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Hong-Hao Ma

Publications and source records attributed to Hong-Hao Ma.

At least 19 recordsLinked to original sources
arXiv2026

Production of doubly heavy quarkonium associated with two heavy quarks via top quark decays

In this paper, we analyze the $1 \rightarrow 4$ decay channel for the production of doubly heavy quarkonium, $(b\bar{c})$ or $(c\bar{c})$, via top-quark decays, $t \to (b\bar{c}) + c + c + \bar{s}$ and $t \to (c\bar{c}) + b + c + \bar{s}$, within the framework of nonrelativistic QCD (NRQCD). The dominant contributions are considered in color-singlet S-wave states, i.e., $(b\bar{c})[^1S_0]$, $(b\bar{c})[^3S_1]$, $(c\bar{c})[^1S_0]$, and $(c\bar{c})[^3S_1]$. Our calculations show that the decay widths for $\bar{B_{c}}$, $\bar{B_{c}^{*}}$, $η_{c}$ and $J/ψ$ production are 0.2251, 0.3099, 0.0537 and 0.0555 MeV, respectively, resulting in ${\cal O}(10^{4}\text{--}10^{6})$ level of $\bar{B}_c^{(*)}$ events and ${\cal O}(10^{3}\text{--}10^{5})$ level of charmonium produced at LHC per year. In particular, we find that the dominant contribution to $η_{c}$ and $J/ψ$ production via top-quark decays arises from this decay channel proposed in this work. Moreover, this multi-body top-quark decay process can serve as a sensitive probe for validating the narrow-width approximation (NWA). Finally, we provide a detailed analysis of theoretical uncertainties and differential distributions to facilitate the corresponding experimental searches. The production of a hadron associated with three quarks contains rich physical information, providing new insights for the LHC to study $B_c$ mesons and charmonia.

hep-ph↗
arXiv2026

Investigation on the photoproduction of bottom-charmed baryon within NRQCD

We present a further theoretical study of the orbital $P$-wave bottom-charmed baryon within the framework of nonrelativistic QCD (NRQCD), considering both the direct photoproduction channel $γ+γ\rightarrow Ξ_{bc} +\bar{c}+\bar{b}$ and the resolved photoproduction channel $γ+g \rightarrow Ξ_{bc} +\bar{c}+\bar{b}$. At future linear colliders, ILC and CLIC, the initial photons can be emitted from the laser back-scattering (LBS) and then the parton gluon can be emitted from the photon. The formation of $Ξ_{bc}$ can be modeled in two-step: a compact diquark state $\langle bc\rangle[n]$ is formed first and subsequently captures a light quark from the vacuum to hadronize into the baryon $Ξ_{bc}$. The color and spin quantum number $[n]$ of $\langle bc\rangle$-diquark can be $[{}^3S_1]_{\bar{\textbf{3}}/\textbf{6}}$, $[{}^1S_0]_{\bar{\textbf{3}}/\textbf{6}}$, $[{}^1P_1]_{\bar{\textbf{3}}/\textbf{6}}$ or $[{}^3P_J]_{\bar{\textbf{3}}/\textbf{6}}$ with $J=0,1,2$. Based on the collision energies and design luminosity of ILC and CLIC, the cross sections, the differential distributions and the estimated produced events of $Ξ_{bc}$ baryon have been analyzed. The results show that the contribution of the orbital excited $P$-wave $Ξ_{bc}$ baryon can reach 7%-9% of the $S$-wave, providing a non-negligible contributions.

hep-ph↗
arXiv2025

Flavor Physics at the CEPC: a General Perspective

We discuss the landscape of flavor physics at the Circular Electron-Positron Collider (CEPC), based on the nominal luminosity outlined in its Technical Design Report. The CEPC is designed to operate in multiple modes to address a variety of tasks. At the $Z$ pole, the expected production of 4 Tera $Z$ bosons will provide unique and highly precise measurements of $Z$ boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean $Z$ decays will facilitate investigations into their flavor physics with unprecedented precision. We investigate the prospects of measuring various physics benchmarks and discuss their implications for particle theories and phenomenological models. Our studies indicate that, with its highlighted advantages and anticipated excellent detector performance, the CEPC can explore beauty and $τ$ physics in ways that are superior to or complementary with the Belle II and Large-Hadron-Collider-beauty experiments, potentially enabling the detection of new physics at energy scales of 10 TeV and above. This potential also extends to the observation of yet-to-be-discovered rare and exotic processes, as well as testing fundamental principles such as lepton flavor universality, lepton and baryon number conservation, etc., making the CEPC a vibrant platform for flavor physics research. The $WW$ threshold scan, Higgs-factory operation and top-pair productions of the CEPC further enhance its merits in this regard, especially for measuring the Cabibbo-Kobayashi-Maskawa matrix elements, and Flavor-Changing-Neutral-Current physics of Higgs boson and top quarks. We outline the requirements for detector performance and considerations for future development to achieve the anticipated scientific goals.

hep-ex↗
arXiv2025

Photoproduction of doubly charmed tetraquark $T_{cc}$ via photon-gluon fusion at ILC and CLIC

The photoproduction of doubly charmed tetraquark $T_{cc}$ is predicted through the resolved channel $γ+g\to \to \langle cc \rangle[n] + \bar{c}+\bar{c} \to T_{cc}+\bar{c}+\bar{c}$ at ILC and CLIC. At $e^{+}e^{-}$ colliders, the initial photons $γ$ can be produced from two primary sources, well-delineated within the $Weiz\ddot{a}cker$ Williams approximation (WWA) and the laser back-scattering (LBS). And the initial gluon can be emitted from the photon. The spin and color quantum number $[n]$ of the intermediate diquark configuration can be $\langle cc\rangle[^3S_1]_{\bar{3}}$. Then its nonperturbative hadronization to $T_{cc}$ was discussed in the phenomenological potential models. Finally, the differential distributions and theoretical uncertainty of the doubly charmed tetraquark $T_{cc}$ were analyzed. The conclusion is that it is promising to observe $T_{cc}$ via the resolved channel of photoproduction both at the ILC and CLIC, and the results have a strong dependence on the mass of constituent charm quark $m_c$ and the potential model.

hep-ph↗
arXiv2025

Application of fragmentation function to the indirect production of fully charmed tetraquark

The indirect production mechanisms of fully charmed tetraquark are analyzed using the NRQCD factorization and Suzuki approach, respectively. The process first produces a heavy charm quark through Higgs, $W^+$, or $Z^0$ decay, and then the resulting charm quark evolves into an $S$-wave fully charmed tetraquark state with quantum number $J^{PC}$, including $0^{++}$, $1^{+-}$, and $2^{++}$, via the fragmentation function. While the transverse momentum $\langle \vec{q}_T^2\rangle$ in Suzuki approach ranges from 2.01 to 299.04 GeV$^2$, the numerical results obtained from these two approaches are consistent with each other. The decay widths, branching ratios, and produced events would be predicted at LHC and CEPC, respectively. The corresponding theoretical uncertainty of heavy quark mass $m_c$ and distribution of energy fraction are also presented. The results show that the contribution for the production of $T_{4c}$ through $W^+$ decay channel at LHC is relatively large. At CEPC, a sufficient number of $T_{4c}$ events are produced through $Z^0$ decays, which is likely to be detected in future experiments.

hep-ph↗
arXiv2025

Indirect production of doubly charmed tetraquarks $T_{cc}$ at high energy colliders

The indirect production mechanisms of doubly charmed tetraquark $T_{cc}$ through three decay channels, Higgs$/Z^{0}\to \langle cc\rangle_{\bar{3}} +\bar{c}+\bar{c} \to T_{cc}^{\bar{q}\bar{q^{\prime}}} +\bar{c}+\bar{c} $ and $W^+\to \langle cc\rangle_{\bar{3}}+\bar{c}+\bar{s} \to T_{cc}^{\bar{q}\bar{q^{\prime}}} +\bar{c}+\bar{s} $, are analyzed within the framework of nonrelativistic QCD. The intermediate $\langle cc\rangle_{\bar{3}}$ diquark cluster in color antitriplet evolves into tetraquark components via the fragmentation process by trapping two light antiquarks ($\bar{q}$ and $\bar{q^{\prime}}$) from the vacuum. After the considered doubly charmed tetraquark components are summed, including $T_{cc}^{\bar{u} \bar{u}}$, $T_{cc}^{\bar{u} \bar{d}}$, $T_{cc}^{\bar{d} \bar{d}}$, $T_{cc}^{\bar{u}\bar{s}}$, and $T_{cc}^{\bar{d}\bar{s}}$, the decay widths, branching ratios, and produced events each year for the production of $T_{cc}$ can be predicted at LHC and CEPC, respectively. The differential distributions and two main sources of theoretical uncertainty are also discussed. The results show that the produced events each year for $T_{cc}$ via $W^{+}$ decays is $1.80\times10^5$, nearly $2$ orders of magnitude larger than that by Higgs decays ($1.11\times10^{3}$) and $Z^{0}$ decays ($4.81\times10^3$) at LHC. However at CEPC, the largest contribution for the production of $T_{cc}$ is through $Z^{0}$ decays, about $1.63\times10^6$. There are only $4.79\times10^{-1}$ and $2.03\times10^{2}$ $T_{cc}$ events produced each year at CEPC through Higgs and $W^+$ decay, respectively.

hep-ph↗
arXiv2025

Further study on excited $Ξ_{QQ^{\prime}}$ via photoproduction at CEPC and FCC-ee

Within the framework of NRQCD, the photoproduction of doubly heavy baryons $Ξ_{cc}$, $Ξ_{bc}$, $Ξ_{bb}$ and their $P$-wave excited states has been systematically investigated. The production mechanism is that a color anti-triplet or sextuplet diquark $\langle QQ^{\prime} \rangle$ is first produced, and then evolved into a corresponding doubly heavy baryon $Ξ_{QQ^{\prime}}$ via the subprocess $γ+γ\rightarrow \langle QQ^{\prime} \rangle[n] +\bar{Q^{\prime}}+\bar{Q} \rightarrow Ξ_{QQ^{\prime}} +\bar{Q^{\prime}}+\bar{Q}$. Here, $Q^{(\prime)}$ denotes the heavy quark $b$ or $c$, [$n$] is the color and spin quantum number of intermediate diquark, which can be $[^3S_1]_{\bar{\textbf{3}}/\textbf{6}}$ and $[^1S_0]_{\bar{\textbf{3}}/\textbf{6}}$ for $S$-wave states, or $[^1P_1]_{\bar{\textbf{3}}/\textbf{6}}$ and $[^3P_J]_{\bar{\textbf{3}}/\textbf{6}}$ with $J=0,~1,~2$ for $P$-wave states. Predictions for the cross sections, differential distributions, and theoretical uncertainty have been analyzed. The results indicate that, at $\sqrt{s}=91$ GeV, the contribution of photoproduction for $P$-wave $Ξ_{cc}$, $Ξ_{bc}$, and $Ξ_{bb}$ is approximately $2.19\%$, $4.23\%$, $1.26\%$ of the contribution for $S$-wave, respectively. As the collision energy increases, the contribution of $P$-wave also increases. Assuming that the highly excited state can decay into ground state with $100\%$ efficiency, the total produced events at CEPC and FCC-ee can be as high as $\mathcal{O}(10^8)$, $\mathcal{O}(10^7),$ and $\mathcal{O}(10^5)$ corresponding to $Ξ_{cc}$, $Ξ_{bc}$, and $Ξ_{bb}$, respectively, which is very promising to be detected in future experiments.

hep-ph↗
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.

hep-ph↗
arXiv2023

Suppression of the multiplicity fluctuations in particle correlations

Multiplicity fluctuations play a crucial role in relativistic heavy-ion collisions. In this work, we explore how the multiplicity fluctuations can be effectively suppressed in the measurement of particle correlations. In particular, through proper normalization, particle correlations can be evaluated in a manner irrelevant to multiplicity. When the multiplicity fluctuations are adequately extracted, Monte Carlo simulations show that the remaining correlations possess distinct features buried in the otherwise overwhelming fluctuations. Moreover, we argue that such a normalization scheme naturally agrees with the multi-particle correlator, which can be evaluated using the Q-vectors. The implications of the present study in the data analysis are also addressed.

nucl-th↗
arXiv2023

Production of Excited Doubly Heavy Baryons at the Super-$Z$ Factory

In the framework of nonrelativistic QCD, the excited doubly heavy baryons are thoroughly studied via the channel $e^{+} e^{-}\rightarrow \langle QQ^{\prime}\rangle[n] \rightarrow Ξ_{QQ^{\prime}} +\bar{Q^{\prime}} +\bar{Q}$, which takes place at the collision energy $Z$-pole. $Q^{(\prime)}$ represents $b$ or $c$ quark for the production of $Ξ_{cc}$, $Ξ_{bc}$, and $Ξ_{bb}$, respectively. All of the intermediate diquark states $\langle QQ'\rangle[n]$ in $P$-wave, $\langle cc\rangle[^{1}P_{1}]_{\mathbf{\bar 3}}$, $\langle cc\rangle[^{3}P_{J}]_{\mathbf{6}}$, $\langle bc\rangle[^{1}P_{1}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bc\rangle[^{3}P_{J}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bb \rangle[^{1}P_{1}]_{\mathbf{\bar 3}}$, and $\langle bb\rangle[^{3}P_{J}]_{\mathbf{6}}$ with $J=0$, 1, or 2, are taken into account. The cross sections and differential distributions, including the transverse momentum, rapidity, angular, and invariant mass, are discussed for the excited baryons production. We find that the contributions of $\langle cc \rangle$, $\langle bc \rangle$, and $\langle bb \rangle$ in $P$-wave are found to be 3.97$\%$, 5.08$\%$, and 5.89$\%$, respectively, compared to $S$-wave. Supposing that all excited states can decay into the ground state 100\%, the total events $N_{Ξ_{cc}}=8.48 \times10^{4-6}$, $N_{Ξ_{bc}}=2.26\times10^{5-7}$, and $N_{Ξ_{bb}}=4.12 \times10^{3-5}$ would be produced at the Super-$Z$ Factory with a high luminosity up to ${\cal L} \simeq 10^{34-36}{\rm cm}^{-2} {\rm s}^{-1}$.

hep-ph↗
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.

hep-ph↗
arXiv2023

On thermodynamically consistent quasiparticle model at finite chemical potential

We explore the quasiparticle model at finite chemical potential related to Ru-Keng Su's distinguished contributions to the topic. Besides, we discuss recent developments in the model, and in particular, one argues that the effective mass of the quasiparticle might attain a specific form as a function of momentum, in addition to its dependence on temperature and chemical potential. Unlike the approaches based on the properties of underlying symmetry or renormalization group, the momentum dependence emerges as a special solution to an integro-differential equation resulting from the underlying thermodynamic consistency. Moreover, this special solution to the problem is shown to be more general than previously explored in the literature. Instead of fitting to the lattice QCD data at vanishing chemical potential, in this work, we adopt a ``bottom-up'' approach by assuming some analytic ansatzes that are manifestly thermodynamically consistent. The remaining physical quantities are subsequently derived, and possible implications are also addressed.

hep-ph↗
arXiv2022

Excited doubly heavy baryons production via Higgs decays

Through the interaction of Higgs with heavy quarks in standard model, we have systematically studied and predicted the production of excited doubly heavy baryons based on non-relativistic QCD theory. The decay widths, differential distributions, and major theoretical uncertainties of the excited doubly heavy baryons via the process $H \rightarrow \langle QQ'\rangle[n] \rightarrow Ξ_{QQ'}+ \bar {Q'} + \bar {Q}$ are discussed in detail. The spin and color quantum number of the intermediate $P$-wave diquark state $\langle QQ'\rangle[n]$ can be $\langle cc\rangle[^{1}P_{1}]_{\mathbf{\bar 3}}$, $\langle cc\rangle[^{3}P_{J}]_{\mathbf{6}}$, $\langle bc\rangle[^{1}P_{1}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bc\rangle[^{3}P_{J}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bb \rangle[^{1}P_{1}]_{\mathbf{\bar 3}}$ and $\langle bb\rangle[^{3}P_{J}]_{\mathbf{6}}$, with $J=0, 1, 2$. The contributions from all summed $P$-wave states can be about $3.05\%$, $3.23\%$ and $2.19\%$ of the $S$-wave states for the production of $Ξ_{cc}$, $Ξ_{bc}$ and $Ξ_{bb}$, accordingly. Therefore, there will be about 0.41$\times10^4$ events of $Ξ_{cc}$, 6.35$\times10^4$ events of $Ξ_{bc}$ and 0.28$\times10^4$ events of $Ξ_{bb}$ produced per year at the HL-LHC, and a smaller number of events would be produced at the CEPC or ILC but with a cleaner background to be measured by the experiments.

hep-ph↗
arXiv2022

Excited doubly heavy baryons production via top-quark decays

Within the framework of NRQCD, we calculate the production of excited doubly heavy baryons $Ξ_{bQ}$ through the semi-inclusive production process $t\rightarrow \langle bQ\rangle[n]\rightarrow Ξ_{bQ}+ \bar {Q} + W^+ $, where $Q= b$ or $c$ quark. The intermediate diquark state $\langle bQ\rangle[n]$ is in the excited $P$-wave state, including $[^1P_1]$ and $[^3P_J]$ ($J=$0, 1 or 2) in both color antitriplet state $\mathbf{\mathbf{\overline 3}}$ and color sixtuplet state $\mathbf{6}$, that is, $\langle bc\rangle[^{1}P_{1}]_{\mathbf{\overline 3}/ \mathbf{6}}$, $\langle bc\rangle[^{3}P_{J}]_{\mathbf{\overline 3}/ \mathbf{6}}$, $\langle bb\rangle[^{1}P_{1}]_{\mathbf{\overline 3}}$, and $\langle bb\rangle[^{3}P_{J}]_{\mathbf{6}}$. We find that the contributions from the P-wave states are about one order lower than the S-wave contributions, and this conclusion is consistent with others. We also analyze the invariant mass and angle differential distributions, and the theoretical uncertainty from the mass parameters and the renormalization scale. Finally, we can expect that about $1.14 \times10^{3-5}$ events of excited $Ξ_{bc}$ and $2.47 \times10^{1-3}$ events of excited $Ξ_{bb}$ can be produced per year at the LHC or HL-LHC with $\mathcal{L}$ =$10^{34-36}~\rm{cm}^{-2}~\rm{s}^{-1}$.

hep-ph↗
arXiv2020

Centrality dependence of multiplicity fluctuations from a hydrodynamical approach

As one of the possible signals for the whereabouts of the critical point on the QCD phase diagram, recently, the multiplicity fluctuations in heavy-ion collisions have aroused much attention. It is a crucial observable of the Beam Energy Scan program of the Relativistic Heavy Ion Collider. In this work, we investigate the centrality dependence of the multiplicity fluctuations regarding the recent measurements from STAR Collaboration. By employing a hydrodynamical approach, the present study is dedicated to the noncritical aspects of the phenomenon. To be specific, in addition to the thermal fluctuations, finite volume corrections, and resonance decay at the freeze-out surface, the model is focused on the properties of the hydrodynamic expansion of the system and the event-by-event initial fluctuations. It is understood that the real signal of the critical point can only be obtained after appropriately subtracting the background, the latter is investigated in the present work. Besides the experimental data, our results are also compared to those of the hadronic resonance gas, as well as transport models.

hep-ph↗
arXiv2020

Hydrodynamic results on multiplicity fluctuations in heavy-ion collisions

Multiplicity fluctuations are one of the most crucial observables in the Beam Energy Scan program of the Relativistic Heavy Ion Collider. It is understood that they can be utilized to probe the whereabouts of the critical point on the phase diagram of the QCD matter. However, a significant portion of these fluctuations is, apart from that related to the QCD phase transition, attributed to the other origins, which we refer to as "noncritical" ones. The present study is dedicated to the noncritical aspects of the multiplicity fluctuations in heavy-ion collisions. In particular, we focus on those of dynamical origin, such as the hydrodynamic expansion of the system and the event-by-event initial fluctuations, in addition to the usual thermal fluctuations, finite volume corrections, and resonance decay at the freeze-out surface. The obtained results are compared to those of the hadronic resonance gas model as well as to the experimental data.

nucl-th↗
arXiv2019

Thermodynamical consistency of quasiparticle model at finite baryon density

In this work, we revisit the thermodynamical self-consistency of the quasiparticle model with the finite baryon chemical potential adjusted to lattice QCD calculations. Here, we investigate the possibility that the effective quasiparticle mass is also a function of its momentum, $k$, in addition to temperature $T$ and chemical potential $μ$. It is found that the thermodynamic consistency can be expressed in terms of an integro-differential equation concerning $k$, $T$, and $μ$. We further discuss two special solutions, both can be viewed as sufficient condition for the thermodynamical consistency, while expressed in terms of a particle differential equation. The first case is shown to be equivalent to those previously discussed by Peshier et al. The second one, obtained through an ad hoc assumption, is an intrinsically different solution where the particle mass is momentum dependent. These equations can be solved by using boundary condition determined by the lattice QCD data at vanishing baryon chemical potential. By numerical calculations, we show that both solutions can reasonably reproduce the recent lattice QCD results of the Wuppertal-Budapest and HotQCD Collaborations, and in particular, those concerning finite baryon density. Possible implications are discussed.

hep-ph↗
arXiv2019

Production of doubly heavy baryons via Higgs boson decays

We systematically analyzed the production of semi-inclusive doubly heavy baryons ($Ξ_{cc}$, $Ξ_{bc}$ and $Ξ_{bb}$) for the process $H^0 \rightarrow Ξ_{QQ'}+ \bar {Q'} + \bar {Q}$ through four main Higgs decay channels within the framework of non-relativistic QCD. The contributions from the intermediate diquark states, $\langle cc\rangle[^{1}S_{0}]_{\mathbf{6}}$, $\langle cc\rangle[^{3}S_{1}]_{\mathbf{\bar 3}}$, $\langle bc\rangle[^{3}S_{1}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bc\rangle[^{1}S_{0}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bb\rangle[^{1}S_{0}]_{\mathbf{6}}$ and $\langle bb\rangle[^{3}S_{1}]_{\mathbf{\bar 3}}$, have been taken into consideration. The differential distributions and three main sources of the theoretical uncertainties have been discussed. At the High Luminosity Large Hadron Collider, there will be about 0.43$\times10^4$ events of $Ξ_{cc}$, 6.32$\times10^4$ events of $Ξ_{bc}$ and 0.28$\times10^4$ events of $Ξ_{bb}$ produced per year. There are fewer events produced at the Circular Electron Positron Collider and the International Linear Collider, about $0.26\times 10^{2}$ events of $Ξ_{cc}$, $3.83\times 10^{2}$ events of $Ξ_{bc}$ and $0.17\times 10^{2}$ events of $Ξ_{bb}$ in operation.

hep-ph↗