Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states

Abstract

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 $e^{+}{e}^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{+}{\mu }^{-}$, $e^{+}{e}^{+}{\mu }^{-}$, and ${\mu }^{+}{\mu }^{+}{e}^{-}$, as well as the tetralepton systems $e^{+}{e}^{+}{e}^{-}{e}^{-}$, ${\mu }^{+}{\mu }^{+}{\mu }^{-}{\mu }^{-}$, and ${\mu }^{+}{\mu }^{+}{e}^{-}{e}^{-}$. 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 $e^{+}{\mu }^{+}{e}^{-}$, ${\mu }^{+}{e}^{+}{\mu }^{-}$ systems, nor in the tetralepton ${\mu }^{+}{e}^{+}{\mu }^{-}{e}^{-}$ 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.

arXiv comment14 pages, 11 figures. Comments are welcome

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