arXiv subjects

Xin-Ru Liu

Publications and source records attributed to Xin-Ru Liu.

6 recordsLinked to original sources

arXiv2026

$\lambda$, $\rho$, and $\sigma$ 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 +\beta_{x_{\lambda}}(x_{\lambda}+c_{0x_{\lambda}})^{2/3}$$+\beta_{x_{\rho_1}}(x_{\rho_1}+c_{0x_{\rho_1}})^{2/3}+\beta_{x_{\rho_2}}\sqrt{x_{\rho_2}+c_{0x_{\rho_2}}} +\beta_{x_{\sigma}}(x_{\sigma}+c_{0x_{\sigma}})^{2/3}$. Four series of Regge trajectories, namely the $\lambda$-, $\rho_1$-, $\rho_2$-, and $\sigma$-trajectories, are investigated. We demonstrate that accounting for the internal structure and substructure of pentaquarks is indispensable for constructing the $\rho_1$-, $\rho_2$-, and $\sigma$-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 (emdedded within the triquark) do not correspond one-to-one to the $\rho_1$-, $\rho_2$-, and $\sigma$-trajectories. Nevertheless, these trajectories govern the behaviors of the respective $\rho_1$-, $\rho_2$-, and $\sigma$-trajectories. For both configurations $(bb)(\bar{u}(cc))$ and $(cc)(\bar{u}(bb))$, the $\lambda$-, $\rho_1$-, and $\sigma$-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 $\rho_2$-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 $\lambda$-, $\rho_1$-, $\rho_2$-, and $\sigma$-excited states.

hep-ph↗

arXiv2026

$\lambda$, $\rho$, and $\sigma$ 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 $\lambda$-, $\rho_1$-, $\rho_2$-, $\sigma_1$-, and $\sigma_2$-trajectories. We demonstrate that, apart from the simplest $\lambda_1$-trajectories, the $\rho_1$-, $\rho_2$-, $\sigma_1$-, and $\sigma_2$-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 $\rho_1$-, $\rho_2$-, $\sigma_1$-, and $\sigma_2$-trajectories could only be obtained through direct fits to available theoretical predictions or future experimental data. We demonstrate that the $\rho_1$-, $\rho_2$-, $\sigma_1$-, and $\sigma_2$-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 $\lambda$-, $\rho_1$-, $\rho_2$-, $\sigma_1$-, and $\sigma_2$-trajectories.

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 $\lambda$-trajectories and the $\rho$-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 $\rho$-mode and $\sigma$-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↗

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

$λ$ 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↗