$λ$ and $ρ$ Regge trajectories for hidden bottom and charm tetraquarks $(Qq)(\bar{Q}\bar{q}')$
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| Format: | Preprint |
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2024
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| _version_ | 1866912097737113600 |
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| author | Xie, Jia-Qi Song, He Feng, Xia Chen, Jiao-Kai |
| author_facet | Xie, Jia-Qi Song, He Feng, Xia Chen, Jiao-Kai |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_04222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $λ$ and $ρ$ Regge trajectories for hidden bottom and charm tetraquarks $(Qq)(\bar{Q}\bar{q}')$ Xie, Jia-Qi Song, He Feng, Xia Chen, Jiao-Kai High Energy Physics - Phenomenology 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. |
| title | $λ$ and $ρ$ Regge trajectories for hidden bottom and charm tetraquarks $(Qq)(\bar{Q}\bar{q}')$ |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2407.04222 |