arXiv subjects

Shi-Lin Zhu

Publications and source records attributed to Shi-Lin Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Investigation of S-wave tetraquark bound and resonant states with all Jacobi coordinates

We systematically explore the $S$-wave tetraquark systems $Qs\bar{n}\bar{n}$, $QQ\bar{n}\bar{n}$, $QQ\bar{Q}\bar{Q}$, and $ss\bar{s}\bar{s}$ ($Q=c,b$; $n=u,d$) within the constituent quark potential model. We incorporate all K-type Jacobi coordinates in addition to the conventional H-type configurations, optimize the basis expansion via a stochastic parameter generation strategy, and apply the complex scaling method to identify bound and resonant states. Our calculations demonstrate that while conventional H-type configurations suffice for low-lying states such as the $T_{cc}(3875)^+$ molecular candidate, the inclusion of K-type configurations becomes important for extracting highly excited resonances, allowing higher-energy resonances absent in H-only calculations to be identified. Furthermore, we identify resonance candidates for the $T_{cs0}(2900)$, $X(6900)$, and $X(7200)$, whereas the absence of fully-strange compact poles below 2.6 GeV challenges the interpretation of $\phi(2170)$ and $X(2370)$ as $S$-wave compact $s s \bar{s} \bar{s}$ tetraquarks.

hep-ph↗

arXiv2026

Bound and Resonant Spectra of Few-Lepton Coulomb Systems

We present a unified calculation of bound and resonant states in purely leptonic Coulomb systems: $e^-e^-e^+$ ($\mathrm{Ps}^-$), $\mu^+e^-e^-$ ($\mathrm{Mu}^-$), $\mu^+\mu^+e^-$ ($\mathrm{Mu}_2^+$), $e^+e^+e^-e^-$ ($\mathrm{Ps}_2$), and $\mu^+\mu^+e^-e^-$ ($\mathrm{Mu}_2$). Using an extended stochastic variational method combined with the complex scaling method, we resolve the natural-parity $S$- and $P$-wave spectra. Near their respective $n=2$ thresholds, all three trilepton systems exhibit Gailitis--Damburg sequences generated by $2S$ and $2P$ Stark mixing and the resulting inverse-square attraction. Although microscopically distinct from the Efimov effect, this mechanism produces the same inverse-square asymptotics and geometric scaling. The $\mathrm{Ps}^-$ and $\mathrm{Mu}^-$ systems exhibit resonance sequences of comparable density, whereas the $\mathrm{Mu}_2^+$ produces a much denser spectrum, with 20 resolved members in the $^3P^o$ channel. In $\mathrm{Mu}_2^+$, the deeper states follow molecular Born--Oppenheimer configurations, while the near-threshold spectrum is governed by the atomic $\mathrm{Mu}(2)+\mu^+$ structure. In $\mathrm{Ps}_2$, coupling between threshold-degenerate configurations is essential for a near-threshold bound state. In $\mathrm{Mu}_2$, the Born--Oppenheimer organization of the resonance spectrum is channel dependent.

physics.atom-ph↗

arXiv2026

The excited baryon spectrum from a unified quark model

A common approach to studying the multiquark states is to solve the few-body Schr\"odinger equation within a quark potential model. The multiquark states may contain quarks with several different flavors and have richer color structures than ordinary hadrons. The reliability of such an investigation requires that the underlying quark potential model can simultaneously describe the meson and baryon spectra across all flavor sectors, including orbital and radial excitations, with a single parameter set. At present, no quark potential model fully satisfies this requirement. We construct a simple nonrelativistic constituent quark potential model that includes spin--orbit and tensor interactions. We refit the model parameters to the latest experimental data. The excited light hadrons and several exotic hadron candidates are excluded from the fit. The resulting parameter set reproduces the spectra across all fitted sectors. The vast majority of deviations are below 20 MeV, while the largest deviations remain of the order of several tens of MeV, which is the typical accuracy of nonrelativistic quark potential models. Using the same parameters, we predict the spectra and internal structures of the orbitally and radially excited heavy baryons, which await further experimental determination. The excited light baryons are calculated with the same parameters. The calculated excited light baryon spectra deviate substantially from experimental values. Our refitted model does not resolve these longstanding discrepancies. The results delimit the range of validity of the nonrelativistic constituent quark potential model. By treating mesons and baryons across all flavor sectors, including both orbital and radial excitations within a unified framework, the model provides a controlled starting point for few-body calculations of multiquark states. We also urge experimental searches for the predicted states.

hep-ph↗

arXiv2026

Spin-dependent polarizabilities of heavy vector mesons

We investigate the spin-dependent electromagnetic polarizabilities of the heavy vector mesons $D^*$ and $B^*$ in heavy meson chiral perturbation theory up to $\mathcal O(p^3)$. Using a twelve-element tensor basis for the real-photon Compton scattering on a spin-1 target, we determine two scalar, four vector and six tensor polarizabilities. We take the charm- and bottom-sector axial couplings from the measured $D^*$ width and lattice-QCD calculations, respectively, and estimate the magnetic couplings in the nonrelativistic constituent-quark model. In the charm sector, the proximity of the charged $D\pi$ thresholds generates strongly nonanalytic $P\phi$-loop contributions, producing large real contributions to several $\bar D^{*0}$ polarizabilities and sizable imaginary parts for $D^{*-}$, whose charged $D\pi$ channel is open. The $E1E1$-type polarizabilities are enhanced much more strongly than their $M1M1$-type counterparts, consistent with the velocity suppression of the pion-cloud magnetic coupling. No analogous enhancement occurs for $B^*$: the Born terms govern the magnetic polarizabilities, and the anomaly poles dominate the vector polarizabilities that receive no Born contribution. These results resolve the spin dependence of the $D\pi$ threshold effect and provide benchmarks for future lattice-QCD studies.

hep-ph↗

arXiv2026

Meson-Nucleus Bound States with Neural-Network Quantum States

We present the first systematic calculations of $\phi$-, $\eta_c$-, and $J/\psi$-nucleus ground states up to mass number $A{=}12$ based on the HAL QCD meson-nucleon potentials at near-physical point. The $(A{+}1)$-body Schr\"odinger equation is solved with a neural-network variational Monte Carlo framework, generalized to incorporate mesonic degrees of freedom. Benchmarking on light nuclei from $^2$H to $^{12}$C yields ground-state energies consistent with experiment. Meson-nucleus bound states emerge at $A\ge2$ for $\phi$, $A\ge4$ for $J/\psi$, and $A\ge6$ for $\eta_c$. The $\phi$-nucleus systems exhibit the strongest binding, with binding energies reaching tens of MeV. The $J/\psi$-nucleus and $\eta_c$-nucleus systems are weakly bound at the few-MeV and sub-MeV scale, respectively. The binding energy per nucleon deepens nearly linearly with $A$ for charmonium systems, whereas the $\phi$-nucleus system exhibits a non-monotonic behavior peaking at $^4$He -- a distinctive hallmark of the short-range and strongly attractive $\phi N$ interaction. The meson compresses the nucleon distribution relative to the parent nucleus, and evolves from a halo configuration to one embedded inside the nucleus with increasing $A$. Our results provide predictions for future experimental searches, and establish a quantitative bridge between lattice QCD meson-nucleon interactions and the emergent many-body phenomena in meson-nucleus bound states.

hep-ph↗

arXiv2026

Existence of the $DD^\bar{K}^$ and $BB^K^$ three-body molecular states

We investigate the existence of the three-body molecular state composed of $DD^*\bar{K}^*$ within the one-boson-exchange (OBE) model. A major challenge is that while the pseudoscalar-meson couplings are well-determined, the couplings for scalar- and vector-meson exchanges render significant model dependence. To ensure the reliability of our predictions and reduce model dependence, we recalibrate the coupling constants of the OBE model. We treat the pole position of $Z_c(3900)$, or equivalently the scalar $\sigma$-exchange coupling constant, as the only unknown parameter. The coupling constants for the vector $\rho$- and $\omega$-exchanges are determined by the pole positions of the well established states $X(3872)$ and $T_{cc}(3875)$. We demonstrate that these parameter sets also successfully describe the $T_{cs0}(2870)$ without further tuning. For the three-body system, our results indicate that an $I\left(J^P\right)=1 / 2\left(0^{-}\right)$ three-body molecular bound state exists when $Z_c(3900)$ is a virtual state located within approximately $-10~\text{MeV}$ of the $D\bar{D}^*$ threshold. Furthermore, we extend our analysis to the complex energy plane using the complex scaling method to search for molecular resonances, though no evidence of resonances is found in considered channels. We also apply this formalism to the bottom analog $BB^*K^*$ system. In this sector, the conditions for the existence of a three-body bound state are more relaxed, as a $Z_c(3900)$ virtual state located within $-25~\text{MeV}$ below the threshold suffices, although three-body molecular resonances remain absent. We suggest that future experiments precisely measure the pole position of $Z_c(3900)$ or search for the three-body bound state in $DD\bar{K}\pi\pi$ and $DD\bar{K}$ channels, as these efforts would mutually illuminate the nature of the associated states.

hep-ph↗

arXiv2026

Electromagnetic polarizabilities of the triplet hadrons in heavy hadron chiral perturbation theory

We investigate the electromagnetic polarizabilities of singly heavy mesons and doubly heavy baryons within the framework of heavy hadron chiral perturbation theory up to $\mathcal{O}(p^3)$. We estimate the low-energy constants using the non-relativistic constituent quark model. A striking prediction of our study is the giant electric polarizabilities of the $D^*$ mesons: $\alpha_E(\bar{D}^{*0}) \approx 291.4 \times 10^{-4} \text{fm}^3$ and $\alpha_E(D^{*-}) \approx -0.4-64.4 i \times 10^{-4} \text{fm}^3$. These anomalously large values arise from the near-degenerate mass between $D^*$ and $D \pi$, which are orders of magnitude larger than those of their bottom counterparts. This kinematic coincidence induces a pronounced cusp structure in the chiral loops, reflecting the long-range dynamics of a pion cloud. For doubly heavy baryons, polarizabilities depend strongly on heavy-flavor composition: the $bcq$ system differs markedly from $ccq$ and $bbq$ due to mixing with scalar heavy-diquark states. Using heavy diquark-antiquark symmetry (HDAS), we unify the chiral dynamics of singly heavy mesons and doubly heavy baryons in the heavy-quark limit. The pion-loop contributions dominate the electromagnetic structure of heavy hadrons and provide essential benchmarks for future lattice QCD simulations.

hep-ph↗

arXiv2026

Decoding $Z_c(4430)$ and $Z_c(4200)$: The role of $P$-wave charmed mesons

In this work, we perform a systematic investigation of the hidden-charm tetraquark states with $I^G(J^{PC})=1^+(1^{+-})$ within the hadronic molecular picture, placing particular emphasis on systems composed of an $S$-wave $(D, D^*)$ meson and a $P$-wave $(D_0^*(2300), D_1(2430), D_1(2420), D_2^*(2460))$ meson. Adopting the One-Boson Exchange potential, we solve the Schr\"odinger equation in momentum space via the Complex Scaling Method. A crucial feature of our approach is the rigorous treatment of the unstable nature of the $P$-wave constituents by incorporating three-body decay effects arising from self-energy corrections and the static limit approximation. Our results demonstrate that these three-body dynamics play a crucial role in determining the pole positions, specifically in reproducing the large decay widths observed experimentally. We identify several broad resonances in the $D^*\bar{D}_1(2420)$ and $D^*\bar{D}_2^*(2460)$ systems as candidates for the $Z_c(4430)$, while the significantly broader resonances in the $D\bar{D}_0^*(2300)$ and $D\bar{D}_1(2430)$ sectors are suggested as candidates for the $Z_c(4200)$. Focusing on the $D^*\bar{D}_2^*(2460)$ assignment as a specific case study, we further analyze the line shape of the $Z_c(4430)$ candidate using a Flatt\'e-like parametrization with energy-dependent self-energy terms, providing predictions for its open-charm decay modes to guide future experimental searches.

hep-ph↗

arXiv2025

Bound and Resonant States of Muonic Few-Body Coulomb Systems: Extended Stochastic Variational Approach

We compute the bound and resonant states of hydrogen-like muonic ions ($\mu\mu p$, $\mu\mu d$, $\mu\mu t$) and three-body muonic molecular ions ($pp\mu$, $pd\mu$, $pt\mu$, $dd\mu$, $dt\mu$, $tt\mu$), and the four-body double-muonic hydrogen molecule ($\mu\mu pp$) using an extended stochastic variational method combined with complex scaling. The approach provides a unified treatment of bound and quasibound states and achieves an energy accuracy better than $0.1~\mathrm{eV}$ across all systems studied. Complete spectra below the corresponding $n=2$ atomic thresholds are obtained, including several previously unresolved shallow resonances in both three- and four-body sectors.

physics.atom-ph↗

arXiv2025

Singly heavy tetraquark resonant states with multiple strange quarks

We systematically investigate the S-wave singly heavy tetraquark systems containing two or three strange quarks, $Qs\bar{s}\bar{s}$, $Qn\bar{s}\bar{s}$ and $Qs\bar{s}\bar{n}\left( Q=c,b,n=u,d \right) $, within the constituent quark potential model. We solve the four-body Schr\"odinger equation using the Gaussian expansion method (GEM) and identify resonances via the complex scaling method (CSM). There are no bound states below the lowest two-meson thresholds. We obtain several compact resonances with $J^P=0^+,2^+$ in $Qs\bar{s}\bar{s}$, and $J^P=2^+$ in $Qn\bar{s}\bar{s}$ and $Qs\bar{s}\bar{n}$. The pole positions are mainly distributed around $7.0-7.2$ GeV (bottom) and $3.7-3.9$ GeV (charm), with widths from a few to several tens of MeV. These resonances decay into $D_s\eta ^\prime ,{D_{(s)}^*}\phi ,{D_s}^*K^*$ and $D_s^*\bar{K}^*$ (and their bottom counterparts), providing targets for future experimental searches.

hep-ph↗

arXiv2025

Tetraquark states in the quark model

We perform systematical investigations of heavy flavor tetraquark systems, including fully heavy $QQ\bar Q\bar Q$ ($Q=b,c$), doubly heavy $QQ^{(\prime)}\bar q\bar q$ ($q=u,d$), and singly heavy $Qs\bar q\bar q$ tetraquark systems, within the framework of quark potential model. We employ the Gaussian expansion method and complex scaling method to solve the four-body Hamiltonian and identify bound and resonant states. We further calculate the root mean square radii to study the spatial configurations of tetraquarks. Our calculations reveal a rich spectrum of tetraquark states exhibiting diverse spatial configurations. In particular, we find good candidates for experimental states $X(6900)$, $X(7200)$, $T_{cc}(3875)^+$, and $T_{\bar c\bar s0}^*(2870)$. The fully charmed tetraquark resonances $X(6900)$ and $X(7200)$ are compact teraquark states, while doubly charmed tetraquark bound state $T_{cc}(3875)^+$ and charm-strange tetraquark resonance $T_{\bar c\bar s0}^*(2870)$ are meson molecules. Additionally, more tetraquark bound and resonant states are predicted and may be searched for in future experiments.

hep-ph↗

arXiv2025

Heavy flavored hydrogen molecule systems

This study provides a comprehensive analysis of $S$-wave exotic hydrogen-like three-body systems ($pp\mu^-$, $pp\tau^-$, $\mu^-\mu^-p$, $\tau^-\tau^-p$, $p\mu^-\tau^-$) with spin-parity $J^P = 1/2^+$ and $3/2^+$, and four-body systems ($pp\mu^-\mu^-$, $pp\tau^-\tau^-$) with $J^P = 0^+$, $1^+$, and $2^+$. We use complex scaling and Gaussian expansion methods to solve the complex-scaled Schr\"{o}dinger equation and obtain possible bound and quasi-bound states. The resulting binding energies range from $-33.8$~keV to $-340$~eV. Notably, we present the first theoretical estimation of the bound-state energy levels of $pp\mu^-\mu^-$ and $pp\tau^-\tau^-$, which is of significant importance for understanding exotic few-body Coulomb systems. We further analyze spin configurations and root-mean-square radii to elucidate the spatial structure of these bound and quasi-bound states. Our results reveal that $K$-type spatial configurations play a crucial role in accurately describing bound and quasi-bound states in the hydrogen-molecule-like systems $pp\mu^-\mu^-$ and $pp\tau^-\tau^-$. Incorporating $K$-type configurations significantly alters the mass spectra of these states. Future muon colliders and muon facilities may offer promising platforms for the possible copious production of such heavy flavored hydrogen molecules and molecular ions. For instance, scattering processes such as $2\mu^- + \mathrm{H_2} \to \mathrm{H_{2\mu}} + 2e^-$, $\mu^- + \mathrm{H_2} \to \mathrm{H_{\mu e}} + e^-$, and $\mu^- + \mathrm{H_2^+} \to \mathrm{H_{2\mu}^+} + e^-$ could be utilized, facilitating detailed studies of intriguing states such as $\mathrm{H_{2\mu}}$, $\mathrm{H_{\mu e}}$, and $\mathrm{H_{2\mu}^+}$.

physics.atom-ph↗

arXiv2025

DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States

For the first time, we implement the deep-neural-network-based variational Monte Carlo approach for the multiquark bound states, whose complexity surpasses that of electron or nucleon systems due to strong SU(3) color interactions. We design a novel and high-efficiency architecture, DeepQuark, to address the unique challenges in multiquark systems such as stronger correlations, extra discrete quantum numbers, and intractable confinement interaction. Our method demonstrates competitive performance with state-of-the-art approaches, including diffusion Monte Carlo and Gaussian expansion method, in the nucleon, doubly heavy tetraquark, and fully heavy tetraquark systems. Notably, it outperforms existing calculations for pentaquarks, exemplified by the triply heavy pentaquark. For the nucleon, we successfully incorporate three-body flux-tube confinement interactions without additional computational costs. In tetraquark systems, we consistently describe hadronic molecule $T_{cc}$ and compact tetraquark $T_{bb}$ with an unbiased form of wave function ansatz. In the pentaquark sector, we obtain weakly bound $\bar D^*\Xi_{cc}^*$ molecule $P_{cc\bar c}(5715)$ with $S=\frac{5}{2}$ and its bottom partner $P_{bb\bar b}(15569)$. They can be viewed as the analogs of the molecular $T_{cc}$. We recommend experimental search of $P_{cc\bar c}(5715)$ in the D-wave $J/\psi \Lambda_c$ channel. DeepQuark holds great promise for extension to larger multiquark systems, overcoming the computational barriers in conventional methods. It also serves as a powerful framework for exploring confining mechanism beyond two-body interactions in multiquark states, which may offer valuable insights into nonperturbative QCD and general many-body physics.

hep-ph↗

arXiv2025

Electromagnetic polarizabilities of the spin-$\frac{3}{2}$ baryons in heavy baryon chiral perturbation theory

We employ Heavy Baryon Chiral Perturbation Theory (HB$\chi$PT), a non-relativistic effective field theory that treats baryons as heavy static sources, to calculate the electromagnetic polarizabilities of spin-3/2 baryons in two sectors: the light-flavor decuplet baryons and singly heavy sextet baryons. We derive the analytical expressions up to $\mathcal{O}\left(p^3\right)$. Our results indicate that the long-range chiral corrections provide substantial contributions to the polarizabilities. In addition, magnetic dipole (M1) transitions of the baryons can significantly affect the magnetic polarizabilities and may even reverse their signs. For the decuplet baryons, the $\Delta^+$ and $\Delta^0$ exhibit the largest electric polarizabilities. Their values, $\alpha_E(\Delta^+) = (17.5 \pm 9.5)\times 10^{-4} \, \mathrm{fm}^3$ and $\alpha_E(\Delta^0) = (17.0 \pm 9.3)\times 10^{-4} \, \mathrm{fm}^3$, significantly exceed those typically observed for nucleons. Meanwhile, the electric polarizabilities of spin-3/2 singly heavy baryons are comparable to those of their spin-1/2 partners.

hep-ph↗

arXiv2025

Emergence of the exotic bottomoniumlike state $Y(10650)$ and support from Belle and Belle II data

Near-threshold exotic hadrons are usually associated with $S$-wave hadron-hadron dynamics, while higher partial waves are expected to be strongly suppressed by the centrifugal barrier. We show that this expectation can be overturned in the bottomonium sector. In a coupled-channel meson exchange framework combined with the complex scaling method, we find a $J^{PC}=1^{--}$ pole, denoted as $Y(10650)$, generated dominantly by the $P$-wave $B^*\bar B^*$ interaction and located close to the $B^*\bar B^*$ threshold. This pole naturally accounts for the anomalous enhancement observed just above the opening of the $B^*\bar B^*$ threshold in $e^+e^-\to B^*\bar B^*$. Once its production strength is fixed by this threshold enhancement, the corresponding cross sections of $\sigma[e^+e^-\to Y(10650)\to B\bar B^*]$ are predicted by the pole residues and phase-space factors, giving a characteristic dip-or-peak structure consistent with the available Belle (II) data. We further study the hidden-bottom transition $Y(10650)\to \Upsilon(2S)\eta$ through a near-threshold $B^*\bar B^*$ loop mechanism. The resulting $\mathcal{O}(10\sim100~\mathrm{keV})$ width for $Y(10650)\to \Upsilon(2S)\eta$ is sufficient to account for the corresponding cross sections measured by Belle II. The simultaneous appearance of this state in open- and hidden-bottom channels provides a direct experimental path to test a $P$-wave near-threshold mechanism and makes $Y(10650)$ a strong candidate for the first neutral isoscalar exotic bottomoniumlike state in the spectral gap between $\Upsilon(4S)$ and $\Upsilon(5S)$.

hep-ph↗

arXiv2025

The ${\phi NN,J/\psi NN,\eta_c NN}$ systems based on HAL QCD interactions

We investigate the existence of bound states and resonances in the ${\phi NN, J/\psi NN, \eta_c NN}$ systems using HAL QCD interactions for ${\phi N, J/\psi N}$, and ${\eta_c N}$. We employ the Gaussian expansion method to solve the complex-scaled Schr\"odinger equation and find no resonances or bound states in the ${J/\psi NN}$ and ${\eta_c NN}$ systems. We estimate the interaction between charmonium and nuclei, concluding that the $J/\psi$ or $\eta_c$ is likely to bind with ${}^3\mathrm{H}$, ${}^3\mathrm{He}$, ${}^4\mathrm{He}$, and heavier nuclei. For the $\phi NN$ system, the lattice QCD $\phi N\left({ }^2 S_{1 / 2}\right)$ interaction is absent. We combine the $\phi p$ correlation function analysis and HAL QCD results in Model A. We assume the spin-spin interactions for $J/\psi N$ and $\phi N$ systems are inversely proportional to their masses in Model B. Model A predicts a stronger $\phi N({}^2 S_{1/2})$ interaction and permits a two-body bound state, whereas Model B suggests the interaction is attractive but too weak to form a bound state. Both models predict bound states for the $I(J^P) = 0(0^-)$ and $0(1^-)$ $\phi NN$ systems. In Model A, these states are deeply bound with binding energies exceeding 15 MeV and remain existent when considering parameter uncertainties. In contrast, these states are very loosely bound in Model B, with binding energies below 1 MeV and an existent probability of about 60\% when parameter uncertainties are considered. In both models, there exist very loosely bound $I(J^P) = 0(2^-)$ three-body states which resemble a $\phi$-d atom with the $\phi$ meson surrounding the deuteron, but their existences are sensitive to parameter uncertainties. No bound states or resonances are found in the isovector $I(J^P) = 1(1^-)$ $\phi NN$ system.

hep-ph↗

arXiv2025

Triply heavy tetraquark states with different flavors

We investigate the $S$-wave triply heavy tetraquark systems, including the $QQ^{(\prime)}\bar Q^{(\prime)}\bar q$ and $QQ^{(\prime)}\bar Q^{(\prime)}\bar s$ configurations ($Q^{(\prime)} = c, b$, $q = u, d$) with spin-parity $J^P = 0^+$, $1^+$, and $2^+$, within the framework of the constituent quark model. We construct the wave functions for these systems, incorporating complete color-spin wave functions and spatial wave functions with three different Jacobi coordinate configurations. We use complex scaling and Gaussian expansion method to solve the complex-scaled four-body Schr\"{o}dinger equation and obtain possible exotic states. To analyze the spatial properties of the tetraquark states, we compute the root-mean-square (rms) radii, which help distinguish between meson-molecular and compact tetraquark states. We find that there do not exist any bound states in the $QQ^{(\prime)}\bar Q^{(\prime)}\bar q$ and $QQ^{(\prime)}\bar Q^{(\prime)}\bar s$ systems. However, we identify a possible molecular resonant state $T_{3c,2}(5819)$ in the $cc\bar c\bar q$ system with spin-parity $J^P = 2^+$, which lies slightly above the $J/\psi D^*(2S)$ threshold and has a large rms radius around 2.2 fm. Furthermore, we obtain a series of compact resonant states, some of which exhibit spatial structure similar to the tritium atom in QED, where the light quark circles around the cluster of three heavy quarks. The lowest resonant state in the triply heavy systems has a mass of $5634$ MeV, a width of $16$ MeV and spin-parity $J^P=1^+$. We suggest searching for this state in the $J/\psi D$, $\eta_c D^*$, and $J/\psi D^*$ decay channels.

hep-ph↗

arXiv2025

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

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 Schr\"odinger 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.

hep-ph↗