arXiv subjects

Jiao-Kai Chen

Publications and source records attributed to Jiao-Kai Chen.

At least 19 recordsLinked to original sources

arXiv2026

$λ$, $ρ$, and $σ$ Regge trajectories for the quadruply heavy pentaquark $bb\bar{u}cc$ in the diquark-triquark picture

Systematic investigations of four series of Regge trajectories for quadruply heavy pentaquarks are still lacking. Using the diquark and triquark Regge trajectory relations, we propose the Regge trajectory relations for the quadruply heavy pentaquark ${bb\bar{u}cc}$: $M=2m_{b}+2m_{c}+m_{u}+5C/2 +β_{x_λ}(x_λ+c_{0x_λ})^{2/3} +β_{x_{ρ_1}}(x_{ρ_1}+c_{0x_{ρ_1}})^{2/3}+β_{x_{ρ_2}}\sqrt{x_{ρ_2}+c_{0x_{ρ_2}}} +β_{x_σ}(x_σ+c_{0x_σ})^{2/3}$. Four series of Regge trajectories, namely the $λ$-, $ρ_1$-, $ρ_2$-, and $σ$-trajectories, are investigated. We demonstrate that accounting for the internal structure and substructure of pentaquarks is indispensable for constructing the $ρ_1$-, $ρ_2$-, and $σ$-trajectories; without such structural considerations, functional form and trajectory parameters can only be obtained via pure fitting against theoretical or experimental data. We further prove that the Regge trajectories of diquark 1, triquark, and diquark 2 (embedded within the triquark) do not correspond one-to-one to the $ρ_1$-, $ρ_2$-, and $σ$-trajectories. Nevertheless, these trajectories govern the behaviors of the respective $ρ_1$-, $ρ_2$-, and $σ$-trajectories. For both configurations $(bb)(\bar{u}(cc))$ and $(cc)(\bar{u}(bb))$, the $λ$-, $ρ_1$-, and $σ$-trajectories exhibit behavior of $M{\sim}x^{2/3}$ ($x=n_{r_1},n_{r_3},l_1,l_3,N_{r},L$), whereas the $ρ_2$-trajectories exhibit behavior of $M{\sim}\sqrt{x}$ ($x=n_{r_2},\,l_2$). The functional behavior of Regge trajectories for diquarks and triquark offers guidance for fitting the pentaquark Regge trajectories. Additionally, we provide rough estimates for spin-averaged masses of the $λ$-, $ρ_1$-, $ρ_2$-, and $σ$-excited states.

hep-ph↗

arXiv2026

Regge trajectories for the doubly heavy triquarks $((Qq)\bar{Q}')$

We attempt to apply the Regge trajectory approach to the doubly heavy triquarks $((Qq)\bar{Q}^{\prime})$ $(Q,\,Q'=b,\,c; q=u,\,d,\,s)$. We propose the Regge trajectory relations for the doubly heavy triquarks, and then employ them to crudely estimate the spectra of the triquarks $((cu)\bar{c})$, $((cu)\bar{b})$, $((cs)\bar{c})$, $((cs)\bar{b})$, $((bu)\bar{c})$, $((bu)\bar{b})$, $((bs)\bar{c})$, and $((bs)\bar{b})$. The $λ$-trajectories and the $ρ$-trajectories are investigated. The triquark Regge trajectory becomes a new and very simple approach for estimating the spectra of triquarks. It also provides a simple method to investigate the $ρ$-mode and $σ$-mode excitations of pentaquarks and hexaquarks in the triquark picutre. Moreover, the spin-averaged masses of the ground states of pentaquarks $(\bar{c}(cu))(cu)$, $(\bar{b}(bu))(bu)$ and $(\bar{c}(cu))(bu)$ are estimated, which are consistent with other theoretical predictions.

hep-ph↗

arXiv2026

$λ$, $ρ$, and $σ$ Regge trajectories for the hexaquark ${(\bar{u}(cc))(b(\bar{b}\bar{b}))}$ in the triquark-antitriquark picture

We propose Regge trajectory relations for the hexaquark ${(\bar{u}(cc))(b(\bar{b}\bar{b}))}$ by using the Regge trajectory relations for diquarks and triquarks. With these newly derived relations, we investigate five series of hexaquark Regge trajectories: the $λ$-, $ρ_1$-, $ρ_2$-, $σ_1$-, and $σ_2$-trajectories. We demonstrate that, apart from the simplest $λ_1$-trajectories, the $ρ_1$-, $ρ_2$-, $σ_1$-, and $σ_2$-trajectories cannot be constructed by merely mimicking the meson Regge trajectories, since mesons possess no internal substructures. To derive these trajectories, one must account for the structure and internal substructure of hexaquark. Without this structural information, the $ρ_1$-, $ρ_2$-, $σ_1$-, and $σ_2$-trajectories could only be obtained through direct fits to available theoretical predictions or future experimental data. We demonstrate that the $ρ_1$-, $ρ_2$-, $σ_1$-, and $σ_2$-trajectories for the hexaquark do not correspond respectively to the Regge trajectories for the triquark, antitriquark, diquark, and antidiquark. Nevertheless, their behaviors match those of the Regge trajectories for the triquark $(\bar{u}(cc))$, the antitriquark $(b(\bar{b}\bar{b}))$, the diquark $(cc)$, and the antidiquark $(\bar{b}\bar{b})$, in that respective order. Furthermore, we present rough mass estimates for the excited states corresponding to the $λ$-, $ρ_1$-, $ρ_2$-, $σ_1$-, and $σ_2$-trajectories.

hep-ph↗

arXiv2025

$λ$ and $ρ$ Regge trajectories for bottom-charm tetraquarks $(bq)(\bar{c}\bar{q}')$ and $(cq)(\bar{b}\bar{q}')$

Using the newly proposed tetraquark Regge trajectory relations, we investigate three series of Regge trajectories for bottom-charm tetraquarks $(bq)(\bar{c}\bar{q}')$ and $(cq)(\bar{b}\bar{q}')$ with $q,q'=u,d,s$: the $ρ_1$-, $ρ_2$-, and $λ$-trajectories. We provide rough estimates for the masses of the $ρ_1$-, $ρ_2$-, and $λ$-excited states. Except for the $λ$-trajectories, the complete forms of the other two series of Regge trajectories for bottom-charm tetraquarks are lengthy and cumbersome. We show that the $ρ_1$- and $ρ_2$-trajectories cannot be obtained by simply imitating meson Regge trajectories, because mesons have no substructures. To derive these trajectories, the tetraquarks' structure and substructure must be taken into consideration. Otherwise, the $ρ_1$- and $ρ_2$-trajectories would have to rely solely on fitting existing theoretical results or future experimental data. Consequently, the fundamental relationship between the slopes of the obtained trajectories and string tension would become unobvious, and the predictive power of the Regge trajectories would be compromised. Moreover, we show that the lengthy complete forms of the $ρ_1$- and $ρ_2$-trajectories can be well approximated by simple fitted formulas. For the bottom-charm tetraquarks $(bq)(\bar{c}\bar{q}')$ and $(cq)(\bar{b}\bar{q}')$, $ρ_1$- and $ρ_2$-trajectories exhibit a behavior of $M{\sim}x^{1/2}$ $(x=n_{r_1},n_{r_2},l_1,l_2)$, whereas $λ$-trajectories exhibit a behavior of $M{\sim}x^{2/3}$ $(x=N_{r},L)$. All three series of trajectories display concave downward behavior in the $(M^2,\,x)$ plane when the confining potential is linear. This conclusion holds irrespective of whether light-quark masses are included, owing to the large masses of the heavy quarks.

hep-ph↗

arXiv2025

$λ$ and $ρ$ Regge trajectories for the pentaquark $P_{cc\bar{c}bb}$ in the diquark-triquark picture

We propose the Regge trajectory relations for the fully heavy pentaquark $P_{cc\bar{c}bb}$ utilizing both diquark and triquark Regge trajectory relations. Using these new relations, we discuss four series of Regge trajectories: the $ρ_1$-, $ρ_2$-, $λ_1$-, and $λ_2$-trajectories. We provide rough estimates for the masses of the $ρ_1$-, $ρ_2$-, $λ_1$-, and $λ_2$-excited states. Except for the $λ_1$-trajectories, the complete forms of the other three series of Regge trajectories for the pentaquark $P_{cc\bar{c}bb}$ are lengthy and cumbersome. We show that the $ρ_1$-, $ρ_2$-, and $λ_2$-trajectories can not be obtained by simply imitating the meson Regge trajectories because mesons have no substructures. To derive these trajectories, pentaquark's structure and substructure should be taken into consideration. Otherwise, the $ρ_1$-, $ρ_2$-, and $λ_2$-trajectories must rely solely on fitting existing theoretical or future experimental data. Consequently, the fundamental relationship between the slopes of the obtained trajectories and constituents' masses and string tension will become unobvious, and the predictive power of the Regge trajectories would be compromised. Moreover, we show that the lengthy complete forms of the $ρ_1$-, $ρ_2$-, and $λ_2$-trajectories can be well approximated by the simple fitted formulas. Four series of Regge trajectories for the pentaquark $P_{cc\bar{c}bb}$ all exhibit a behavior of $M{\sim}x^{2/3}$, where $x=n_{r_1},n_{r_2},l_1,l_2,N_{r_1},N_{r_2},L_1,L_2$. All four series of trajectories exhibit concave downward behavior in the $(M^2,\,x)$ plane.

hep-ph↗

arXiv2025

Regge trajectories for the triply heavy triquarks

We attempt to apply the Regge trajectory approach to the triply heavy triquarks $((QQ')\bar{Q}^{\prime\prime})$ $(Q,\,Q',\,Q^{\prime\prime}=b,\,c)$. We present the triquark Regge trajectory relations, and then employ them to crudely estimate the spectra of the triquarks $((cc)\bar{c})$, $((cc)\bar{b})$, $((bc)\bar{c})$, $((bc)\bar{b})$, $((bb)\bar{c})$, and $((bb)\bar{b})$. The $λ$-trajectories and the $ρ$-trajectories are discussed. The triquark Regge trajectory becomes a new and very simple approach for estimating the spectra of triquarks. Moreover, the spin-averaged masses of the ground states of pentaquarks $(\bar{c}(cc))(cc)$, $(\bar{b}(cc))(cc)$ and $(\bar{c}(bb))(cc)$ are estimated, which are consistent with other theoretical predictions.

hep-ph↗

arXiv2025

$λ$ and $ρ$ trajectories for the doubly heavy baryons in the diquark picture

We present the explicit form of the Regge trajectory relations for the doubly heavy baryons $Ξ_{QQ'}$ and $Ω_{QQ'}$ $(Q,Q'=b,c)$ in the diquark picture. Using the derived Regge trajectory relations, we estimate the masses of the $λ$-excited states and the $ρ$-excited states, which are consistent with other theoretical predictions. Both the $λ$-trajectories and $ρ$-trajectories are discussed. We show that the $ρ$-trajectories behave differently from the $λ$-trajectories. Specifically, the $ρ$-trajectories behave as $M{\sim}x_ρ^{2/3}$ $(x_ρ=n_r,l)$, whereas the $λ$-trajectories follow $M{\sim}x_λ^{1/2}$ $(x_λ=N_r,L)$. By using the obtained relations, the baryon Regge trajectory provides a straightforward and easy method for estimating the spectra of both the $λ$-excited states and $ρ$-excited states.

hep-ph↗

arXiv2024

$λ$ and $ρ$ Regge trajectories for hidden bottom and charm tetraquarks $(Qq)(\bar{Q}\bar{q}')$

We propose the Regge trajectory relations for the heavy tetraquarks $(Qq)(\bar{Q}\bar{q}')$ $(Q=b,\,c;\,q,\,q'=u,\,d,\,s)$ with hidden bottom and charm. By employing the new relations, both the $λ$-trajectories and the $ρ$-trajectories for the tetraquarks $(Qq)(\bar{Q}\bar{q}')$ can be discussed. The masses of the $λ$-mode excited states and the $ρ$-mode excited states are estimated, and they agree with other theoretical predictions. We show that the behaviors of the $ρ$-trajectories are different from those of the $λ$-trajectories. The $ρ$-trajectories behave as $M{\sim}x_ρ^{1/2}$ $(x_ρ=n_r,\,l)$ while the $λ$-trajectories behave as $M{\sim}x_λ^{2/3}$ $(x_λ=N_r,\,L)$. Moreover, the Regge trajectory behaviors for other types of tetraquarks are investigated based on the spinless Salpeter equation. We show that both the $λ$-trajectories and the $ρ$-trajectories are concave downward in the $(M^2,\,x)$ plane. The Regge trajectories for the tetraquarks containing the light diquark and/or the light antidiquark also are concave in the $(M^2,\,x)$ plane when the masses of the light constituents are included and the confining potential is linear.

hep-ph↗

arXiv2024

Regge trajectories for the triply heavy bottom-charm baryons in the diquark picture

We present the explicit form of the Regge trajectory relations for the triply heavy bottom-charm baryons, which can be applied to investigate both the $λ$-mode excited states and the $ρ$-mode excited states. We estimate the masses of the $λ$-excited states and the $ρ$-excited states. The results are in agreement with other theoretical predictions. Both the $λ$-trajectories and the $ρ$-trajectories are discussed. Moreover, the behaviors of the $λ$- and $ρ$-trajectories for various baryons are discussed. It is shown that both the $λ$-trajectories and the $ρ$-trajectories for baryons are concave downwards in the $(M^2,\,x)$ plane. The Regge trajectories for the light baryons are approximately linear and become concave as the masses of the light constituents are considered.

hep-ph↗

arXiv2024

Regge trajectory relation for the universal description of the heavy-heavy systems: diquarks, mesons, baryons and tetraquarks

By employing the nonlinear Regge trajectory relation $M=m_R+β_x(x+c_{0x})^{2/3}\,\,(x=l,\,n_r)$, we investigate the heavy-heavy systems, such as the doubly heavy diquarks, the doubly heavy mesons, the heavy-heavy baryons, and the heavy-heavy tetraquarks. The fitted Regge trajectories illustrate that these heavy-heavy systems satisfy the above formula and show the existence of an universal description of the heavy-heavy systems. The universality embodies not only the universal behavior $M{\sim}x^{2/3}$ but also the universal parameters. The values of $c_{fn_r}$ and $c_{fl}$ vary with different heavy-heavy systems, but they are close to one. There is an inequality $β_{n_r}>β_{l}$, and it holds for all the discussed heavy-heavy systems. Moreover, the expression of $β_x$ [Eq. (11)] explains its variation with the change of the constituents' masses.

hep-ph↗

arXiv2024

Regge trajectory relations for the universal description of the heavy-light systems: diquarks, mesons, baryons and tetraquarks

Two newly proposed Regge trajectory relations are employed to analyze the heavy-light systems. One of the relations is $M=m_1+m_2+C'+β_x\sqrt{x+c_{0x}}$, $(x=l,\,n_r)$. Another reads $M=m_1+C'+\sqrt{β_x^2(x+c_{0x})+\frac{4}{3}\sqrt{π{β_x}}m^{3/2}_2(x+c_{0x})^{1/4}}$. $M$ is the bound state mass. $m_1$ and $m_2$ are the masses of the heavy constituent and the light constituent, respectively. $l$ is the orbital angular momentum and $n_r$ is the radial quantum number. $β_x$ and $c_{0x}$ are fitted. $m_1$, $m_2$ and $C'$ are input parameters. These two formulas consider both of the masses of heavy constituent and light constituent. We find that the heavy-light diquarks, the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks satisfy these two formulas. When applying the first formula, the heavy-light systems satisfy the universal description irrespective of both of the masses of the light constituents and the heavy constituent. When using the second relation, the heavy-light systems satisfy the universal description irrespective of the mass of the heavy constituent. The fitted slopes differ distinctively for the heavy-light mesons, baryons and tetraquarks, respectively. When employing the first relation, the average values of $c_{fn_r}$ ($c_{fl}$) are $1.026$, $0.794$ and $0.553$ ($1.026$, $0.749$ and $0.579$) for the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks, respectively. Upon application of the second relation, the mean values of $c_{fn_r}$ ($c_{fl}$) are $1.108$, $0.896$ and $0.647$ ($1.114$, $0.855$ and $0.676$) for the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks, respectively. Moreover, the fitted results show that the Regge trajectories for the heavy-light systems are concave downwards in the $(M^2,\,n_r)$ and $(M^2,\,l)$ planes.

hep-ph↗

arXiv2023

Regge trajectories for the light diquarks

We attempt to present an unified description of the light meson spectra and the light diquark spectra by applying the Regge trajectory approach. However, we find that the direct application of the linear Regge trajectory formula for the light mesons and baryons fails. To address this issue, we fit the experimental data of light meson spectra and the light diquark spectra obtained by other theoretical approaches. By considering the light quark mass and the parameter $C$ in the Cornell potential, we provide a provisional Regge trajectory formula. We also crudely estimate the masses of the light diquarks $(ud)$, $(us)$, and $(ss)$, and find that they agree with other theoretical results. The diquark Regge trajectory not only becomes a new and very simple approach for estimating the spectra of the light diquarks, but also can explicitly show the behavior of the masses with respect to $l$ or $n_r$. Moreover, it is expected that the diquark Regge trajectory can provide a simple method for investigating the $ρ$-mode excitations of baryons, tetraquarks and pentaquarks containing diquarks.

hep-ph↗

arXiv2023

Regge trajectories for the heavy-light diquarks

We attempt to apply the Regge trajectory approach to the heavy-light diquarks composed of one heavy quark and one light quark. However, we find that the direct application of the usual Regge trajectory formula for the heavy-light mesons and baryons fails. In order to correctly estimate the masses of the heavy-light diquarks, it is needed to consider the light quark mass correction and the parameter $C$ in the Cornell potential within the Regge trajectory formula. By using the modified Regge trajectory formulas, we are able to estimate the masses of the heavy-light diquarks $(cu)$, $(cs)$, $(bu)$ and $(bs)$, which agree with other theoretical results. It is illustrated that the heavy-light diquarks satisfy the universal descriptions irrespective of heavy quark flavors, similar to other heavy-light systems such as the heavy-light mesons, the heavy-light baryons composed of one heavy quark (diquark) and one light diquark (quark), and the heavy-light tetraquarks composed of one heavy diquark (antidiquark) and one light antidiquark (diquark). The diquark Regge trajectory provides a new and very simple approach for estimating the spectra of the heavy-light diquarks.

hep-ph↗

arXiv2023

Regge trajectories for the doubly heavy diquarks

The concept of diquark is important for understanding hadron structure and high-energy particle reactions. We attempt to apply the Regge trajectory approach to the doubly heavy diquarks. We present a method for determining the parameters in the diquark Regge trajectory. The spectra of diquarks $(cc)$, $(bb)$, and $(bc)$ are obtained by using the {\rt} approach and are found to agree with other theoretical results. The diquark Regge trajectory becomes a new and very simple approach for estimating the spectra of diquarks.

hep-ph↗

arXiv2022

Revisiting the pion Regge trajectories

We propose a model-independent ansatz $M={β_x}\left(x+c_0\right)^ν+c_1$ ($x=l,\,n_r$) and then use it to fit the orbital and radial pion Regge trajectories without the preset values. It is shown that nonzero $c_1$ is reasonable and acceptable. Nonzero $c_1$ gives an explanation for the nonlinearity of the pion Regge trajectories in the usually employed $(M^2,\,x)$ plane. As $m_R$ or $c_1$ is chosen appropriately, both the orbital and radial pion Regge trajectories are linear in the $((M-m_R)^2,\,x)$ plane whether the $π^0$ is included or not on the Regge trajectories. The fitted pion Regge trajectories suggest $0.45\leν\le0.5$, which indicates the confining potential $r^a$ with $9/11{\le}a\le1$. Moreover, it is illustrated in the appendix B that $m_R$ can be nonzero for the light nonstrange mesons. We present discussions in the appendix A on the structure of the Regge trajectories plotted in the $(M,\,x)$ plane and on the structure of the Regge trajectories in the $((M-m_R)^2,\,x)$ plane based on the potential models and the string models.

hep-ph↗

arXiv2021

Structure of the meson Regge trajectories

We investigate the structure of the meson Regge trajectories based on the quadratic form of the spinless Salpeter-type equation. It is found that the forms of the Regge trajectories depend on the energy region. As the employed Regge trajectory formula does not match the energy region, the fitted parameters neither have explicit physical meanings nor obey the constraints although the fitted Regge trajectory can give the satisfactory predictions if the employed formula is appropriate mathematically. Moreover, the consistency of the Regge trajectories obtained from different approaches is discussed. And the Regge trajectories for different mesons are presented. Finally, we show that the masses of the constituents will come into the slope and explain why the slopes of the fitted linear Regge trajectories vary with different kinds of mesons.

hep-ph↗

arXiv2019

Identical ideal individual hypothesis

The identical ideal individual hypothesis is proposed. According to this hypothesis, the identical ideal individuals should be classified into two classes: the bosonic individuals and the fermionic individuals. The bosonic individuals can occupy the same behavior state while the fermionic individuals can not be in the same behavior state. We propose that human beings and many species of animals are fermionic, which can not occupy the same behavior state according to the Pauli exclusion principle. An unified theoretical explanation is given for the natures of two important and seemingly irrelated phenomena in psychology: the existence of the personal space and the behavior differentiation under high population density condition.

q-bio.NC↗

arXiv2019

A novel quantum theory of psychology

The behavior coordinate system and the ideal individual model are presented. The behavior state of an ideal individual is assumed to be represented by a behavior state function. Based on the ideal individual model, the behavior coordinate system and the quantum probability, a novel quantum theory of psychology is offered here in a different way. It can give some enlightening viewpoints through which some phenomena can be discussed from a different perspective.

q-bio.NC↗