arXiv subjects

Xing-Gang Wu

Publications and source records attributed to Xing-Gang Wu.

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 $\mathcal{B}(H \to J/ψ+ γ) = 3.485_{-0.161}^{+0.152} \times 10^{-6}$.

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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.

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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 $\text{Br}(η_{b2}\toγγ) = \big(6.460^{+0.481}_{-0.447}\big)\times 10^{-7}$.

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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 ($Ξ_{cc}$, $Ξ_{bc}$, and $Ξ_{bb}$) via $e^+e^-$ annihilation. Based on nonrelativistic QCD effective theory, the generator calculates the process $e^{+}+e^{-}\rightarrow Ξ_{QQ'}+\bar{Q}'+\bar{Q}$ 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.

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arXiv2026

New Determinations of the Charm and Bottom Quark Masses Using QCD Quarkonium Sum Rules

We reanalyze the perturbative QCD (pQCD) corrections to quarkonium QCD sum rules and extract the heavy quark masses $\overline{m}_{q}(\overline{m}_{q})$ ($q=c,b$). At present, the pQCD corrections to the correlation functions of two heavy-quark pseudoscalar and vector currents at zero momentum transfer, denoted as $M_{n,q}^{X,\rm th}$ ($X = P, V$), are calculated up to the $\mathcal{O}(α_s^3)$ order. These corrections exhibit significant renormalization scheme and scale dependence, which introduces large theoretical uncertainties and deteriorates the precision of heavy quark mass determinations. In this work, we eliminate the renormalization scheme and scale ambiguities in the perturbative part of $M_{n,q}^{X,\rm th}$ by adopting the Principle of Maximum Conformality (PMC) within the characteristic operator (CO) approach. The CO approach, a novel extension of the standard PMC procedure, simultaneously determines the effective coupling $α_s(Q_*)$ and the effective quark mass $\overline{m}_q(Q_*)$. It systematically absorbs the nonconformal $\{β_i\}$-terms and $\{γ_i\}$-terms via the renormalization group equations, yielding a strictly scheme- and scale-independent conformal perturbative series. Based on the improved PMC conformal series, we further provide reliable estimates for the unknown $\mathrm{N^4LO}$ contributions using the Padé approximation method. The final predicted heavy quark masses in the $\overline{\mathrm{MS}}$ scheme read: $\overline{m}_c(\overline{m}_c)=1275.8\pm 0.4~\text{MeV}$, extracted from the second moment of the charmed pseudoscalar correlator $M_{2,c}^{P}$; and $\overline{m}_b(\overline{m}_b) = 4177.0 \pm 7.2~\text{MeV}$, extracted from the first moment of the bottom vector correlator $M_{1,b}^{V}$. Both results agree well with the PDG world averages with deviations smaller than $1σ$.

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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.

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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

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

We investigate the $J/ψ$ direct production mechanism in the rare exclusive Higgs decay $H\to J/ψ+γ$ 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 $J/ψ$ and the N$^2$LO perturbative result, we extract the factorization-scale-dependent long-distance matrix element $\langle J/ψ({\bm ε})|ψ^{\dagger}{\bm σ}\cdot{\bm ε}χ(μ_Λ) |0\rangle$. 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 $Γ(H\to J/ψ+γ)$ is more robust and precise, with good convergence and no renormalization- or factorization-scale dependence. We find $Γ(H\to J/ψ+γ) = (6.4574^{+0.3995}_{-0.3995}) \times 10^{-11}$ GeV, where the uncertainty is the quadratic sum of contributions from $Δα_s(m_Z) = \pm 0.0009$, $ΔΓ_{J/ψ\to e^+e^-} = \pm 0.10\ \text{GeV}$, $Δ\overline{m}_c(\overline{m}_c) = \pm 0.0046\ \text{GeV}$, 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.

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arXiv2026

Fragmentation functions for gluon into $P$-wave $B_c$ mesons

We calculate the fragmentation functions for a gluon into $P$-wave $B_c$ mesons within the nonrelativistic QCD factorization framework, incorporating color-singlet and color-octet contributions. Ultraviolet divergences arising from phase-space integrals are removed via operator renormalization in the modified minimal subtraction scheme. The resulting fragmentation functions are presented in both graphical form and as fitted analytic expressions.

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arXiv2026

Probing the $γγ^*\to η^{(\prime)}$ Transition Form Factors with Newly Derived $η^{(\prime)}$-Meson Light-Cone Distribution Amplitudes

In the present work, we analyze the properties of the transition form factors (TFFs) for the $γγ^*\to η^{(\prime)}$ process, employing the $η^{(\prime)}$-meson light-cone distribution amplitude (LCDA) derived within the light-cone sum rule framework. To this end, we adopt the quark-flavor mixing scheme for the $η^{(\prime)}$ meson, and compute the TFFs by systematically incorporating transverse-momentum corrections and contributions beyond the leading Fock state. We utilize light-cone harmonic oscillator models to parameterize the longitudinal and transverse behavior of the leading-twist light-cone wavefunction, for which the corresponding LCDA exhibits a unimodal profile. We further examine the potential contributions of intrinsic charm components to the scaled TFFs $Q^2 F_{ηγ}(Q^2)$ and $Q^2 F_{η^\prime γ}(Q^2)$. Leveraging a range of values for the decay constant $f_{η_{c_0}}$ and implementing the $η$-$η'$-$η_c$ and $η$-$η^\prime$-$G$-$η_c$ mixing mechanisms accordingly, together with the recently updated mixing angles, we investigate the impact of the intrinsic $c\bar{c}$ and gluonic component on these observables. In high-$Q^2$ regime, $Q^2 F_{η^\primeγ}(Q^2)$ exhibits a marked increase in sensitivity to the charm quark component, whereas $Q^2F_{ηγ}(Q^2)$ becomes notably stabilized. A detailed discussion of $χ^2/d.o.f$ and $p$-values indicates that the intrinsic charm quark component is important and yields a substantial, non-negligible contribution across the entire $Q^2$ range.

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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 $Q^2F_π(Q^2)$.

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arXiv2025

$η$-$η'$ mixing and its application in the $B^+/D^+/D_s^+\toη^{(\prime)}\ell^+ ν_\ell$ decays

In this paper, we take into account the intrinsic charm and gluonic contents into the $η-η^\prime$ mixing scheme and formulate the tetramixing $η-η^\prime-G-η_c$ to study the mixing properties of $η^{(\prime)}$ mesons. Using the newly derived mixing parameters, we calculate the transition form factors (TFFs) of $B^+/D^+/D_s^+\toη^{(\prime)}$ within the QCD light-cone sum rules up to next-to-leading order QCD corrections and twist-4 contributions. Using the extrapolated TFFs, we then calculate the decay widths and branching fractions of the semi-leptonic decays $B^+/D^+/D_s^+\toη^{(\prime)}\ell^+ν_{\ell}$. Our results are consistent with the recent Belle and BES-III measurements within reasonable errors.

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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...

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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.

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arXiv2025

The Electromagnetic Form Factors of Pseudoscalar Mesons within the Light-Front Quark Model

In this paper, we investigate the electromagnetic form factors (EMFFs) and charge radii of pseudoscalar mesons within the light-front quark model (LFQM). Using parameters derived from the confinement of mesonic decay constants, we obtain numerical results, which indicate the following: (i) The EMFFs of charged and neutral mesons exhibit significant differences in their endpoint behaviors but show similar asymptotic behavior in the high momentum transfer ($Q^2$) regions. For the EMFFs of light mesons such as $π$ and $K^+$, our results are in excellent agreement with experimental data in the low $Q^2$ regions. For the charge radii of mesons, our results also show rough consistency with predictions from other approaches. (ii) For charged mesons, the peak values of $Q^2 F_P(Q^2)$ are approximately proportional to the mass difference $Δm$ between their constituent quarks. Moreover, the mean square radii $\left\langle r^2 \right\rangle_P$ of charged mesons decrease with increasing meson mass and decreasing $Δm$. For neutral mesons, their charge radii are primarily determined by the electric charge of the heavy quark. These results indicate that quark mass asymmetry significantly influences the behavior of the EMFFs and charge radii of mesons. Experimental data to test these predictions would thus be of great interest.

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arXiv2025

Determination of $|V_{\rm cb}|$ using Bayesian analysis of the $B \rightarrow D^{*}\ell {\bar ν}_\ell$ semileptonic decay width with four-loop QCD corrections

The Cabibbo-Kobayashi-Maskawa matrix element $|V_{\rm cb}|$ is an important Standard Model parameter, whose value can be determined by using the semi-leptonic decay $B\rightarrow D^{*}\ell{\bar ν}_\ell$. The perturbative QCD (pQCD) corrections to the $B \to D^{*}$ transform form factor ${\cal F}(w)$ has been known up to the N$^3$LO level, whose magnitude remains sensitive to the choice of renormalization scale $μ_r$. To improve the precision of ${\cal F}(w)$ and hence $|V_{\rm cb}|$, we first apply the single-scale approach of Principle of Maximum Conformality (PMC) to eliminate the conventional (Conv.) renormalization scale dependence of the short-distance parameter $η_A$ and then predict the contribution of its unknown N$^4$LO term via Bayesian analysis. In this paper, we adopt two probabilistic models for Bayesian analysis: the Cacciari-Houdeau model (CH model) and the geometric behavior model (GB model). It is shown that by using the PMC series in combination with Bayesian analysis, one can achieve high degree of reliability in estimating unknown higher-order terms. A more convergent behavior is achieved by applying the PMC, confirmed by the predicted N$^4$LO contributions: for the CH model, $η_A|_{\rm Conv.}^{\rm N^4LO}=\{-0.0032,+0.0052\}$ and $η_A|_{\rm PMC}^{\rm N^4LO}=\{-0.0004,+0.0004\}$; for the GB model, $η_A|_{\rm Conv.}^{\rm N^4LO}=\{-0.0049,+0.0075\}$ and $η_A|_{\rm PMC}^{\rm N^4LO}=\{-0.0007,+0.0007\}$. Comparing with the latest experimental measurements, we obtain $|V_{\rm cb}||_{\rm PMC}=(40.58^{+0.53}_{-0.57})\times10^{-3}$, which is consistent for both CH and GB models and in good agreement with the PDG world average, $|V_{\rm cb}|_{\rm PDG}=(41.1\pm1.2)\times10^{-3}$ within errors.

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arXiv2025

Light-cone sum rules analysis of the semi-leptonic $D^+_s\to f_0(980)(\toπ^+π^-)e^+ν_e$ decay incorporating $f_0(980)$ mixing state twist-2 distribution amplitudes

The isospin-singlet scalar meson $f_0(980)$ is hypothesized to consist of two energy eigenstates, forming a mixture of $\frac{1}{\sqrt{2}}(\bar{u}u + \bar{d}d)$ and $\bar{s}s$. Building on this framework, we apply the QCD sum rules approach in the background field theory to compute the $f_0(980)$ decay constant, yielding $f_{f_0}(μ_0=1\,\text{GeV}) = 0.386\pm0.009 \, \text{GeV}$. Subsequently, we derive the first two $ξ$-moments of the leading-twist light-cone distribution amplitude $ϕ_{2;f_0}$. Using QCD light-cone sum rules, we then calculate the $D^+_s \to f_0(980)$ transition form factor (TFF) $f_+(q^2)$, obtaining $f_+(0) = 0.516^{+0.027}_{-0.024}$ at the large-recoil point. We extend $f_+(q^2)$ to the full physical region via a simplified series expansion parameterization, enabling calculations of the differential decay widths and the branching fraction $\mathcal{B}(D^+_s \to f_0(980)(\to π^+π^-)e^+ν_e) = (1.783^{+0.227}_{-0.189}) \times 10^{-3}$. Our theoretical predictions align well with the latest BESIII Collaboration measurements within reasonable errors.

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arXiv2025

$η_c$ leading-twist distribution amplitude and the $B_c \to η_c\ell\barν_\ell$ semileptonic decays using QCD Sum Rules

In this paper, we investigate the semileptonic decays $B_c \to η_c\ell\barν_\ell$ using the quantum chromodynamics(QCD) sum rules within the framework of Standard Model (SM). We further explore the potential to probe signatures of new Physics (NP) beyond the SM through these decays. First, we derive the $ξ$-moments $\langleξ_{2;η_c}^{n}\rangle$ of the $η_c$-meson leading-twist distribution amplitude $ϕ_{2;η_c}$ using the QCD sum rules within the background field theory. Considering contributions from the vacuum condensates up to dimension-six, the first two nonzero $ξ$-moments at the scale of $4$ GeV are found to be $\langleξ_{2;η_c}^{2}\rangle = 0.103^{+0.009}_{-0.009}$ and $\langleξ_{2;η_c}^{4}\rangle = 0.031^{+0.003}_{-0.003}$. Using these moments, we then fix the Gegenbauer expansion series of $ϕ_{2;η_c}$ and apply it to compute the $B_c \to η_c$ transition form factors (TFFs) using QCD light cone sum rules. Second, we extrapolate those TFFs to physically allowable $q^2$-range via a simplified series expansion, and we obtain $R_{η_c}|_{\rm SM} = 0.308^{+0.084}_{-0.062}$. Furthermore, we explore the potential impacts of various NP scenarios on $R_{η_c}$. Specifically, we compute the forward-backward asymmetry $\mathcal{A}_{\rm FB}({q^2})$, the convexity parameter $\mathcal{C}_F^τ({q^2})$, and the longitudinal and transverse polarizations $\mathcal{P}_L ({q^2})$ and $\mathcal{P}_T ({q^2})$ for $B_c \to η_c$ transitions within both the SM and two types of NP scenarios. Our results contribute to a deeper understanding of $B_c$-meson semileptonic decays and provide insights into the search for the NP beyond the SM.

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