arXiv subjects

Xu-Dong Huang

Publications and source records attributed to Xu-Dong Huang.

At least 19 recordsLinked to original sources

arXiv2026

Semi-analytical results for $e^+e^-\to J/ψ+ X_{{\rm non\,}c\bar{c}}$ up to $\mathcal{O}(α_s v^2)$ at B factories

Within the NRQCD factorization framework, we investigate the color-singlet contribution to $e^+e^- \to J/ψ+ X_{{\rm non\,}c\bar{c}}$ at B factories, computing the $\mathcal{O}(α_s)$, $\mathcal{O}(v^2)$, and $\mathcal{O}(α_s v^2)$ corrections to both the unpolarized cross section and the $J/ψ$ angular distribution. The $\mathcal{O}(α_s v^2)$ correction is obtained for the first time, and the validity of NRQCD factorization at this order is explicitly verified. Using the differential equation method, the short-distance coefficients are obtained as asymptotic expansions in $r = m_c/\sqrt{s}$ up to $r^{40}$, which reproduce exact results with high precision at B factory energies, achieving relative errors around $10^{-14}$ for the cross section and around $10^{-7}$ for the angular distribution. Notably, with the same input parameters, our $\mathcal{O}(α_s)$ and $\mathcal{O}(v^2)$ corrections are consistent with those reported in the literature. Phenomenologically, the $\mathcal{O}(α_s)$ correction (with $μ_R=\sqrt{s}/2$) reaches about $50\%$ of the leading-order cross section, while the $\mathcal{O}(v^2)$ and $\mathcal{O}(α_s v^2)$ corrections are accidentally small. After including feeddown contributions from $ψ(2S)$, the predicted cross section $0.523_{-0.197}^{+0.285}$ pb agrees with the {\tt Belle} measurement within uncertainties. However, the predicted angular distribution parameter $0.120_{-0.036}^{+0.041}$ deviates from the experimental value $5.71\pm 2.51$ by more than $2σ$, calling for further experimental and theoretical investigations.

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arXiv2026

Reanalysis of exclusive charmonium production at the $B$ factories

In this paper, we present a comprehensive analysis of the next-to-next-to-leading-order (NNLO) QCD corrections to the exclusive processes $e^{+}e^{-}\to J/ψ+η_{c}$, $e^{+}e^{-}\to J/ψ+χ_{cJ}$, $e^{+}e^{-}\to η_{c}+γ$, and $e^{+}e^{-}\to χ_{cJ}+γ$ $(J=0,1,2)$ at the $B$ factories, comparing perturbative expansions truncated at the amplitude level and squared-amplitude level. Our results show that the amplitude-level prescription improves the perturbative convergence, with the NNLO/LO ratios lying closer to the corresponding NLO/LO ratios than those in the squared-amplitude-level prescription. This improvement is particularly pronounced for $e^{+}e^{-}\toχ_{c2}+γ$, where the NNLO prediction is about 27\% of the LO result in the amplitude-level prescription, compared with only 12\% in the squared-amplitude-level prescription. The amplitude-level prescription also reduces the residual renormalization scale dependence, particularly for the $P$-wave channels. Finally, the NNLO predictions are generally in good agreement with the available Belle and BaBar measurements and have central values closer to the data than those obtained with the squared-amplitude-level prescription. For channels with only upper limits, the predictions from both prescriptions are consistent with the experimental constraints, except for $e^{+}e^{-}\toη_c+γ$, where both NNLO predictions remain above the current upper limit.

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arXiv2026

Next-to-leading-order QCD corrections to $S$- and $P$-wave heavy quarkonium decay to $l^{+}l^{-} γ$

In this work, we comprehensively study the total and differential decay widths of the radiative Dalitz decays $H \to l^+l^-γ$ up to QCD next-to-leading order (NLO) accuracy within the framework of NRQCD factorization. Our calculation includes the decays of $S$-wave states ($η_c, η_b$) and the $P$-wave triplets ($χ_{cJ}, χ_{bJ}$ for $J=0,1,2$) to both electron ($l=e$) and muon ($l=μ$) final states. To match realistic experimental detection thresholds, systematic kinematic cuts are implemented on the final-state photon energy. Our analysis of the lepton-pair invariant mass distribution shows distinct singular behaviors across the multiplets originating from the lepton-pair threshold region, which is regularized by the lepton mass, and the soft-photon region, respectively. For the $S$-wave states, there is only one peak near the lepton-pair threshold region, while for the $J=0$ and $J=2$ $P$-wave states, the peaks show up in both regions. However, for the $J=1$ $P$-wave states, the peak only appears in the soft-photon region. Such features provide a rich venue to probe the $γ^{\ast}\to l^{+}l^{-}$ form factor in heavy quarkonium decay. Integrating over the bounded phase spaces reveals a distinct hierarchy among the $χ_{QJ}$ states in the sensitivity of our theoretical predictions to the soft-photon energy cuts, ordered as $χ_{Q1} >χ_{Q2}>χ_{Q0}$. In the $χ_{cJ}\to l^{+}l^{-}γ$ cases, as the energy cut increases from 100 $\mathrm{MeV}$, to 500 $\mathrm{MeV}$ the theoretical predictions at QCD NLO are reduced by $6\%(χ_{c0})$,$66\%(χ_{c1})$, and $21\%(χ_{c2})$ for $l=e$, and by $17\%(χ_{c0})$,$66\%(χ_{c1})$, and $39\%(χ_{c2})$ for $l=μ$. Comparing our predictions with the upcoming high-precision experimental tests at BESIII will definitely deepen our understanding of the predictive power of perturbative calculations.

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arXiv2026

Complete Next-to-Next-to-Leading-Order QCD Correction to $J/ψ\to 3γ$ Decay

We address the long-standing problem of negative decay and production rates in perturbative QCD for exclusive processes by proposing amplitude-level NRQCD factorization as a systematic prescription. Building on this, we present the first complete next-to-next-to-leading-order (NNLO) QCD correction to the decay $J/ψ\to 3γ$. The resulting partial width, $Γ(J/ψ\to 3γ) = 0.96^{+4.32}_{-0.13}$ eV, combines this NNLO contribution with the known up to $\mathcal{O}(α_s v^2)$ relativistic correction and shows markedly improved agreement with the high-precision BESIII measurement. In the same way, $Γ(Υ\to 3γ) = 0.0086^{+0.0028}_{-0.0006}$ eV is obtained. The dominant theoretical uncertainty originates from the renormalization scale variation, underscoring the challenge of perturbative convergence at this order and the necessity for future higher-order calculations.

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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.

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arXiv2026

Two loop QCD corrections to $e^+ e^- \to J/ψ+ η_c$ in asymptotic expansion

Within the framework of NRQCD, the short-distance coefficients (SDCs) for the process $e^+e^-\to J/ψ+η_c$ have been obtained up to NNLO in asymptotic expansions over $r={16m_c^2}/{s}$ up to $r^{15}$. Although these asymptotic expressions are deviated from the full results near the threshold $r= 1$, they provide excellent approximations to the full results for $r<0.8$, with deviations less than $3\%$. Therefore, these asymptotic expressions offer reliable applications for phenomenological predictions across a wide range of center-of-mass energies $\sqrt{s}$. Utilizing these asymptotic expressions, we present phenomenological predictions for the cross sections in both the on-shell mass scheme and the $\overline{\rm MS}$ mass scheme, with the uncertainty arising from the renormalization scale $μ_R$ included. The $μ_R$ uncertainty for predictions from the $\overline{\rm MS}$ mass scheme is slightly larger than that from the on-shell mass scheme, which is partly attributed to the helicity flip in the process $e^+e^-\to J/ψ+η_c$. We observe that both mass schemes yield quite similar predictions, and our theoretical results are consistent with the available experimental data.

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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 ${\rm DoB}=95.5\%$.

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arXiv2024

QCD corrections of $e^+e^- \to J/ψ+c+\bar{c}$ using the principle of maximum conformality

In this paper, we compute the total and differential cross sections for $e^+e^- \to J/ψ+c+\bar{c}$ at the $B$ factories up to next-to-leading order (NLO) corrections within the framework of nonrelativistic QCD factorization theory. We then obtain improved pQCD series of those cross sections by using the Principle of Maximum Conformality (PMC). We show that the PMC can be applied for any pQCD calculable observable at the total and differential levels via a self-consistent way in perturbation theory. We observe that a more precise prompt total cross section at the NLO level can be achieved after applying the PMC, e.g. $σ|_{\rm prompt}^{\rm PMC}= 0.565^{+0.144}_{-0.125}~\text{pb}$. Here the uncertainty is the squared average of those from the $α_s$ fixed-point uncertainty $Δα_s(M_Z)$, the uncertainty of charm quark mass $Δm_c$, and an estimated contribution of the uncalculated NNLO-terms as predicted by the Padé approximation approach. The differential cross sections $dσ/dP_{J/ψ}$, $dσ/d|\cos θ|$, and $dσ/dz$ for $e^+e^- \to J/ψ+c+\bar{c}$ are further examined. Those results show that by further considering the feed-down contributions, the PMC predictions show better agreement with the Belle measurements.

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arXiv2024

Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\rm MS}$-scheme running mass

In this paper, we explore the properties of the bottom-quark on-shell mass ($M_b$) by using its relation to the $\overline{\rm MS}$ mass (${\overline m}_b$). At present, this $\overline{\rm MS}$-on-shell relation has been known up to four-loop QCD corrections, which however still has a $\sim 2\%$ scale uncertainty by taking the renormalization scale as ${\overline m}_b({\overline m}_b)$ and varying it within the usual range of $[{\overline m}_b({\overline m}_b)/2, 2 {\overline m}_b({\overline m}_b)]$. The principle of maximum conformality (PMC) has been adopted to achieve a more precise $\overline{\rm MS}$-on-shell relation by eliminating such scale uncertainty. As a step forward, we also estimate the magnitude of the uncalculated higher-order terms by using the Padé approximation approach. Numerically, by using the $\overline{\rm MS}$ mass ${\overline m}_b({\overline m}_b)=4.183\pm0.007$ GeV as an input, our predicted value for the bottom-quark on-shell mass becomes $M_b\simeq 5.372^{+0.091}_{-0.075}$ GeV, where the uncertainty is the squared average of the ones caused by $Δα_s(M_Z)$, $Δ{\overline m}_b({\overline m}_b)$, and the estimated magnitude of the higher-order terms.

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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.

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arXiv2024

Next-to-next-to-leading-order QCD corrections to double $J/ψ$ production at the $B$ factories

In this paper, we study the next-to-next-to-leading-order (NNLO) QCD corrections for the process $e^+e^- \to J/ψ+J/ψ$ at the $B$ factories. By including the NNLO corrections, the cross section turns negative due to the poor convergence of perturbative expansion. Consequently, to obtain a reasonable estimation for the cross section, the square of the amplitude up to NNLO is used. In addition, the contributions from the bottom quark and the light-by-light part, which are usually neglected, are also included. The final cross section is obtained as $1.76^{+2.42}_{-1.66} ~{\rm fb}$ at a center-of-mass energy of $\sqrt{s}=10.58$ GeV. Our result for total cross section and differential cross section could be compared with precise experimental measurement in future at the $B$ factories.

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arXiv2023

Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality

The {\it Principle of Maximum Conformality} (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs) and the procedures based on ``intrinsic conformality" (PMC$_\infty$). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities $R_{e^+e^-}$, $R_τ$, and $Γ(H \to b \bar{b})$ up to four-loop pQCD corrections. The PMCs approach determines an overall effective running coupling $α_s(Q)$ by the recursive use of the renormalization group equation, whose argument $Q$ represents the actual momentum flow of the process. Our numerical results show that the PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with small residual scale dependence.

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arXiv2023

Next-to-next-to-leading-order QCD corrections to $J/ψ$ plus $η_c$ production at the $B$ factories

In this paper, we calculate the next-to-next-to-leading-order (NNLO) QCD corrections to $e^+e^- \to J/ψ+η_c$ at the $B$ factories. After including the NNLO corrections, the cross section of $e^+e^- \to J/ψ+η_c$ is enhanced by about $17\%$, and the perturbative series of the prediction shows the convergent behavior. It is also found that the contribution from bottom quark starts at the $α_s^3$-order, which is about $2.4\%$ of the total prediction. The renormalization scale $μ_R$ dependence of the cross section is reduced at the NNLO level, but the prediction is sensitive to the charm quark mass $m_c$. By considering the uncertainties caused by renormalization scale $μ_R$, charm quark mass $m_c$ and the NRQCD factorization scale $μ_Λ$, our prediction shows agreement with the BABAR and BELLE measurements within errors.

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arXiv2022

Total decay width of $H \to gg$ using the infinite-order scale-setting approach based on the intrinsic conformality

We make a detailed study on the properties of the total decay width of Higgs decay channel $H\to gg$ up to $α_s^6$-order QCD corrections by using the newly suggested infinite-order scale-setting approach, which is based on the ideas of both the principle of maximum conformality and the intrinsic conformality. This approach is called as the PMC$_\infty$ approach. By using the PMC$_\infty$ approach, we observe that the conventional renormalization scale ambiguity in perturbative QCD calculation is eliminated and the residual scale dependence due to unknown higher-order terms can also be highly suppressed. We then obtain an accurate perturbative QCD prediction on the total decay width, e.g. $Γ(H \to gg)|_{\rm PMC_\infty} =336.42^{+7.01}_{-6.92}$ KeV, where the errors are squared averages of those from all the mentioned error sources.

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arXiv2022

Novel and self-consistency analysis of the QCD running coupling $α_s(Q)$ in both the perturbative and nonperturbative domains

The QCD coupling $α_s$ is the most important parameter for achieving precise QCD predictions. By using the well measured effective coupling $α^{g_1}_{s}(Q)$ defined from the Bjorken sum rules as a basis, we suggest a novel and self-consistency way to fix the $α_s$ at all scales: The QCD light-front holographic model is adopted for its infrared behavior, and the fixed-order pQCD prediction under the principle of maximum conformality (PMC) is used for its high-energy behavior. Using the PMC scheme-and-scale independent perturbative series, and by transforming it into the one under the physical $V$-scheme, we observe that a precise $α_s$ running behavior in both the perturbative and nonperturbative domains with a smooth transition from small to large scales can be achieved.

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arXiv2021

Inclusive production of heavy quarkonium $η_Q$ via $Z$ boson decays within the framework of nonrelativistic QCD

In the paper, the inclusive production of heavy quarkonium $η_Q$ ($Q=b$ or $c$) via $Z$ boson decays within the framework of nonrelativistic QCD effective theory are studied. The contributions from the leading color-singlet and color-octet Fock states are considered. Total and differential decay widths for the inclusive decays $Z \to η_Q+X$ are presented. It is found that the decays $Z\to η_Q +X$ are dominated by the $^3S_1^{[8]}$ component, so the decays can be inversely adopted to determine the values of the long-distance matrix elements $\langle {\cal O}^{η_{c}}(^{3}S_{1}^{[8]})\rangle$ and $\langle {\cal O}^{η_{b}}(^{3}S_{1}^{[8]})\rangle$, respectively. Our numerical results show that at an $e^+e^-$ collider running at the $Z$ pole with a high luminosity around $10^{35}{\rm cm}^{-2}{\rm s}^{-1}$ (a super $Z$ factory), there are about $4.5\times 10^7$ $η_c$ meson events and $6.1\times 10^5$ $η_b$ meson events to be produced per operation year, and the inclusive decays may be used for clarifying some problems on the heavy quarkonium $η_Q$ and nonrelativistic QCD.

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arXiv2021

A new analysis of the pQCD contributions to the electroweak parameter $ρ$ using the single-scale approach of principle of maximum conformality

It has been observed that conventional renormalization scheme and scale ambiguities for the pQCD predictions can be eliminated by using the principle of maximum conformality (PMC). However, being the intrinsic nature of any perturbative theory, there are still two types of residual scale dependences due to uncalculated higher-order terms. In the paper, as a step forward of our previous work [Phys.Rev.D {\bf 89},116001(2014)], we reanalyze the electroweak $ρ$ parameter by using the PMC single-scale approach. Using the PMC conformal series and the Pad$\acute{e}$ approximation approach, we observe that the residual scale dependence can be greatly suppressed and then a more precise pQCD prediction up to ${\rm N^4LO}$-level can be achieved, e.g. $Δρ|_{\rm PMC}\simeq(8.204\pm0.012)\times10^{-3}$, where the errors are squared averages of those from unknown higher-order terms and $Δα_s(M_Z)=\pm 0.0010$. We then predict the magnitudes of the shifts of the $W$-boson mass and the effective leptonic weak-mixing angle: $δM_{W}|_{\rm N^4LO} =-0.26$ MeV and $δ\sin^2θ_{\rm eff}|_{\rm N^4LO}=0.14\times10^{-5}$, which are well below the precision anticipated for the future electron-position colliders such as FCC, CEPC and ILC. Thus by measuring those parameters, it is possible to test SM with high precision.

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arXiv2021

Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders

In the paper, we make a detailed study on the generalized Crewther Relation (GCR) between the Adler function ($D$) and the Gross-Llewellyn Smith sum rules coefficient ($C^{\rm GLS}$) by using the newly suggested single-scale approach of the principle of maximum conformality (PMC). The resultant GCR is scheme-independent, whose residual scale dependence due to unknown higher-order terms are highly suppressed. Thus a precise test of QCD theory without renormalization scheme and scale ambiguities can be achieved by comparing with the data. Moreover, a demonstration of the scheme independence of commensurate scale relation up to all orders has been presented. And as the first time, the Pade approximation approach has been adopted for estimating the unknown $5_{\rm th}$-loop contributions from the known four-loop perturbative series.

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