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.

14 pages, 11 figures. Comments are welcome

References in corpus (22)

• Multiquark Resonances
• Pentaquark and Tetraquark states
• An updated review of the new hadron states
• Observation of structure in the $J/\psi$-pair mass spectrum
• Study of the doubly charmed tetraquark $T_{cc}^{+}$
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• STCF Conceptual Design Report: Volume 1 -- Physics & Detector
• Precision Study of Positronium: Testing Bound State QED Theory
• New structures in the J/$\psi$J/$\psi$ mass spectrum in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• $T_{cc}^{+}$ coupled channel analysis and predictions
• Observation of an excess of di-charmonium events in the four-muon final state with the ATLAS detector
• Doubly-heavy tetraquarks
• Tetraquark bound states in constituent quark models: benchmark test calculations
• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Benchmark calculations of fully heavy compact and molecular tetraquark states
• $T_{cc}^{+}$ and $X(3872)$ with the complex scaling method and $DD(\bar{D})\pi$ three-body effect
• Doubly heavy tetraquark bound and resonant states
• Unified description of the $Qs\bar{q}\bar{q}$ molecular bound states, molecular resonances and compact tetraquark states in the quark potential model
• Virtual states in the coupled-channel problems with an improved complex scaling method
• Fully strange tetraquark resonant states as the cousins of $X(6900)$
• Fully heavy tetraquark resonant states with different flavors
• Lowest Open Channels, Bound States, and Narrow Resonances of Dipositronium

Cited by in corpus (3)

• DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States
• The $\varphi NN,J/\psi NN,{\eta }_{c}NN$ systems based on HAL QCD interactions
• New Types of Hydrogenlike matter Composed of Electron(s) and Meson(s)