Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states
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| Format: | Preprint |
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2025
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| _version_ | 1866913775901212672 |
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| author | Ma, Yao Meng, Lu Wen, Liang-Zhen Zhu, Shi-Lin |
| author_facet | Ma, Yao Meng, Lu Wen, Liang-Zhen Zhu, Shi-Lin |
| contents | This work presents the first prediction of tetralepton resonant states containing muons, extending beyond the simplest tetralepton system, dipositronium ($\mathrm{Ps}_2$). With the rapid advancements in experimental facilities, the production and study of these intriguing states may be within reach. We perform a comprehensive analysis of S-wave trilepton and tetralepton systems within the framework of a QED Coulomb potential. We employ the Gaussian expansion method to solve the three- or four-body Schrödinger equation and utilize the complex scaling method to identify resonant states. We uncover a series of bound and resonant states in the trilepton systems $e^+e^+e^-$, $μ^+μ^+μ^-$, $e^+e^+μ^-$, and $μ^+μ^+e^-$, as well as the tetralepton systems $e^+e^+e^-e^-$, $μ^+μ^+μ^-μ^-$, and $μ^+μ^+e^-e^-$. The energies of these states range from $-30$ eV to $-1$ eV below the total mass of three or four leptons, with their widths varying from less than $0.01$ eV to approximately $0.07$ eV. Additionally, we calculate the spin configurations and root mean square radii of these states, providing insight into their spatial structures. No bound or resonant states are found in the trilepton $e^+μ^+e^-$, $μ^+e^+μ^-$ systems, nor in the tetralepton $μ^+e^+μ^-e^-$ system. A comparison with fully heavy tetraquark systems reveals that the additional color degree of freedom in QCD results in the absence of low-energy bound and resonant states. However, this extra degree of freedom allows for a broader range of $J^{PC}$ quantum numbers to produce resonant states, highlighting the rich complexity of QCD systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states Ma, Yao Meng, Lu Wen, Liang-Zhen Zhu, Shi-Lin High Energy Physics - Phenomenology High Energy Physics - Experiment Atomic Physics This work presents the first prediction of tetralepton resonant states containing muons, extending beyond the simplest tetralepton system, dipositronium ($\mathrm{Ps}_2$). With the rapid advancements in experimental facilities, the production and study of these intriguing states may be within reach. We perform a comprehensive analysis of S-wave trilepton and tetralepton systems within the framework of a QED Coulomb potential. We employ the Gaussian expansion method to solve the three- or four-body Schrödinger equation and utilize the complex scaling method to identify resonant states. We uncover a series of bound and resonant states in the trilepton systems $e^+e^+e^-$, $μ^+μ^+μ^-$, $e^+e^+μ^-$, and $μ^+μ^+e^-$, as well as the tetralepton systems $e^+e^+e^-e^-$, $μ^+μ^+μ^-μ^-$, and $μ^+μ^+e^-e^-$. The energies of these states range from $-30$ eV to $-1$ eV below the total mass of three or four leptons, with their widths varying from less than $0.01$ eV to approximately $0.07$ eV. Additionally, we calculate the spin configurations and root mean square radii of these states, providing insight into their spatial structures. No bound or resonant states are found in the trilepton $e^+μ^+e^-$, $μ^+e^+μ^-$ systems, nor in the tetralepton $μ^+e^+μ^-e^-$ system. A comparison with fully heavy tetraquark systems reveals that the additional color degree of freedom in QCD results in the absence of low-energy bound and resonant states. However, this extra degree of freedom allows for a broader range of $J^{PC}$ quantum numbers to produce resonant states, highlighting the rich complexity of QCD systems. |
| title | Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment Atomic Physics |
| url | https://arxiv.org/abs/2501.00871 |