arXiv subjects

Guang-Zhi Xu

Publications and source records attributed to Guang-Zhi Xu.

At least 19 recordsLinked to original sources

arXiv2026

Relativistic corrections to heavy quarkonium $+γ$ production at super Z factory

In the framework of nonrelativistic quantum chromodynamics, we study the $\mathcal{O}(v^2)$ relativistic corrections to heavy-quarkonium production associated with a photon at future electron-positron colliders operated in the Z-factory mode. S-, P-, and D-wave heavy quarkonia as well as the mixed state $ψ(3770)$ are considered. We comprehensively investigate tree-level $s$-channel processes for all states, together with $t$-channel contributions that apply only to ${}^3L_1$ states. It is found that the relativistic corrections substantially reduce the LO cross sections for charmonium states by roughly $20\%$-$70\%$, while the reduction is milder for bottomonium, at the level of $10\%$-$30\%$. Event yields for all studied channels are calculated, and sizable event yields are expected for $η_c$, $J/ψ$, $ψ(2S)$, $Υ$, and $ψ(3770)$, especially at FCC-ee.

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arXiv2026

Resonance-continuum interference with a possible tensor $X(6900)$ in radiative double-charmonium production at $\sqrt{s}=10.58~{\rm GeV}$

We study radiative double-charmonium production, $e^+e^-\to HHγ$ with $H=J/ψ$ and $η_c$, at $\sqrt{s}=10.58~{\rm GeV}$, including a possible tensor contribution from the fully charmed state $X(6900)$. The nonresonant amplitudes are calculated within the color-singlet non-relativistic QCD framework, while the $J^{PC}=2^{++}$ resonance is combined coherently with the continuum. We find that continuum--resonance interference significantly modifies the invariant-mass distributions near $M_{HH}\simeq M_X$. The $J/ψJ/ψγ$ channel exhibits a pronounced phase-dependent resonant structure, with a near-resonance cross section of $0.038$--$0.111~{\rm fb}$. In contrast, the $η_cη_cγ$ channel is continuum dominated and shows only a localized interference effect with an extremely suppressed production rate, rendering its experimental observation extremely challenging. These channel-dependent features arise from the different effective decay structures and demonstrate the importance of an amplitude-level treatment of the $X(6900)$ contribution.

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arXiv2026

Next-to-leading order QCD and relativistic corrections to $Z \to J/ψ+Υ(nS)$

In this paper, we calculate the decay widths and branching fractions for the decays $Z \to J/ψ+Υ(nS)$ ($n=1,2,3$) at future super $Z$ factory and at the CEPC/FCC-ee, including both the relativistic and QCD corrections within the framework of nonrelativistic QCD. Both the relativistic and QCD corrections are found to be large and negative. Compared to the leading-order results, the decay widths are significantly reduced by the higher-order corrections due to significant numerical cancellations. Despite the resulting large theoretical uncertainties, sizable event rates from these rare decay channels could still be anticipated at future high-luminosity electron-positron colliders running around the Z-pole. Ultimately, our results provide an essential theoretical baseline, highlighting the necessity of incorporating even higher-order corrections and resummation techniques for future precision phenomenological studies.

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arXiv2026

Revisiting relativistic corrections to inclusive $J/ψ$ production at B factories: Complete expansion for three-body quarkonium production

We revisit the calculations of relativistic corrections to inclusive $J/ψ$ production at B factories. For quark-level subprocesses with three-body final states, we carry out a full expansion of the final-state kinematic parameters. The resulting cross sections are theoretically self-consistent and independent of the choice of integration variables. In the high-energy limit, both cross-section magnitudes and the line shapes of correction curves for energy and momentum distributions agree remarkably well with fragmentation-function calculations. We find that $\mathcal{O}(v^2)$ corrections suppress the cross section by roughly $14.55\%$ in the $J/ψ+ X_{c\bar{c}}$ channel and enhance it by approximately $12.18\%$ for the $J/ψ+ X_{\text{non-}c\bar{c}}$ channel. After incorporating published $\mathcal{O}(α_s)$ corrections, color-octet contributions, two-photon production channels, and feed-down effects, tension persists between theoretical predictions and experimental measurements. This indicates that complete prompt-quarkonium calculations through $\mathcal{O}(α_s, v^2)$, or evaluations incorporating higher-order corrections, are required to resolve this tension.

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arXiv2026

Rare Radiative Decays of Z boson into S- and P-wave Charmonium within the Bethe-Salpeter Model

We employ the Bethe-Salpeter (BS) model to investigate radiative decays of the Z boson into charmonium. Within the instantaneous approximation of the BS equation, we analyze the relevant decay channels for S-wave charmonium states ($ψ(nS)$, $η_{c}(nS)$, $n=1,2,3$) and P-wave charmonium states ($χ_{c0}(mP)$, $χ_{c1}(mP)$, $h_{c}(mP)$, $m=1,2$). We compute all branching fractions using leading-order Feynman diagrams. For the $J/ψ$ channel, our BS calculations suggest that prior theoretical results were likely underestimated, making our prediction more promising for future experimental measurements.

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arXiv2026

Exclusive process $γγ\rightarrow J/ψ+γ$ production in ultraperipheral proton and nuclear collisions at the HL-LHC and FCC

We present a next-to-leading-order (NLO) analysis of exclusive $J/ψ+γ$ production via photon-photon fusion in ultraperipheral collisions at the High-Luminosity Large Hadron Collider (HL-LHC) and the Future Circular Collider (FCC). The study is performed within the NRQCD factorization framework for proton-proton, proton-nucleus, and nucleus-nucleus collisions, with nuclear species spanning a wide range of nuclear charges (O, Ca, Ar, Kr, Xe, and Pb), enabling a systematic investigation of nuclear effects on the production cross sections. The photon fluxes are modeled using an electric-dipole form factor, with the impact-parameter dependence strictly enforced to ensure the exclusivity of the process. We present predictions for total cross sections and kinematic distributions at leading order and NLO. With a transverse momentum cut of $p_T > 2\,\mathrm{GeV}$, the NLO corrections reduce the cross section by approximately $35\%$ at the central scale. The associated theoretical uncertainties are systematically estimated via renormalization scale variations. Despite this suppression, the cross sections remain sizable and indicate that exclusive $J/ψ+ γ$ production serves as a sensitive probe of photon-induced quarkonium production mechanisms. We thus present the corresponding event yields predicted for the HL-LHC and the FCC.

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arXiv2026

Rare Exclusive Decays of the Z-boson into S-wave Quarkonia within the Bethe-Salpeter Formalism

This paper investigates the rare decays of the Z boson into S-wave quarkonia within the Bethe-Salpeter formalism. Both the production of double S-wave quarkonia and radiative decays into single S-wave quarkonium are analyzed. For double quarkonia production, i.e., $Z\to VV$ and $Z\to VP$ (where $V$ and $P$ represent vector and pseudoscalar quarkonia, respectively), we consider the leading order contribution from both QCD as well as electromagnetic transition via virtual photon (QED) amplitudes. The heavy quark limit is adopted to simplify calculations. Additionally, we have introduced another possible leading order channel for Z-boson decays to double S-wave quarkonia, where the Z boson decays into bottomonium plus charmonium via QED amplitude. Such processes may include $Z\to J/ψ+Υ(1S)$, $Z\toη_{b}+J/ψ$ and $Z\toη_{c}+Υ(1S)$. Moreover, we have also studied radiative Z boson decays to S-wave quarkonium, namely $Z\to X(Q\bar{Q})γ$, where $X(Q\bar{Q})=J/ψ$, $Υ$, $η_{c}$, and $η_{b}$. Interestingly, for double charmonium and radiative charmonium production, our results are larger than the NRQCD finding, while for the bottomonium case, our findings are comparatively smaller. This shows that charmonium is a relativistic particle, while bottomonium is a non-relativistic particle.

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arXiv2026

Associated Production of Charmonia-Bottomonia with Color-Octet Channels at the Z Factory, CEPC and FCC-ee

Within the nonrelativistic QCD (NRQCD) framework, we investigate the associated production of charmonia+bottomonia at future super $Z$ factory and at the CEPC/FCC-ee. The color-octet(CO) channels in the $γ^*/Z^0$-propagated process are considered besides the color-singlet(CS) channels. We find that the contributions of the CO states to the total cross section are dominant for almost all processes from the production threshold to the $Z^0$ mass. Thus, the comparison between the theoretical results and future data may give constraints to the CO matrix elements. In addition, we calculate the relativistic corrections to both the CS and CO channels, which decrease the cross sections significantly, with the $K$ factor $\simeq0.5$. The predicted events of ($J/ψ+Υ$, $Υ+η_c$) production, with $J/ψ, Υ$ reconstructed by lepton pair and $η_c$ reconstructed by hadronic decays, are (1,1) and (13,10) at the CEPC(2-yr) and FCC-ee(4-yr), respectively.

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arXiv2026

Order-$v^2$ relativistic corrections to heavy-quark fragmentation into $P$-wave quarkonium states

Within the framework of nonrelativistic QCD (NRQCD) factorization,and based on the Collins--Soper operator definition of fragmentation functions, we present a systematic calculation of the fragmentation functions for a heavy quark fragmenting into color-singlet $P$-wave quarkonium states. After reproducing and confirming the known leading-order results, we further compute the relativistic corrections up to order $\mathcal{O}(v^{2})$. Our analysis applies both to quarkonium systems composed of heavy quarks with the same flavor and to $B_c$-type mesons formed by heavy quarks of different flavors. Numerical results show that, for all color-singlet $P$-wave channels, the $\mathcal{O}(v^{2})$ relativistic corrections give sizable negative contributions over most of the momentum-fraction $z$ region. We further compute inclusive cross sections for $P$-wave quarkonium plus charmed hadrons in $e^+e^-$ annihilation via the single photon process up to $\mathcal{O}(v^{2})$ by applying our obtained fragmentation functions, and the resulting predictions are consistent with the full fixed-order results in the high-energy region.

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arXiv2025

Relativistic corrections to double $B_c$ meson production in $e^+e^-$ annihilation

Within the framework of nonrelativistic QCD (NRQCD) factorization, we investigate the relativistic corrections to the production of double $B_c$ mesons in $e^+e^-$ annihilation. The study covers center-of-mass energies from the production threshold up to $2m_Z$, considering both the photon and $Z^0$-boson propagated processes. We find that the relativistic corrections are significant, with the corresponding $K$ factors of approximately 0.6. The azimuthal asymmetry, angular distribution, and transverse momentum distribution are also presented.

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arXiv2025

Order-$v^4$ corrections to heavy quark fragmentation to S-wave heavy quarkonium

Within the framework of nonrelativistic quantum chromodynamics (NRQCD) factorization, we compute the $\mathcal{O}(v^{4})$ relativistic corrections to the fragmentation of a heavy quark into the color-singlet $^{1}S_{0}^{[1]}$ and $^{3}S_{1}^{[1]}$ quarkonium states. Using the Collins--Soper definition of the fragmentation function, we reproduce the known $\mathcal{O}(v^{2})$ results. We find that the $\mathcal{O}(v^{4})$ correction gives a positive contribution relative to the leading order result over a wide range of the light-cone momentum fraction $z$, while its magnitude remains much smaller than that of the $\mathcal{O}(v^{2})$ correction. This behavior indicates a good convergence of the NRQCD relativistic expansion in this process. We further extend the calculation to the fragmentation functions in the unequal-mass case at $\mathcal{O}(v^{4})$ and obtain the corresponding analytical expressions.

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arXiv2025

Toponium: Implementation of a toponium model in FeynRules

Toponium -- a bound state of the top-antitop pair ($t\bar{t}$) -- emerges as the smallest and simplest hadronic system in QCD, with an ultrashort lifetime ($τ_t \sim 2.5\times 10^{-25}$~s) and a femtometer-scale Bohr radius ($r_{\text{Bohr}} \sim 7\times 10^{-18}$~m). We present a computational framework extending the Standard Model (SM) with two S-wave toponium states: a spin-singlet $η_t$ ($J^{PC}=0^{-+}$) and a spin-triplet $J_t$ ($J^{PC}=1^{--}$). Using nonrelativistic QCD (NRQCD) and a Coulomb potential, we derived couplings to SM particles (gluons, electroweak bosons, Higgs boson, and fermion pairs) and implemented the Lagrangian in FeynRules, generating FeynArts, MadGraph, and WHIZARD models for collider simulations. Key results include dominant decay channels ($η_t \to gg/ZH$, $J_t \to W^+W^-/b\bar{b}$) and leading order (LO) cross sections for $pp \to η_t(nS) \to {\rm non-}t\bar{t}$ ({66 fb} at 13 TeV). The model avoids double-counting artifacts by excluding direct $t\bar{t}$ couplings, thereby ensuring consistency with perturbative QCD. This work establishes a complete pipeline for precision toponium studies, bridging NRQCD, collider phenomenology, and tests of SM validity at future lepton colliders (e.g., CEPC, FCC-ee, muon colliders) and the LHC. This provides the first publicly available UFO model for toponium, enabling direct integration with MadGraph and WHIZARD for simulations.

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arXiv2025

Double heavy quarkonia production with color-octet channels at Z factory and at the CEPC/FCC-ee

Within the NRQCD framework, we calculate the exclusive production of double heavy quarkonium(double charmonium and double bottomonium) at future super $Z$ factory and at the CEPC/FCC-ee. The color-octet(CO) channels in the $γ^*/Z^*$-propagated process are considered along with the color-singlet(CS) channels. We found that the contributions of CO states to the total cross section are significant or dominant for many processes within energy region at $Z$ factory and at the CEPC/FCC-ee. The experimental measurements will help us to verify the CO mechanism. Among these CO channels, the gluon fragmentation into $^3S_1^{8}$ states is most important. Thus, the comparison between the theoretical results and future data will give a strong constraint to the matrix elements $\langle\mathcal{O}\left(^3S_1^{[8]}\right)\rangle$. Additionally, we consider the relativistic corrections to both the CS and CO channels which decrease the cross sections significantly. Specially, the $K$ factors are about $0.5$ for most charmonium channels. We get estimates of the events for double heavy quarkonium production. The final events of $J/ψ+η_c$, $J/ψ+J/ψ$, $Υ+η_b$, $Υ+Υ$ production would be (22, 570, 71, 61) and (206, 5343, 665, 576) at the CEPC (2-year) and at the FCC-ee (4-year) for the $Z$ factory mode, respectively.

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arXiv2024

Study on Toponium: Spectrum and Associated Processes

In this paper, we calculate the toponium spectrum in the potential model with the screened effects. Coulombic part is dominant for toponium, and the coefficient of the Coulomb potential is chosen from lattice QCD calculations at an infinite quark mass in accord with the ultrasoft scale choice. We also derive the relative E1 transitions, decays, and production.

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arXiv2023

$Z$-boson decays into $S$-wave quarkonium plus a photon up to ${\cal O}(α_{s} v^2)$ corrections

In this paper, we calculate the decay widths and branching fractions for the decays $Z \to H+ γ$ up to ${\cal O}(α_{s} v^2)$ accuracy within the framework of nonrelativistic QCD, where $H$ stands for the $S$-wave quarkonium $η_c$, $J/ψ$, $η_b$ or $Υ$, respectively. To compare with the leading-order terms, those corrections show good perturbative behavior as expected. It is found that contributions from the next-to-leading order QCD correction ${\cal O}(α_{s}v^0)$, the relativistic correction ${\cal O}(α^{0}_{s}v^2)$ and their joint correction ${\cal O}(α_{s} v^2)$ are sizable and comparable to each other, especially for the charmonium case. Thus we need to take all of them into consideration for a sound estimation. For a high luminosity electron-positron collider running around the $Z$-pole, due to $Z$-boson resonance effect, sizable events could be produced from those rare decay channels.

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arXiv2016

Study of Color Octet Matrix Elements Through $J/ψ$ Production in $e^{+}e^{-}$ Annihilation

In this paper, the color-octet long distance matrix elements are studied though the inclusive $J/ψ$ production in $e^{+}e^{-}$ annihilation within the non-relativistic QCD frame. The calculations are up-to next-to-leading order with the radiative corrections and relativistic corrections at the B-factory energy region and the near-threshold region of $4.6\sim5.6~{\rm GeV}$. A constraint of the long distance matrix elements ($\langle^1S_0^{8}\rangle$, $\langle^3P_0^{8}\rangle$) is obtained. Through our estimation, the P-wave color-octet matrix element ( $\langle0|^3P^8_0|0\rangle$ ) should be the order of $0.005m_c^2~{\rm GeV}^3$ or less. The constraint region is not compatible with the values of the long distance matrix elements fitted at hadron colliders.

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arXiv2016

$B^*_{s,d} \to μ^+ μ^-$ and its impact on $B_{s,d} \to μ^+ μ^-$

The decay of $B^*_{s,d} \to μ^+ μ^-$~ and its impact on $B_{s,d} \to μ^+ μ^-$ is studied here. The $ μ^+ μ^-$ decay widths of vector mesons $B^*_{s,d}$ are about a factor of 700 larger than the corresponding scalar mesons $B_{s,d}$. The obtained ratio of the branching fractions $Br({B_{s,d}^*\to μ^+μ^-})/{Br({B_{s,d}\toμ^+μ^-})}$ is about $\frac{0.3 \times {\rm eV}}{{Γ(B^*_{s,d} \to B_{s,d} γ)}}$. At the same time, the hadronic contribution $B_{s,d} \to B^*_{s,d} γ\to μ^+ μ^-$ is estimated too. The relative increase of the amplitude of $B_{s,d}\to μ^+μ^-$ is about $(0.01\pm 0.006) \sqrt{\frac{{Γ(B^*_{s,d} \to B_{s,d} γ)}}{100~ {\rm eV}}}$. If we choose $Γ(B^*_{s,d} \to B_{s,d} γ)=2~$eV, the branching fractions of the vector mesons to lepton pair are $(6.2 \pm 0.6) \times 10^{-10}$ and $(1.7 \pm 0.2) \times 10^{-11}$ for $B^*_{s}$ and $B^*_{d}$ respectively. If we choose $Γ(B^*_{s,d} \to B_{s,d} γ)=200~$eV, the updated branching fractions of the scalar mesons to muon pair are $(3.78 \pm 0.25)\times 10^{-9}$ and $(1.09 \pm 0.09)\times 10^{-10}$ for $B_{s}$ and $B_{d}$ respectively. Further studies on $B^*_{s,d}$ are usefully here, including dielectron decay, two-body decay with $J/ψ$, and so on.

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arXiv2015

Interference effects on Higgs mass measurement in $e^+e^-\to H(γγ) Z$ at CEPC

A high luminosity Circular Electron Positron Collider (CEPC) as a Higgs Factory will be helpful to the precision measurement of the Higgs mass. The signal-background interference effect is carefully studied for the Higgs diphoton decay mode in the associated Z boson production at the future $e^+e^-$ colliders at energy $246 {\rm GeV}$. The mass shifts go up from about $20 {\rm MeV}$ to $50 {\rm MeV}$ for the experimental mass resolution ranging from $0.8 {\rm GeV}$ to $2 {\rm GeV}$.

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