arXiv subjects

Wen-Long Sang

Publications and source records attributed to Wen-Long Sang.

At least 19 recordsLinked to original sources

arXiv2026

Next-to-next-to-leading-order QCD corrections to ${}^3S_1^{(8)}$ gluon fragmentation function for quarkonium

We present the first computation of the next-to-next-to-leading-order (NNLO) QCD corrections to the ${}^3S_1^{(8)}$ gluon fragmentation function for quarkonium within the nonrelativistic QCD (NRQCD) factorization framework, accurate to the lowest order in the velocity expansion. The calculation is performed with high numerical precision and encompasses both polarized and unpolarized cases. We find that the NNLO corrections are positive and substantial across most of the $z$ region. Furthermore, the logarithmic singularities near the endpoint $z\to 1$ are fully reconstructed, providing essential inputs for future threshold resummation beyond leading-logarithmic accuracy. Combined with threshold-resummed formulas in the large-$z$ region, our results yield phenomenologically viable inputs for the $^3S_1^{(8)}$ gluon fragmentation function. This enables a more reliable description of large-$p_T$ $J/ψ$ ($ψ'$) and $χ_{cJ}$ production and polarization at hadron colliders, representing a crucial step toward a definitive test of the color-octet mechanism.

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arXiv2026

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

Within the NRQCD factorization framework, we investigate the color-singlet contribution to $e^+e^- \to J/\psi + X_{{\rm non\,}c\bar{c}}$ at B factories, computing the $\mathcal{O}(\alpha_s)$, $\mathcal{O}(v^2)$, and $\mathcal{O}(\alpha_s v^2)$ corrections to both the unpolarized cross section and the $J/\psi$ angular distribution. The $\mathcal{O}(\alpha_s v^2)$ 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 $\mathcal{O}(\alpha_s)$ and $\mathcal{O}(v^2)$ corrections are consistent with those reported in the literature. Phenomenologically, the $\mathcal{O}(\alpha_s)$ correction (with $\mu_R=\sqrt{s}/2$) reaches about $50\%$ of the leading-order cross section, while the $\mathcal{O}(v^2)$ and $\mathcal{O}(\alpha_s v^2)$ corrections are accidentally small. After including feeddown contributions from $\psi(2S)$, 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 $2\sigma$, calling for further experimental and theoretical investigations.

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arXiv2026

Semi-analytical two-loop QCD corrections to $e^+e^-\to J/ψ+χ_{cJ}$ at B factories

In this work, we compute the next-to-next-to-leading-order (NNLO) QCD corrections to the process $e^+e^-\to J/ψ+χ_{cJ}$ at B factories within the NRQCD factorization framework. The helicity amplitudes are obtained via asymptotic expansions around $r=0$ and $r=1$, with $r=16m_c^2/s$. Our asymptotic expressions reproduce the exact numerical results with high accuracy across the entire range $0\le r \le 1$, achieving a relative error below $10^{-5}$, which is sufficient for phenomenological applications. Notably, the large logarithmic terms are obtained analytically. We compute the unpolarized cross sections. The $\mathcal{O}(α_s)$ correction is found to be large, while the $\mathcal{O}(α_s^2)$ correction for $χ_{c0}$ production amounts to $33\%$ of the leading-order (LO) cross section, significantly reducing the scale uncertainties. For $χ_{c1}$, the $\mathcal{O}(α_s)$ and $\mathcal{O}(α_s^2)$ corrections correspond to $35\%$ and $-15\%$, respectively. For $χ_{c2}$, the corresponding corrections are $25\%$ and $-38\%$. The large cancellation between the corrections for $χ_{c2}$ brings the NNLO cross section close to the LO prediction. Our prediction for $χ_{c0}$ is consistent with the {\tt Belle} measurement and agrees with the {\tt BaBar} data within $2σ$. We also predict the angular distribution parameters $α^J_θ$, which are independent of nonperturbative inputs. A sharp discrepancy between the theory and the {\tt Belle} measurement is observed for $α^0_θ$, calling for further experimental and theoretical investigations. Moreover, future measurements of the angular distribution parameters for $χ_{c1}$ and $χ_{c2}$ will provide important tests of the theoretical framework.

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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

Azimuthal asymmetry in $J/ψ+γ$ and $J/ψ+J/ψ$ production in ultraperipheral heavy-ion collisions at LHC

Two-photon collision in ultraperipheral heavy-ion collisions (UPCs) provides a unique and powerful platform for probing QCD with linearly polarized quasi-real photons. While photon polarization effects have been recognized in dilepton and even in light hadrons production, their consequences for heavy quarkonium production remain unexplored. In this work we investigate for the first time the $γγ\to J/ψ+γ(J/ψ)$ channels in Pb-Pb UPCs at the Large Hadron Collider (LHC), by integrating the non-relativistic QCD (NRQCD) factorization approach with the transverse-momentum-dependent (TMD) photon distributions. Based on the helicity amplitudes at lowest order in strong coupling and velocity expansion, we predict sizable $\cos(2ϕ)$ and $\cos(4ϕ)$ azimuthal asymmetries arising from the interference of linearly polarized photon states. These azimuthal-dependent observables, defined as the ratios of weighted to unweighted cross sections, are expected to be stable against including the higher-order radiative corrections and varying nonperturbative NRQCD matrix elements, thus offering a fresh test of quarkonium production mechanism and the photon TMD structure in the ultrarelativistic limit.

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arXiv2025

The next-to-next-to-leading-order QCD corrections to $e^+e^-\to η_c/χ_{cJ}+γ$ at B factories

We investigate the processes $e^+e^-\to η_c+γ$ and $e^+e^-\to χ_{cJ}+γ$ at B factories within the NRQCD factorization framework, computing the corresponding helicity amplitudes through $\mathcal{O}(α_s^2)$. The short-distance coefficients are obtained as series expansions in $r=\frac{4m_c^2}{s}$ around $r=0, 1/3, 2/3, 1$, using the method of differential equations. By combining the expansions from all four points, we construct composite asymptotic expressions that reproduce the exact results accurately over the full range $0 \leq r\leq 1$, with relative errors below $0.1\%$ over most of the domain and remaining under $1\%$ elsewhere. Analytic expressions for the leading and next-to-leading logarithmic terms are extracted in the limit $r\to 0$. Using these results, we compute the unpolarized cross sections and observe that the perturbative corrections are small for $χ_{c0}+γ$, moderate for $χ_{c1}+γ$, and substantial for $η_c+γ$ and $χ_{c2}+γ$. Theoretical prediction for $χ_{c1}+γ$ is consistent with the {\tt Belle} measurement within $2σ$, showing good agreement between theory and experiment. We also predict the angular distribution parameters $α^H_θ$, which are insensitive to NRQCD matrix elements and exhibit small theoretical uncertainties. These parameters further display good stability across different perturbative orders. With the high luminosity anticipated at {\tt Belle 2}, future experimental measurements will thus provide a clear test of NRQCD factorization.

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arXiv2025

Mixed Electroweak-QCD Corrections to $H\to γγ$

We present for the first time the complete three-loop mixed electroweak-QCD ($\mathcal{O}(αα_s)$) corrections for the decay channel $H \to γγ$, by implementing three different on-shell $α$ schemes in computing the electroweak correction. Our studies indicate that the $\mathcal{O}(α_s)$ correction amounts to approximately $1.7\%$ of the leading-order prediction for the diphoton width, while the $\mathcal{O}(α)$ correction varies from $-4.8\%$ to $1.4\%$ depending on the specific $α$ scheme. The three-loop mixed electroweak-QCD correction may reach $0.6\%$, $0.5\%$, and $0.2\%$ of the LO diphoton width in $α(0)$, $α(M_Z)$, and $G_μ$ schemes, respectively, which is much more significant than the less-than-$0.1\%$ contribution from the three-loop QCD correction. It is also worth noting that the inclusion of the ${\cal O}(αα_s)$ correction significantly reduces the scheme dependence of the partial width from $0.6$ keV at leading order down to $0.03$ keV. The state-of-the-art Standard Model predictions are $Γ[H \to γγ] = 9.389÷9.420$ keV, providing a valuable theoretical benchmark for future Higgs factory collider program.

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arXiv2025

Electroweak corrections to Higgs+jet production in gluon fusion

We present the calculation of complete next-to-leading order electroweak corrections to the Higgs boson production in $gg\to g H$ channel. We apply the method of differential equations combined with the selection of optimized master integrals to accomplish the calculation of master integrals. We consider three distinct renormalization schemes. At leading order, the differential distributions and the total cross section show a strong dependence on the renormalization scheme. However, these discrepancies are considerably suppressed once electroweak corrections are taken into account. For $G_μ$ scheme, the electroweak correction amounts to approximately $4.3\%$ of the total cross section. Importantly, we find that the EW corrections exhibit a strong dependence on Higgs transverse momentum.

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arXiv2025

Optimized QCD two-loop correction to exclusive double $J/ψ$ production at B factories

We report the calculation of the process $e^+ e^- \to J/ψJ/ψ$ up to next-to-next-to-leading order (NNLO) at a center-of-mass (CM) energy of $\sqrt{s}=10.58$ GeV. We employ an improved NRQCD factorization approach, decomposing the amplitude into photon-fragmentation and non-fragmentation components. The fragmentation contribution is determined using the measured $J/ψ$ decay constant, while the interference and non-fragmentation parts are computed at NNLO in $α_s$ and lowest order in velocity. In this optimized scheme, both ${\cal O}(α_s)$ and ${\cal O}(α^2_s)$ corrections in the interference part are positive and exhibit good convergence. The non-fragmentation part is numerically insignificant. Our results indicate that with the projected 50 ${\rm ab}^{-1}$ dataset at \texttt{Belle 2}, the prospects for observing exclusive double $J/ψ$ production are very promising.

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arXiv2025

Perturbative QCD Evidence for Spin-2 Particles in the Di-$J/ψ$ Resonances

We extend the nonrelativistic QCD framework to explore the nature of the newly discovered di-$J/ψ$ resonances. Assuming them as either molecule-like states or tetraquarks, we calculated their hadroproduction cross sections at the LHC. We find that the observed resonances are most likely spin-2 particles, and there should exist their spin-0 counterparts near these resonances. The ratio of production cross sections of the observed resonances to the latent spin-0 ones are also presented, which might help to distinguish molecule-like states from tetraquarks.

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arXiv2025

Light quark fragmentation into S-wave fully charmed tetraquark

We compute the fragmentation function of a light quark into S-wave fully-charmed tetraquarks ($T_{4c}$) within the nonrelativistic QCD (NRQCD) framework, at leading order in $α_{s}$ and $v$. We present results for light quark fragmentation into $T_{4c}$ and predict its contribution to $T_{4c}$ production at high transverse momentum ($p_{T}$) at the LHC and EIC. We also compare light quark fragmentation with charm quark and gluon fragmentation channels. Our analysis shows that the production cross section for $T_{4c}$ from light quark fragmentation is smaller than that from gluon fragmentation but larger than that from charm quark fragmentation.

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arXiv2025

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

We calculate the cross sections for the processes $e^+e^-\to \jpsi η$ and $e^+e^-\to \jpsi η^\prime$ 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 $e^+e^-\to \jpsi η^\prime$, and less than 1 fb for $e^+e^-\to \jpsi η$, 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 $J/ψη$ 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 $e^+e^-\to \jpsi η$ through a coherent sum of contributions from various resonances and the continuum. The relative phase angles between these contributions are determined through a least-$χ^2$ 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 $e^+e^-\to \jpsi η$ is significantly larger than those for $e^+e^-\to \jpsi η^\prime$ measured by the BESIII collaboration.

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arXiv2024

Electromagnetic and hadronic decay of fully heavy tetraquark

In this study, we compute the electromagnetic and hadronic decay widths of the S-wave fully heavy tetraquark $T_{4Q}$ ($Q=c$ or $b$) at lowest order in $α_s$ and $v$, in the framework of nonrelativistic QCD. The short-distance coefficients are determined through the standard procedure of matching. The nonperturbative long-distance matrix elements are related to the phenomenological four-body Schrödinger wave functions at the origin, whose values are taken from literature. The branching fractions are predicted to be around $10^{-4}$ and $10^{-7}-10^{-6}$ for the $T_{4c}$ hadronic decay and electromagnetic decay, respectively. Combing our results with the $T_{4c}$ production cross sections at the LHC, we also predict the event numbers for various decay channels. With integrated luminosity $\mathcal{L}=100 \,{\rm fb}^{-1}$, it is expected that the event numbers can reach $10^3$ for $T_{4c}\to γγ$, and $10^6$ for $T_{4c}\to {\rm LH}$, at the LHC. The detecting prospect is promising. In addition, the decay widths of $T_{4b}$ are estimated based on simple dimensional analysis as well as velocity scaling rule.

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arXiv2024

Next-to-leading-order electroweak correction to $H\to Z^0γ$

Inspired by the recent observation of the Higgs boson radiative decay into $Z^0$ by {\tt ATLAS} and {\tt CMS} Collaborations, we investigate the next-to-leading-order (NLO) electroweak correction to this rare decay process in Standard Model (SM). Implementing the on-shell renormalization scheme, we find that the magnitude of the NLO electroweak correction may reach $7\%$ of the leading order (LO) prediction, much more significant than that of the NLO QCD correction, which is merely about $0.3\%$. After incorporating the ${\cal O}(α)$ correction, the predicted partial width from various $α$ schemes tend to converge to each other. Including both NLO electroweak and QCD corrections, the SM prediction for the branching fraction shifts from the LO value of $(1.40-1.71)\times 10^{-3}$ to $(1.55\pm 0.06)\times 10^{-3}$, considerably lower than the measured value ${\cal B}_{\rm exp}[H\to Z^0γ]=(3.4\pm 1.1)\times 10^{-3}$. Resolving this alarming discrepancy clearly calls for further theoretical investigations, and, more importantly, experimental efforts from {\tt HL-LHC} and the prospective Higgs factories such as {\tt CEPC} and {\tt FCC-ee}.

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arXiv2024

Photoproduction of fully charmed tetraquark at electron-ion colliders

In this work, we investigate the inclusive photoproduction of the $C$-odd, $S$-wave fully charmed tetraquark at electron-ion colliders within the nonrelativistic QCD (NRQCD) factorization framework, at the lowest order in velocity and $α_s$. The value of the NRQCD long-distance matrix element is estimated from two phenomenological potential models. Our studies reveal that the photoproduction of the $1^{+-}$ fully charmed tetraquark may be difficult to observe at HERA and the EicC; nevertheless, its observation prospect at the EIC appears to be bright.

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arXiv2024

Producing Fully-Charmed Tetraquarks via Charm Quark Fragmentation in Colliders

Within the framework of nonrelativistic QCD (NRQCD), we calculate the fragmentation function for a charm quark into an $S$-wave fully-charmed tetraquark, denoted as $T_{4c}$. The charm-to-$T_{4c}$ fragmentation function is expressed as a sum of products of the perturbatively calculable short-distance coefficients and the nonperturbative long-distance matrix elements (LDMEs). The short-distance coefficients are ascertained through the perturbative matching procedure at lowest order in $α_{s}$ expansion. The LDMEs are approximated using the $T_{4c}$ four-body wave functions at the origin, which have been evaluated by various phenomenological potential models in literature. Incorporating the celebrated QCD factorization and the charm-to-$T_{4c}$ fragmentation function, we predict the $T_{4c}$ production rate at high transverse momentum $p_T$ regime in colliders. %After implementing appropriate kinematic constraints, Both the differential distribution over $p_T$ and the integrated cross sections are predicted at the \texttt{LHC}. The cross sections for $T_{4c}$ states production can reach several femtobarns to several hundreds femtobarns, suggesting a substantial potential for $T_{4c}$ event production at the \texttt{LHC}. Additionally, we estimate for the photoproduction of $T_{4c}$ in electron-proton ($ep$) collisions. It is observed that the cross sections for these processes are moderate at the \texttt{HERA} and \texttt{EIC}, and relatively small at the \texttt{EicC}. Given the luminosities of these colliders, the prospect of detecting these fully-charmed tetraquarks at $ep$ colliders is somewhat challenging.

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arXiv2023

Two-Loop QCD Corrections to C even Bottomonium Exclusive Decays to Double $J/ψ$

In the framework of nonrelativistic QCD (NRQCD) factorization, we compute both the polarized and the unpolarized decay widths for the processes $η_b(χ_{bJ})\to J/ψJ/ψ$, accurate up to next-to-next-to-leading-order (NNLO) in $α_s$. For the first time, we confirm that the NRQCD factorization does hold at NNLO for the process involving triple quarkonia. We find the radiative corrections are considerable. In particular for $χ_{b2}$, both $\mathcal{O}(α_s)$ and $\mathcal{O}(α_s^2)$ corrections are sizable and negative, and can significantly reduce the leading order prediction. At NNLO, the branching fractions are $8.2\times 10^{-7}$, $6.2\times 10^{-6}$, $7.2\times 10^{-7}$ and $2.7\times 10^{-6}$ for $η_b$, $χ_{b0}$, $χ_{b1}$ and $χ_{b2}$ decay, respectively. Our theoretical predictions are consistent with the upper limits measured by the {\tt Belle} Collaboration. Moreover, we investigate the dependence of the theoretical predictions on the ratio of the charm quark mass and the bottom quark mass. By fixing $m_b$ and varying $m_c$ from $1.25$ to $1.9$ GeV, we find the branching fraction can change a factor of $2$, $3$, and $6$ for $η_b$, $χ_{b0}$, and $χ_{b1}$, respectively. In the phenomenological analysis, with the integrate luminosity $\mathcal{L}=100\,{\rm fb}^{-1}$, we expect about $(5-10)\times 10^3$ $η_b(χ_{bJ})\to J/ψJ/ψ\to \ell \bar{\ell}\ell \bar{\ell}$ events produced at the {\tt LHC}, thus it might be hopeful to search for these processes. On the other hand, there are less than $100$ $η_b(χ_{bJ})\to J/ψJ/ψ$ signal events at the B factory, so it seems the experimental measurements on these channels are quite challenging based on current dataset.

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arXiv2023

${\mathcal O}(α_s^2)$ corrections to $J/ψ+χ_{c0,1,2}$ production at $B$ factories

We compute the ${\mathcal O}(α_s^2)$ corrections to the exclusive channels $e^+e^-\to J/ψ+χ_{cJ}$ ($J=0,1,2$) at $\sqrt{s}=10.58$ GeV within the nonrelativistic QCD (NRQCD) factorization framework. The validity of NRQCD factorization at ${\cal O}(α_s^2)$ has been confirmed for these double-charmonium exclusive production processes. We analyze the impact of the $\mathcal{O}(α_s^2)$ corrections on the polarized and unpolarized cross sections, as well as the $J/ψ$ angular distributions, which largely reduce the renormalization scale dependence but increase the ${\mathcal O}(α_s)$ NRQCD predictions to some extent for $χ_{c0,1}$. With high numerical accuracy, our predictions for $σ(J/ψ+χ_{c1,2})$ through ${\mathcal O}(α_s^2)$ are compatible with the upper limit of the \texttt{Belle} measurement. Although the theoretical prediction for $σ(J/ψ+χ_{c0})$ is consistent with both \texttt{Belle} and \texttt{BaBar} measurements within uncertainties, there still exists serious tension between the predicted and the measured profiles for the $J/ψ$ angular distribution. Regarding the bright observation prospect of the $e^+e^-\to J/ψ+χ_{c1,2}$ channels in \texttt{Belle 2} experiment, it is interesting to compare the future measurements with our NRQCD predictions. The more accurate measurement of $e^+e^-\to J/ψ+χ_{0}$ at \texttt{Belle 2} will also help to clarify the long-standing puzzle of $J/ψ$ angular distribution.

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