arXiv subjects

Jun-Kang He

Publications and source records attributed to Jun-Kang He.

11 recordsLinked to original sources

arXiv2026

Radiative decays $J/\psi,\,\psi(2S)\rightarrow\gamma\eta^{(\prime)}$ in perturbative QCD with relativistic corrections

We present the first calculation of the radiative decays $J/\psi,\psi(2S)\rightarrow\gamma\eta^{(\prime)}$ in perturbative QCD that includes the order-$q^{2}$ relativistic corrections in all three short-distance contributions, namely the quark-antiquark, two-gluon, and QED contributions. The amplitudes are found to be remarkably insensitive to the light-cone distribution amplitude and to the light-quark mass, a robustness that persists through order $q^{2}$ and makes the predictions correspondingly reliable. The relativistic correction enhances the $J/\psi$ branching ratios by roughly a factor of two, narrowing their shortfall from experiment, whereas for the $\psi(2S)$ it is about twice as large as for the $J/\psi$ and the low-order expansion converges poorly. In two representative $\eta$--$\eta'$ mixing schemes, the ratio $\mathcal{R}_{1S}=\mathcal{B}(\gamma\eta')/\mathcal{B}(\gamma\eta)$ proves sharply sensitive to the mixing angle and favours the smaller of the two. The predicted $\psi(2S)$ rates lie well above the data in both channels, already at leading order, and most severely for the anomalously small $\gamma\eta$ channel. Such a discrepancy suggests that a mechanism beyond the hard perturbative process is at work. As a physically motivated attempt, we explore the $\eta_{c}$-mixing contribution, which adds coherently to the perturbative one and is comparable to it in the $\gamma\eta$ channel, and find that the interference can bring the $\psi(2S)$ rates into agreement with the data, although its extraction is limited by a strong sensitivity to the mixing parameters.

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arXiv2026

Twist-3 contributions to $\gamma\gamma\to\pi^0\pi^0,\,K_S^0K_S^0$ in $k_T$ factorization

We compute the cross sections for the two-photon processes $\gamma\gamma\to\pi^0\pi^0$ and $\gamma\gamma\to K_S^0K_S^0$ in $k_T$ factorization, including the chirally enhanced two-parton twist-3 light-cone distribution amplitudes. For these charge-suppressed neutral channels the twist-3 cross sections exceed the twist-2 ones by close to an order of magnitude in the intermediate-energy region, bringing the predictions much closer to the Belle data, the residual underestimate being plausibly attributable to higher-order QCD corrections. The calculation reproduces the measured angular distributions and the energy dependence of the charged channels and the neutral pion, though not the steeper fall of the neutral kaon. The neutral-to-charged ratios are the most discriminating observables. They depend strongly on energy in the data, whereas our calculation, like other approaches in the literature, yields a nearly flat ratio. Finally, in a phenomenological discussion, we combine our contribution with the soft handbag contribution and largely reproduce the observed energy dependence, suggesting that the hard and soft contributions are comparably important in the few-GeV region.

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arXiv2026

Three-gluon decays of radially excited quarkonia $\psi(2S)$ and $\Upsilon(2S)$ with both relativistic and QCD radiative corrections

For the radially excited heavy quarkonia $V=\psi(2S)$ and $\Upsilon(2S)$, the nodal structure of the wave function renders the three-gluon decay $V\to ggg$ acutely sensitive to relativistic corrections, a longstanding challenge for reliable theoretical predictions. Within the Bethe-Salpeter formalism under the covariant instantaneous ansatz, we construct analytic harmonic-oscillator wave functions incorporating the $2S$ node and derive model-independent relations among the polarized decay widths from helicity-flip and phase-space symmetries. Motivated by the strikingly slow $\hat{q}^{2}$-order convergence driven by destructive interference at the node, we introduce a concise phenomenological treatment of the higher-order contributions that preserves the correct low-momentum limit. Including both relativistic and QCD radiative corrections, our predictions for $\Gamma(V\to ggg)$, $\Gamma(V\to e^{+}e^{-})$ and $R_{V}$ agree well with experiment, and the extracted $\beta_{V}$ lies at the lower end of typical phenomenological ranges, reflecting a more localized momentum-space wave function.

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arXiv2025

Heavy quarkonium decay $V \to ggg$ with both relativistic and QCD radiative corrections

In the heavy quarkonium decay process $ V \to ggg $ ($ V=J/\psi, \Upsilon $), making a definite prediction including relativistic corrections has so far remained a significant challenge. In this work, we study this decay process by taking into account the relativistic corrections in the Bethe-Salpeter formalism, where the relativistic bound-state wave function of quarkonium is obtained by solving the Bethe-Salpeter equation under the covariant instantaneous ansatz. Through analytical calculation, we find that some polarized decay widths vanish due to the helicity selection rule, which suppresses the corresponding helicity amplitudes. Owing to helicity flip symmetry and phase space symmetry, the nonvanishing polarized decay widths are not all independent; they are related through a set of symmetry relations. Then we obtain the unpolarized decay width formula $\Gamma(V \to ggg)=\frac{80(\pi^{2}-9)\alpha_{s}^{3}N_{V}^{2}\beta_{V}^{3}}{81\pi^{9/2} M } (1-\kappa\frac{\beta_{V}^{2}}{M^{2}})$, where the factor $\kappa\frac{\beta_{V}^{2}}{M^{2}}$ arises from the relativistic corrections with $\kappa\equiv\frac{3(112+25\pi^{2})}{16(\pi^{2}-9)}$. Furthermore, including both relativistic and QCD radiative corrections within the factorization assumption, our predictions of $\mathcal{B}(V \to ggg)$ and $\mathcal{B}(V \to e^{+}e^{-})$ agree well with their experimental data. As a crossing check, with the experimental value of the ratio $R_{V} = \frac{\Gamma(V \to ggg)}{\Gamma(V \to e^{+}e^{-})}$ and our result for $R_{V}$, we extract $\alpha_{s}(M_{J/\psi}/2)=0.31$ and $\alpha_{s}(M_{\Upsilon}/2)=0.20$, respectively.

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arXiv2025

Revisiting the line shape of $e^+e^-\to \jpsi \eta$ cross section

We calculate the cross sections for the processes $e^+e^-\to \jpsi \eta$ and $e^+e^-\to \jpsi \eta^\prime$ at various CM energies $\sqrt{s}$. We first predict these cross sections by combining NRQCD with LC factorization. The predicted cross sections are on the order of several femtobarns for $e^+e^-\to \jpsi \eta^\prime$, and less than 1 fb for $e^+e^-\to \jpsi \eta$, which are significantly smaller than the experimental measurements. It is anticipated that the cross sections are dominated by resonant contributions when $\sqrt{s}$ is close to the resonance mass. In this study, we employ the Vector Meson Dominance (VMD) model to predict these resonant contributions. The effective coupling constants between the photon and the resonance, as well as between the resonance and $J/\psi\eta$ are extracted from the data either provided by the latest PDG or predicted by theoretical calculations. Taking the predictions from the factorization calculation as the continuum contribution, we predict the cross section of $e^+e^-\to \jpsi \eta$ through a coherent sum of contributions from various resonances and the continuum. The relative phase angles between these contributions are determined through a least-$\chi^2$ fit to the experimental data. We then compare our theoretical predictions with the experimental data. Additionally, we find our theoretical prediction for the cross section of $e^+e^-\to \jpsi \eta$ is significantly larger than those for $e^+e^-\to \jpsi \eta^\prime$ measured by the BESIII collaboration.

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arXiv2024

QCD analysis of the $P$-wave charmonium electromagnetic Dalitz decays $h_{c}\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-}$

The $P$-wave charmonium electromagnetic Dalitz decays $h_{c}\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-}$ $(\ell=e, \mu)$ with large recoil momentum are investigated in the framework of perturbative QCD, and the contributions from the small recoil momentum region are described by the overlap of soft wave functions. The transition form factors $f_{h_{c}\eta^{(\prime)}}(q^{2})$ and the normalized transition form factors $F_{h_{c} \eta^{(\prime)}}(q^{2})$ in full kinematic region are derived for the first time. It is noticed that there are no IR divergences at one-loop level, and the transition form factors with the relativistic corrections from the internal momentum of $h_{c}$ are insensitive to both the shapes of $\eta^{(\prime)}$ distribution amplitudes and the invariant mass of the lepton pair in the large recoil momentum region. Intriguingly, unlike the situation in the $S$-wave charmonium decays $J/\psi\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-}$, we find the contributions from the small recoil momentum region are comparable with those from the large recoil momentum region in the $P$-wave charmonium decays $h_{c}\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-}$. By employing the obtained $F_{h_{c} \eta^{(\prime)}}(q^{2})$, we give the predictions of the branching ratios $\mathcal{B}(h_{c}\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-})$, which may come within the range of measurement of present or near-future experiments.

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arXiv2021

Revisiting the $P$-wave charmonium radiative decays $h_{c}\rightarrowγη^{(\prime)}$ with relativistic corrections

The $P$-wave charmonium decays $h_{c}\rightarrowγη^{(\prime)}$ are revisited by taking into account relativistic corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, in which the involved one-loop integrals are evaluated analytically. Intriguingly, from both the quark-antiquark content and the gluonic content of $η^{(\prime)}$, the relativistic corrections make significant contributions to the decay rates of $h_{c}\rightarrowγη^{(\prime)}$. By comparison with the leading-order contributions from the quark-antiquark content (one-loop level), the ones from the gluonic content (tree level) are also important, which is compatible with the conclusion obtained without relativistic corrections. Usually, for $η$ production processes, the predicted branching ratios are sensitive to the angle of $η-η^{\prime}$ mixing. As an illustration, using the Feldmann-Kroll-Stech result about the mixing angle $ϕ=39.3^{\circ}\pm1.0^{\circ}$ as input, we find that the predicted ratio $R_{h_{c}}=\mathcal{B}(h_{c}\rightarrowγη)/\mathcal{B}(h_{c}\rightarrowγη^{\prime})$ is much smaller than the experiment measurement. While, with $ϕ=33.5^{\circ}\pm0.9^{\circ}$ extracted from the asymptotic limit of the $γ^{\ast}γ-η^{\prime}$ transition form factor, we obtain $R_{h_{c}}=30.3\%$ in consistent with $R_{h_{c}}^{exp}=(30.7\pm11.3\pm8.7)\%$. As a cross-check, the mixing angle $ϕ=33.8^{\circ}\pm2.5^{\circ}$ is extracted by employing the ratio $R_{h_{c}}$, and a brief discussion on the difference in the determinations of $ϕ$ is given.

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arXiv2020

QCD analysis of electromagnetic Dalitz decays $J/\psi\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-}$

The electromagnetic Dalitz decays $J/\psi\rightarrow\eta^{(\prime)}e^{+}e^{-}$ with large recoil momentum are studied in the framework of perturbative QCD. Meanwhile, the soft contributions from the small recoil momentum region are described by the overlap of soft wave functions, and the resonance contributions are estimated by the vector meson dominance model. Based on this dynamical picture, the transition form factors $f_{\psi\eta^{(\prime)}}(q^{2})$ in full kinematic region are calculated for the first time, and we find that the transition form factors are insensitive to the shapes of $\eta^{(\prime)}$ distribution amplitudes. Our prediction of the normalized transition form factor $F_{\psi \eta}(q^{2})\equiv f_{\psi\eta}(q^{2})/f_{\psi\eta}(0)$ agrees well with its experimental data. In addition, we also find that the branching ratios $\mathcal{B}(J/\psi\rightarrow\eta^{(\prime)}e^{+}e^{-})$ are dominated by the contributions of perturbative QCD, and the resonance contributions are negligibly small as well as the soft contributions due to the suppression of the kinematic factor. With all these contributions, our results of the branching ratios $\mathcal{B}(J/\psi\rightarrow\eta^{(\prime)}e^{+}e^{-})$ and the ratio $R_{J/\psi}^{e}=\mathcal{B}(J/\psi\rightarrow\eta e^{+}e^{-})/\mathcal{B}(J/\psi\rightarrow\eta^{\prime}e^{+}e^{-})$ are in good agreement with their experimental data. Using the obtained $F_{\psi \eta^{(\prime)}}(q^{2})$, we give the predictions of the branching ratios $\mathcal{B}(J/\psi\rightarrow\eta^{(\prime)}\mu^{+}\mu^{-})$ and their ratio $R_{J/\psi}^{\mu}$.

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arXiv2019

Radiative decays of $h_{c}$ to the light mesons $η^{(\prime)}$: A perturbative QCD calculation

We study the radiative decays $h_{c}\rightarrowγη^{(\prime)}$ in the framework of perturbative QCD and evaluate analytically the one-loop integrals with the light quark masses kept. Interestingly, the branching ratios $\mathcal{B}(h_{c}\rightarrowγη^{(\prime)})$ are insensitive to both the light quark masses and the shapes of $η^{(\prime)}$ distribution amplitudes. And it is noticed that the contribution of the gluonic content of $η^{(\prime)}$ is almost equal to that of the quark-antiquark content of $η^{(\prime)}$ in the radiative decays $h_{c} \rightarrow γη^{(\prime)}$. By employing the ratio $R_{h_{c}}=\mathcal{B}(h_{c}\rightarrowγη)/\mathcal{B}(h_{c}\rightarrowγη^{\prime})$, we extract the mixing angle $ϕ=33.8^{\circ}\pm2.5^{\circ}$, which is in clear disagreement with the Feldmann-Kroll-Stech result $ϕ=39.0^{\circ}\pm1.6^{\circ}$ extracted from the ratio $R_{J/ψ}$ with nonperturbative matrix elements $\langle 0\mid G^{a}_{μν}\tilde{G}^{a,μν}\midη^{(\prime)}\rangle$, but in consistent with $ϕ=33.5^{\circ}\pm0.9^{\circ}$ extracted from the asymptotic limit of the $γ^{\ast}γ-η^{\prime}$ transition form factor and $ϕ=33.9^{\circ}\pm0.6^{\circ}$ extracted from $R_{J/ψ}$ in perturbative QCD. We also briefly discuss possible reasons for the difference in the determinations of the mixing angle.

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arXiv2019

Twist-3 contributions to $γγ\rightarrowπ^+π^-,K^+K^-$ processes in perturbative QCD approach

As one of the simplest hadronic processes, $γγ\rightarrow M^{+}M^{-}$ ($M=π,K$) could be a good testing ground for our understanding of the perturbative and nonperturbative structure of QCD, and will be studied with high precision at BELLE-\RNum{2} in the near future. In this paper, we revisit these processes with twist-3 corrections in the perturbative QCD approach based on the $k_{T}$ factorization theorem, in which transverse degrees of freedom as well as resummation effects are taken into account. The influence of the distribution amplitudes on the cross sections are discussed in detail. Our work shows that not only the transverse momentum effects but also the twist-3 corrections play a significant role in the processes $γγ\rightarrow M^{+}M^{-}$ in the intermediate energy region. Especially in the few GeV region, the twist-3 contributions become dominant in the cross sections. And it is noteworthy that both the twist-3 result of the $π^{+}π^{-}$ cross section and that of the $K^{+}K^{-}$ cross section agree well with the BELLE and ALEPH measurements. For the pion and kaon angular distributions, there still exist discrepancies between our results and the experimental measurements. Possible reasons for these discrepancies are discussed briefly.

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arXiv2019

Revisiting the radiative decays $J/ψ\rightarrow γη^{(\prime)}$ in perturbative QCD

In the framework of perturbative QCD, the radiative decays $J/ψ\rightarrowγη^{(\prime)}$ are revisited in detail, where the involved one-loop integrals are evaluated analytically with the light quark masses kept. We have found that the sum of loop integrals is insensitive to the light quark masses and the branching ratios $\mathcal{B}(J/ψ\rightarrowγη^{(\prime)})$ barely depend on the shapes of $η^{(\prime)}$ distribution amplitudes. With the parameters of $η-η^{\prime}$ mixing extracted from low energy processes and $J/ψ\rightarrowγη^{(\prime)}$ by means of nonperturbative matrix elements $\langle0|G_{μν}^a\tilde{G}^{a,μν}|η^{(\prime)}\rangle$ based on $U_{A}(1)$ anomaly dominance argument, we could not give the ratio $R_{J/ψ}$ in agreement with experimental result. However, using the parameters, especially the mixing angle $ϕ=33.5^{\circ}\pm0.9^{\circ}$, extracted from $γ^{\ast}γ-η^{\prime}$ transition form factor measured at $q^{2}=112~\mathrm{GeV}^{2}$ by BaBar collaboration, we obtain $R_{J/ψ}=4.70$ in good agreement with $R_{J/ψ}^{exp}=4.65\pm0.21$. As a crossing check, with $Γ^{exp}(η^{(\prime)}\rightarrowγγ)$ and our results for $J/ψ\rightarrowγη^{(\prime)}$, we get $ϕ=33.9^{\circ}\pm0.6^{\circ}$. The difference between the determinations of $ϕ$ is briefly discussed.

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