arXiv subjects

Jiang Yan

Publications and source records attributed to Jiang Yan.

At least 19 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 $\alpha_s(Q_*)$, 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 $\Delta\delta_\mathrm{QCD}|_{\mathrm{PMC, BA}}^{\mathrm{N^5LO}} = \pm 1.0\times 10^{-5}$. 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

EEXICC: An event generator for doubly heavy baryon production at $e^+e^-$ colliders

We present EEXICC, a Monte Carlo event generator designed to simulate the production of doubly heavy baryons ($\Xi_{cc}$, $\Xi_{bc}$, and $\Xi_{bb}$) via $e^+e^-$ annihilation. Based on nonrelativistic QCD effective theory, the generator calculates the process $e^{+}+e^{-}\rightarrow \Xi_{QQ'}+\bar{Q}'+\bar{Q}$ using an improved trace technique at the amplitude level, which greatly improves numerical efficiency compared with traditional squared-amplitude methods. EEXICC is developed in Fortran with a modular structure and is fully compatible with the PYTHIA framework, enabling convenient integration into complete event simulation workflows. The program supports both weighted and unweighted event generation, and its numerical reliability has been verified against existing theoretical results. EEXICC provides a flexible and robust tool for studying the properties of doubly heavy baryons at future high-luminosity and high-energy $e^+e^-$ colliders such as the CEPC and FCC-ee.

hep-ph↗

arXiv2026

Renormalization and Factorization Scale-Invariant Predictions for the Higgs Rare Decay $H\to J/\psi+\gamma$ via the Principle of Maximum Conformality

We investigate the $J/\psi$ direct production mechanism in the rare exclusive Higgs decay $H\to J/\psi+\gamma$ within nonrelativistic QCD (NRQCD), which provides a clean probe for extracting the charm-quark Yukawa coupling to the Higgs boson. The Principle of Maximum Conformality (PMC) is used to remove conventional renormalization-scheme and scale ambiguities in the next-to-next-to-leading-order (N$^2$LO) perturbative QCD series. Large logarithmic contributions arising from Yukawa coupling renormalization are resummed, providing a reliable foundation for subsequent analyses. Using the experimentally measured leptonic decay width of $J/\psi$ and the N$^2$LO perturbative result, we extract the factorization-scale-dependent long-distance matrix element $\langle J/\psi({\bm \epsilon})|\psi^{\dagger}{\bm \sigma}\cdot{\bm \epsilon}\chi(\mu_\Lambda) |0\rangle$. Combining this with the factorization-scale-dependent short-distance coefficient, we obtain a factorization-scale-invariant decay width for the channel. Compared with earlier predictions in the literature, our fixed-order result for $\Gamma(H\to J/\psi+\gamma)$ is more robust and precise, with good convergence and no renormalization- or factorization-scale dependence. We find $\Gamma(H\to J/\psi+\gamma) = (6.4574^{+0.3995}_{-0.3995}) \times 10^{-11}$ GeV, where the uncertainty is the quadratic sum of contributions from $\Delta\alpha_s(m_Z) = \pm 0.0009$, $\Delta\Gamma_{J/\psi\to e^+e^-} = \pm 0.10\ \text{GeV}$, $\Delta\overline{m}_c(\overline{m}_c) = \pm 0.0046\ \text{GeV}$, and the estimated magnitude of N$^3$LO contributions from Bayesian analysis. This work demonstrates for the first time how the PMC can be applied to obtain fixed-order perturbative predictions that are invariant under both renormalization and factorization scale variations.

hep-ph↗

arXiv2026

Low-energy scattering of the $J/\psi \pi$ and $J/\psi K$ system

We investigate the low-energy interactions between the charmonium state $J/\psi$ and the light pseudoscalar mesons ($\pi$ and $K$) within the framework of dispersion relations. We demonstrate that the symmetry-breaking terms in the chiral Lagrangian induce mixing between the bare charmonium fields, necessitating a diagonalization procedure to correctly identify the physical $J/\psi$ and $\psi'$ states. Using the resulting diagonalized Lagrangian, we construct the crossed-channel amplitudes for $J/\psi J/\psi \to {\cal P}\bar{\cal P}$ and incorporate the $\pi\pi$ and $K\bar{K}$ rescattering effects through dispersion relations. This framework is used consistently both in the phenomenological extraction of the transition parameters from $\psi' \to J/\psi\pi\pi$ and in the continuation of the crossed amplitudes to the near-threshold $J/\psi{\cal P}~({\cal P}=\pi,K)$ region. As a result, we determine both the scattering lengths and the effective ranges. We obtain the upper-bound estimates $a_{J/\psi\pi}\lesssim -0.0037$~fm and $a_{J/\psi K}\lesssim -0.049$~fm, where the negative sign indicates an attractive interaction without a bound state in our convention. Our results show that the $J/\psi K$ interaction is moderately enhanced relative to the pion channel, driven by explicit chiral symmetry breaking. Furthermore, a quantitative comparison of the coupled-channel mechanism, where $J/\psi\pi$ and $J/\psi K$ couple to open-charm channels, reveals that both $J/\psi\pi$ and $J/\psi K$ scatterings are predominantly governed by the soft-gluon exchange mechanism.

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 $Q^2F_\pi(Q^2)$ 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 $Q^2F_\pi(Q^2)$.

hep-ph↗

arXiv2025

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 $R_\tau$, 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↗

arXiv2024

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

In this paper, a novel method via using the characteristic operator~(CO) ${\cal \hat{D}}_{n_{\gamma}, n_{\beta}}$ 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 $\overline{\rm MS}$-scheme. Using the CO framework, its effective coupling $\alpha_{s}(Q_{*})$ and effective $b$-quark $\overline{\rm MS}$-mass $\overline{m}_{b}(Q_{*})$ 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, $Q_{*} = 55.2916$~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 $\Delta\Gamma= \pm0.0001$~MeV predicted via Bayesian analysis with the degree-of-belief ${\rm DoB}=95.5\%$.

hep-ph↗

arXiv2024

BioDeepHash: Mapping Biometrics into a Stable Code

With the wide application of biometrics, more and more attention has been paid to the security of biometric templates. However most of existing biometric template protection (BTP) methods have some security problems, e.g. the problem that protected templates leak part of the original biometric data (exists in Cancelable Biometrics (CB)), the use of error-correcting codes (ECC) leads to decodable attack, statistical attack (exists in Biometric Cryptosystems (BCS)), the inability to achieve revocability (exists in methods using Neural Network (NN) to learn pre-defined templates), the inability to use cryptographic hash to guarantee strong security (exists in CB and methods using NN to learn latent templates). In this paper, we propose a framework called BioDeepHash based on deep hashing and cryptographic hashing to address the above four problems, where different biometric data of the same user are mapped to a stable code using deep hashing instead of predefined binary codes thus avoiding the use of ECC. An application-specific binary string is employed to achieve revocability. Then cryptographic hashing is used to get the final protected template to ensure strong security. Ultimately our framework achieves not storing any data that would leak part of the original biometric data. We also conduct extensive experiments on facial and iris datasets. Our method achieves an improvement of 10.12$\%$ on the average Genuine Acceptance Rate (GAR) for iris data and 3.12$\%$ for facial data compared to existing methods. In addition, BioDeepHash achieves extremely low False Acceptance Rate (FAR), i.e. 0$\%$ FAR on the iris dataset and the highest FAR on the facial dataset is only 0.0002$\%$.

cs.CR↗

arXiv2024

Improved analysis of the decay width of $t\to Wb$ up to N$^{3}$LO QCD corrections

In this paper, we analyze the top-quark decay $t\to Wb$ up to next-to-next-to-next-to-leading order (N$^{3}$LO) QCD corrections. For the purpose, we first adopt the principle of maximum conformality (PMC) to deal with the initial pQCD series. Then we adopt the Bayesian analysis approach, which quantifies the unknown higher-order terms' contributions in terms of a probability distribution, to estimate the possible magnitude of the uncalculated N$^{4}$LO-terms. In our calculation, an effective strong coupling constant $\alpha_{s}(Q_{*})$ is determined by using all non-conformal $\{\beta_{i}\}$ terms associated with the renormalization group equation. This leads to a next-to-leading-log PMC scale $Q_{*}^{(\rm NLL)}=10.3048$ GeV, which can be regarded as the correct momentum flow of the process. Consequently, we obtain an improved scale-invariant pQCD prediction for the top-quark decay width, e.g. $\Gamma_{t}^{\rm tot} = 1.3120 \pm 0.0038$ GeV, whose error is the squared average of the uncertainties from the decay width of $W$-boson $\Delta \Gamma_{W} = \pm 0.042$ GeV, the coupling constant $\Delta \alpha_{s}(m_{Z}) = \pm 0.0009$, and the predicted N$^{4}$LO-terms. The magnitude of the top-quark pole mass greatly affects the total decay width. By further taking the PDG top-quark pole mass error from cross-section measurements into consideration, e.g. $\Delta m_{t} = \pm 0.7$ GeV, we obtain $\Gamma_{t}^{\rm tot} = 1.3120 ^{+0.0194}_{-0.0192}$ GeV.

hep-ph↗

arXiv2024

Improved analysis of double $J/\psi$ production in $Z$-boson decay

In this paper, we present an improved calculation for the decay rate of the rare $Z$-boson decay into $J/\psi + J/\psi$. This decay is dominated by the photon fragmentation mechanism, i.e., the transition $Z\to J/\psi + \gamma^{*}$ followed by the fragmentation $\gamma^{*}\to J/\psi$. In our calculation, the amplitude of $\gamma^{*}\to J/\psi$ is extracted from the measured value of $\Gamma(J/\psi \to e^+ e^-)$, and the amplitude of $Z\to J/\psi + \gamma^{*}$ is calculate through the light-cone approach. The higher-order QCD and relativistic corrections in the amplitude of $\gamma^{*}\to J/\psi$ and the large logarithms of $m_{_Z}^2/m_c^2$ that appear in the amplitude of $Z\to J/\psi + \gamma^{*}$ are resummed in our calculation. Besides, the non-fragmentation amplitude is calculated based on the NRQCD factorization, and the next-to-leading order QCD and relativistic corrections are included. The obtained branching fraction for this $Z$ decay channel is $8.66 ^{+1.48} _{-0.69}\times 10^{-11}$.

hep-ph↗

arXiv2023

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 $e^{+}e^{-}\to \gamma^{*}\to t\bar{t}$ 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↗

arXiv2023

Approximate N$^5$LO Higgs boson decay width $\Gamma(H\to\gamma\gamma)$

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 $\alpha_s$ of the process, the remaining conformal coefficients will be well matched with the corresponding $\alpha_s$ 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 $\Gamma(H\to\gamma\gamma)$ 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 $\Gamma(H\to\gamma\gamma) =9.56504~{\rm keV}$ and the estimated N$^5$LO contribution to the total decay width is $\Delta\Gamma_H=\pm1.65\times10^{-4}~{\rm keV}$ for the smallest credible interval of $95.5\%$ degree-of-belief.

hep-ph↗

arXiv2023

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↗

arXiv2023

An updated determination of the pion-photon transition form factor

In this paper, we study the properties of the pion-photon transition form factor (TFF), $\gamma\gamma^{\ast} \rightarrow \pi^{0}$, by using the principle of maximum commonality (PMC) to deal with its perturbative QCD contribution up to next-to-next-to-leading order (NNLO) QCD corrections. Applying the PMC, we achieve precise pQCD approximant for the TFF in large $Q^2$-region without conventional renormalization scale ambiguity. We also discuss the power suppressed non-valence quark contribution to the TFF, which is important for a sound prediction in low and intermediate $Q^2$-region, e.g. the non-valence quark components affect the TFF by about $1\%$ to $23\%$ when $Q^{2}$ changes down from $40~{\rm GeV^{2}}$ to $4~{\rm GeV^{2}}$. The resultant pion-photon TFF shows a better agreement with previous Belle data. It is hoped that previous discrepancies between the experimental measurements and theoretical predictions could be clarified by the forth-coming precise data on the Belle II measurements.

hep-ph↗

arXiv2023

Novel Method to Reliably Determine the QCD Coupling from $R_{\rm uds}$ Measurements and its effects to Muon $g-2$ and $\alpha(M_Z^2)$ 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 $\alpha_s(Q_*^2)$ 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 $\alpha_s(M_Z^2)=0.1227^{+0.0117}_{-0.0132}({\rm exp.})\pm0.0016({\rm the.})$, 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 $\alpha(M_Z^2)$ within the tau-charm energy range.

hep-ph↗

arXiv2022

Hadronic production of $\Xi_{bc}$ with the intrinsic heavy-quark content at a fixed-target experiment at the LHC

In this paper, we make a detailed study on the hadronic production of the $\Xi_{bc}$ baryon at a fixed target experiment at the LHC (After@LHC). In estimating the production cross sections, the $(g+g)$, $(g+c)$ and $(g+b)$ production mechanisms are considered. For the initial heavy quarks, in addition to the extrinsic component, we also consider the intrinsic component. It is found that the $(g+c)$ and $(g+b)$ production mechanisms give sizable contributions to the $\Xi_{bc}$ production, and the $(g+b)$ mechanism dominates the production. The results show that there are about $3.40\times10^5$ $\Xi_{bc}$ events can be produced per year at After@LHC if the integrated luminosity of After@LHC can be up to $2\,{\rm fb}^{-1}$ per year. Moreover, the intrinsic heavy quarks can have significant impact on the production, which inversely makes the intrinsic component be possibly tested at the After@LHC.

hep-ph↗

arXiv2022

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 $\alpha_s$, and hence an overall effective scale is achieved by identifying the $\{\beta_0\}$-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 $\Gamma_{\rm H}\big|_{\text{PMC}_{\infty}\text{-s}}^{\rm PAA} = 334.45^{+7.07}_{-7.03}~{\rm KeV}$ and $\Gamma_{\rm H}\big|_{\text{PMC}_{\infty}\text{-s}}^{\rm B.A.} = 334.45^{+6.34}_{-6.29}~{\rm KeV}$. 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 $\{\beta_i\}$-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↗

arXiv2022

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 $\beta$-function and the quark mass anomalous dimension $\gamma_m$-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 $\Delta \alpha_s(M_Z)$ and the approximate uncertainty stemming from the uncalculated five-loop terms predicted through the Pad\'{e} approximation approach.

hep-ph↗