+π^-π^0$, we predict branching fraction of five body decay as $\mathcal{B}(D^+\to ω(\to π^+π^-π^0)e^+ν_{e})=(1.648^{+0.341}_{-0.305})\times 10^{-3}$ and $\mathcal{B}(D^+\to ω(\to π^+π^-π^0)μ^+ν_μ)=(1.589^{+0.313}_{-0.281})\times 10^{-3}$. Finally, we predict the forward-backward asymmetry $A_{\rm{FB}}^{\ell}$, lepton-side convexity parameter $C^{\ell}_{\rm{F}}$, longitudinal (transverse) polarization $P_{\rm{L}(\rm{T})}^{\ell}$, as well as longitudinal polarization fraction $F_{\rm{L}}^{\ell}$.

hep-ph↗

arXiv2026

Novel analysis for the energy-energy correlation in electron-positron annihilation in the perturbative domain

The energy-energy correlation (EEC) in electron-positron annihilation plays a crucial role in precision tests of quantum chromodynamics (QCD) and measurements of the QCD coupling constant. In this paper, we provide a novel analysis for the EEC by using the Principle of Maximum Conformality (PMC), a systematic method for eliminating renormalization scheme-and-scale ambiguities. The PMC scales are determined by resumming the non-conformal $β$-terms that govern the behavior of the QCD running coupling via the renormalization group equation, and reflect the virtuality of the propagating gluons in QCD. It is noteworthy that the resulting PMC scale varies dynamically with the EEC's angular distribution, reflecting the expected scale's physical behavior. Moreover, due to the reabsorption of all $β$-terms, including also those related to the divergent renormalon terms such as $n!β^n_0α^n_s$, in the pQCD series, the behavior of the QCD perturbative coefficient using PMC, differs entirely from that of the conventional coefficient. Consequently, the PMC predicted EEC distribution agrees well with the experimental data in the perturbative domain.

hep-ph↗

arXiv2025

Analysis of the Pion Electromagnetic Form Factor with Next-to-Next-to-Leading Order QCD Corrections

NNLO QCD corrections for the pion electromagnetic form factor at large momentum transfer have been recently performed in [Phys. Rev. Lett. 132, 201901 (2024); Phys. Rev. Lett. 134, 221901 (2025)], revealing that the NLO and NNLO contributions are positive and sizeable. Unfortunately, these predictions have been obtained using the conventional scale-setting method and thus they are plagued by large renormalization scale ambiguities. In this paper, we analyze the pion electromagnetic form factor at NNLO by applying the Principle of Maximum Conformality (PMC), which is introduced with the aim of resolving renormalization scheme and scale ambiguities. By applying the PMC, a more precise perturbative QCD (pQCD) prediction for the pion EMFF $Q^2F_π(Q^2)$ without conventional renormalization scale ambiguity can be achieved. This improved pQCD prediction is highly beneficial for the precise determination of the pion light-cone distribution amplitude. We then conduct a comprehensive comparison between theoretical predictions and experimental measurements of the pion EMFF $Q^2F_π(Q^2)$.

hep-ph↗

arXiv2025

Scheme-independent determination of the QCD running coupling at all scales from jet observables using the principle of maximum conformality and infinite-order scale setting

We present a new approach to determining the strong coupling $α_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $Λ_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the highest precision and using the data of a single experiment. In particular, we use the results obtained for the thrust ($T$) and $C$-parameter ($C$) distributions in $e^+e^-$ annihilation at a single annihilation energy $\sqrt{s}=M_Z$ (i.e.\ at the $Z^0$ peak). This new method is based on the \emph{intrinsic conformality} (iCF) and on the Infinite-Order Scale Setting, using the Principle of Maximum Conformality (i.e.\ the PMC$_\infty$), which allows a rigorous determination of the renormalization scales for the event-shape variable distributions satisfying all of the requirements of Renormalization Group Invariance, including renormalization-scheme independence and consistency with Abelian theory in the $N_C \to 0$ limit. This new method is based on the scale-invariance of the iCF, which allows determination of $α_s(μ_0)$ at any scale $μ_0$, and on the Maximum Likelihood statistical approach. We propose a novel approach to determining the best-fitting range by considering all possible intervals over the entire range of bins available in the perturbative region and selecting that which returns the most-likely-lowest $χ^2_{\rm min}$. This new method is designed to eliminate the errors that arise due to selection of the bin-interval and that have been neglected in previous analyses. In particular, using data for thrust and $C$-parameter at the $Z^0$ peak from ALEPH, OPAL, DELPHI and L3 experiments, we obtain the average value: $α_s(M_Z)= 0.1182^{+0.0007}_{-0.0007}$, for the strong coupling. This determination of $α_s(M_Z)$ is consistent with the world average...

hep-ph↗

arXiv2025

A reanalysis of event shape distributions in electron-positron annihilation

Theoretical calculations for event shape observables are often determined by using the conventional scale setting; i.e. the procedure defined by setting the renormalization scale to the center-of-mass energy $μ_r=\sqrt{s}$ and evaluating theoretical uncertainties by varying the same scale $μ_r$ in an arbitrary range. Both the event shape distributions and the extracted QCD coupling $α_s$ are plagued by the large renormalization scale uncertainties when using the conventional scale setting. The Principle of Maximum Conformality (PMC) provides a rigorous method to eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions. In this paper, we perform a detailed analysis of the event shape observables by applying the PMC method together with the use of the physical $V$-scheme. The PMC scales are not simple single-valued functions, but depend with continuity on the value of the unintegrated event shape variable. This reflects the virtuality of the underlying quark and gluon subprocess and yields to a physical behavior of the scale all over the entire range of each observable. Moreover, the PMC scales in the $V$-scheme exhibits a faster increase compared to the $\overline{\rm MS}$ scheme, and a better convergence in the perturbative series can be obtained. Results obtained by the PMC method for the event shape variables, thrust ($T$), heavy jet mass ($ρ=M^2_H/s$), wide jet broadening ($B_W$), total jet broadening ($B_T$), C-parameter ($C$), are in agreement with the high precision experimental data, and for the case of the jet transition variable $Y_3$, we obtain a first improvement in the results to some extent compared with the $\overline{\rm MS}$ scheme.

hep-ph↗

arXiv2025

Self-consistent analysis for the $η_c\rightarrow γγ$ process

The next-to-next-to-leading-order (NNLO) pQCD predictions for both the decay width and the transition form factor in the $η_c\rightarrow γγ$ process, based on nonrelativistic QCD (NRQCD), deviate from precise experimental measurements. These significant discrepancies have cast doubt on the applicability of NRQCD to charmonium processes. In this paper, we analyze the $η_c\rightarrow γγ$ process by applying the Principle of Maximum Conformality (PMC), a systematic method for eliminating renormalization scheme and scale ambiguities. The PMC renormalization scales are determined by absorbing the non-conformal $β$ terms which govern the behavior of the QCD running coupling via the Renormalization Group Equation. We obtain the PMC scale $Q_\star=4.49\,m_c$ for the $η_c\rightarrow γγ$ decay width. Even after using the PMC method, the convergence of the pQCD series is still poor, which indicates the importance of uncalculated NNNLO and higher-order terms. The resulting value for $Γ_{η_c\rightarrow γγ}$ is in agreement with the Particle Data Group's reported value of $Γ_{η_c\rightarrow γγ}=5.1\pm0.4$ keV within the bounds of uncertainties. Moreover, the transition form factor obtained using the PMC is also in good agreement with precise experimental measurements. The application of the PMC suggests a potential resolution to $η_c\rightarrow γγ$ puzzle and supports the applicability of NRQCD to charmonium processes.

hep-ph↗

arXiv2025

The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem

In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can be served as a mini review of PMC. We emphasize that the purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization scheme and scale ambiguities. We demonstrate that the PMC predictions satisfy all of the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann--Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially-divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.

hep-ph↗

arXiv2025

Probing $|V_{cs}|$ and lepton flavor universality through $D\to K_0^\ast(1430)\ellν_{\ell}$ decay

In this paper, we calculate the semileptonic decays $D\to K_0^\ast(1430)\ellν_{\ell}$ with $\ell=(e,μ)$ induced by $c\to s\ellν_{\ell}$ transition. For the key component, $D\to K_0^\ast(1430)$ transition form factors (TFFs) $f_{\pm}(q^2)$ are calculated within the framework of QCD light cone sum rule. Then, we consider two scenarios for $K_0^\ast(1430)$-meson twist-2 distribution amplitude. For the scenario 1 (S1), we take the truncated form based on Gegenbauer polynomial series. Meanwhile, we also consider the scenario 2 (S2) constructed by light cone harmonic oscillator model, where the model parameters are fixed by the $K_0^\ast(1430)$-meson twist-2 distribution amplitude tenth-order $ξ$ moments calculated by using the background field theory. For the TFFs at a large recoil point, we have $f_+^{\rm (S1)}(0)=0.597^{+0.122}_{-0.121}$ and $f_-^{\rm (S1)}(0)=-0.136^{+0.023}_{-0.035}$, $f_+^{\rm (S2)}(0)= 0.663^{+0.135}_{-0.134}$, and $f_-^{\rm (S2)}(0)=-0.202^{+0.026}_{-0.046}$. After extrapolating TFFs to the whole physical $q^2$ region, we calculate the branching fractions of $D^0\to K_0^{\ast +}(1430)\ell^-\barν_\ell$ and $D^+\to K_0^{\ast 0}(1430)\ell^+ν_\ell$, which at $10^{-4}$-order level for the S1 and S2 cases. Meanwhile, we predict the CKM matrix $|V_{cs}|^{\rm (S1)}=0.973^{+0.259}_{-0.183}, |V_{cs}|^{\rm (S2)}=0.880^{+0.234}_{-0.165}$, and lepton flavor universality $\mathcal{R}^{\rm (S1)}_{K_0^*}=0.768^{+0.560}_{-0.368}, \mathcal{R}_{K_0^*}^{\rm (S2)}=0.764^{+0.555}_{-0.365}$. Finally, we discuss the angular observables of forward-backward asymmetries, lepton polarization asymmetries, and $q^2$-differential flat terms for this decay.

hep-ph↗

arXiv2024

Revisiting the top-quark pair production at future $e^+e^-$ colliders

In this paper, we reanalyze the top-quark pair production at the next-to-next-to-leading order (NNLO) in QCD at future $e^+e^-$ colliders by using the Principle of Maximum Conformality (PMC) method. The PMC renormalization scales in $α_s$ are determined by absorbing the non-conformal $β$ terms by recursively using the Renormalization Group Equation (RGE). Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energy $μ_r=\sqrt{s}$, the determined PMC scale $Q_\star$ is far smaller than the $\sqrt{s}$ and increases with the $\sqrt{s}$, yielding the correct physical behavior for the top-quark pair production process. Moreover, the convergence of the pQCD series for the top-quark pair production is greatly improved due to the elimination of the renormalon divergence. For a typical collision energy of $\sqrt{s}=500$ GeV, the PMC scale is $Q_\star=107$ GeV; the QCD correction factor $K$ for conventional results is $K\sim1+0.1244^{+0.0102+0.0012}_{-0.0087-0.0011}+0.0184^{-0.0086+0.0002}_{+0.0061-0.0003}$, where the first error is caused by varying the scale $μ_r\in[\sqrt{s}/2, 2\sqrt{s}]$ and the second error is from the top-quark mass $Δ{m_t}=\pm0.7$ GeV. After applying the PMC, the renormalization scale uncertainty is eliminated and the QCD correction factor $K$ is improved to $K\sim 1+0.1507^{+0.0015}_{-0.0015}-0.0057^{+0.0001}_{-0.0000}$, where the error is from the top-quark mass $Δ{m_t}=\pm0.7$ GeV. The PMC improved predictions for the top-quark pair production are helpful for detailed studies of properties of the top-quark at future $e^+e^-$ colliders.

hep-ph↗

arXiv2023

High precision tests of QCD without scale or scheme ambiguities

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale $μ_R$ and thus determining the correct values of the QCD running coupling $α_s(μ_R^2)$ at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process $Q$ and vary it in the range $μ_R \in [Q/2,2Q]$ in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist's choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann--Low scheme in the $N_C\to 0$ Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. [full abstract is in the paper].

hep-ph↗

arXiv2023

Elimination of QCD Renormalization Scale and Scheme Ambiguities

We present results for the thrust distribution in the electron positron annihilation to the three jet process at NNLO in the perturbative conformal window of QCD, as a function of the number of flavors $N_f$. Given the existence of an infrared interacting fixed point in this region, we can compare the Conventional Scale Setting (CSS) and the Principle of Maximum Conformality (PMC$_\infty$) methods along the entire renormalization group flow from the highest energies to zero energy. We then consider also the QED thrust, obtained as the limit $N_c \rightarrow 0$ of the number of colors and we show analogous comparison. QED in the low energy regime develops an infrared non-interacting fixed point. Using these quantum field theory limits as theoretical laboratories, we arrive at interesting results showing new features of the PMC$_\infty$.

hep-ph↗

arXiv2023

Novel Method to Reliably Determine the QCD Coupling from $R_{\rm uds}$ Measurements and its effects to Muon $g-2$ and $α(M_Z^2)$ within the Tau-Charm Energy Region

We present a novel method for precisely determining the QCD running coupling from $R_{\rm uds}$ measurements in electron-positron annihilation. When calculating the fixed-order perturbative QCD (pQCD) approximant of $R_{\rm uds}$, its effective coupling constant $α_s(Q_*^2)$ is determined by using the principle of maximum conformality, a systematic scale-setting method for gauge theories, whose resultant pQCD series satisfies all the requirements of renormalization group. Contribution due to the uncalculated higher-order (UHO) terms is estimated by using the Bayesian analysis. Using $R_{\rm uds}$ data measured by the KEDR detector at $22$ centre-of-mass energies between $1.84$ GeV and $3.72$ GeV, we obtain $α_s(M_Z^2)=0.1227^{+0.0117}_{-0.0132}({\rm exp.})\pm0.0016({\rm the.})$, where the theoretical uncertainty (the.) is negligible compared to the experimental one (exp.). Numerical analyses confirm that the new method for calculating $R_{\rm uds}$ removes conventional renormalization scale ambiguity, and the residual scale dependence due to the UHO-terms will also be highly suppressed due to a more convergent pQCD series. This leads to a significant stabilization of the perturbative series, and a significant reduction of theoretical uncertainty. It thus provides a reliable theoretical basis for precise determination of the QCD running coupling from $R_{\rm uds}$ measurements at future Tau-Charm Facility. It can also be applied for the precise determination of the hadronic contributions to muon $g-2$ and QED coupling $α(M_Z^2)$ within the tau-charm energy range.

hep-ph↗

arXiv2023

Elimination of QCD Renormalization Scale and Scheme Ambiguities

The setting of the renormalization scale ($μ_r$) in the perturbative QCD (pQCD) is one of the crucial problems for achieving precise fixed-order pQCD predictions. The conventional prescription is to take its value as the typical momentum transfer $Q$ in a given process, and theoretical uncertainties are then evaluated by varying it over an arbitrary range. The conventional scale-setting procedure introduces arbitrary scheme-and-scale ambiguities in fixed-order pQCD predictions. The principle of maximum conformality (PMC) provides a systematic way to eliminate the renormalization scheme-and-scale ambiguities. The PMC method has rigorous theoretical foundations; it satisfies the renormalization group invariance (RGI) and all of the self-consistency conditions derived from the renormalization group. The PMC has now been successfully applied to many physical processes. In this paper, we summarize recent PMC applications, including event shape observables and heavy quark pair production near the threshold region in $e^+e^-$ annihilation and top-quark decay at hadronic colliders. In addition, estimating the contributions related to the uncalculated higher-order terms is also summarized. These results show that the major theoretical uncertainties caused by different choices of $μ_r$ are eliminated, and the improved pQCD predictions are thus obtained, demonstrating the generality and applicability of the PMC.

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

QCD improved top-quark decay at next-to-next-to-leading order

We analyse the top-quark decay at the next-to-next-to-leading order (NNLO) in QCD by using the Principle of Maximum Conformality (PMC) which provides a systematic way to eliminate renormalization scheme and scale ambiguities in perturbative QCD predictions. The PMC renormalization scales of the coupling constant $α_s$ are determined by absorbing the non-conformal $β$ terms that govern the behavior of the running coupling by using the Renormalization Group Equation (RGE). We obtain the PMC scale $Q_\star=15.5$ GeV for the top-quark decay, which is an order of magnitude smaller than the conventional choice $μ_r=m_t$, reflecting the small virtuality of the QCD dynamics of the top-quark decay process. Moreover, due to the non-conformal $β$ terms disappear in the pQCD series, there is no renormalon divergence and the NLO QCD correction term is greatly increased while the NNLO QCD correction term is suppressed compared to the conventional results obtained at $μ_r=m_t$. By further including the next-to-leading (NLO) electroweak corrections, the finite $W$ boson width and the finite bottom quark mass, we obtain the top-quark total decay width $Γ^{\rm tot}_t=1.3112^{+0.0190}_{-0.0189}$ GeV, where the error is the squared averages of the top-quark mass $Δm_t=\pm0.7$ GeV, the coupling constant $Δα_s(M_Z)=\pm0.0009$ and the estimation of unknown higher-order terms using the PAA method with [N/M]=[1/1]. The PMC improved predictions for the top-quark decay are complementary to the previous PMC calculations for top-quark pair production and helpful for detailed studies of properties of the top-quark.

hep-ph↗

arXiv2022

New analyses of event shape observables in electron-positron annihilation and the determination of $α_s$ running behavior in perturbative domain

In this paper, we give comprehensive analyses for event shape observables in electron-positron annihilation by using the Principle of Maximum Conformality (PMC) which is a rigorous scale-setting method to eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions. Conventionally the renormalization scale and theoretical uncertainties in event shape observables are often evaluated by setting the scale to the center-of-mass energy $\sqrt{s}$. The event shape distributions using this conventional scale setting are plagued by the large renormalization scale uncertainty and underestimate the experimental data. Moreover, since the renormalization scale is simply fixed to the center-of-mass energy $\sqrt{s}$, only one value of the coupling $α_s$ at the single scale $\sqrt{s}$ can be extracted. In contrast, the PMC renormalization scales are determined by absorbing the nonconformal $β$ contributions that govern the behavior of the running coupling via the Renormalization Group Equation (RGE). The resulting PMC scales change with event shape kinematics, reflecting the virtuality of the underlying quark and gluon subprocess. The PMC scales thus yield the correct physical behavior of the scale and the PMC predictions agree with precise event shape distributions measured at the LEP experiment. More importantly, we can precisely determine the running of the QCD coupling constant $α_s(Q^2)$ over a wide range of $Q^2$ in perturbative domain from event shape distributions measured at a single center-of-mass energy $\sqrt{s}$.

hep-ph↗