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Is the existence of a $J/\psi J/\psi$ bound state plausible?
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abstract
In a recent measurement LHCb reported pronounced structures in the $J/\psi J/\psi$ spectrum. One of the various possible explanations of those is that they emerge from non-perturbative interactions of vector charmonia. It is thus important to understand whether it is possible to form a bound state of two charmonia interacting through the exchange of gluons, which hadronise into two pions at the longest distance. In this paper, we demonstrate that, given our current understanding of hadron-hadron interactions, the exchange of correlated light mesons (pions and kaons) is able to provide sizeable attraction to the di-$J/\psi$ system, and it is possible for two $J/\psi$ mesons to form a bound state. As a side result we find from an analysis of the data for the $\psi(2S)\to J/\psi \pi\pi$ transition including both $\pi\pi$ and $K\bar K$ final state interactions an improved value for the $\psi(2S)\to J/\psi$ transition chromo-electric polarisability: $|\alpha_{\psi(2S)J/\psi}|= (1.8\pm 0.1)~\mbox{GeV}^{-3}$, where the uncertainty also includes the one induced by the final state interactions.
Forward citations
Cited by 7 Pith papers
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Tensor Resonance in $J/\psi J/\psi$ Scattering from Lattice QCD
A lattice QCD computation predicts a 2++ J/psi J/psi resonance with mass 6.54 GeV and width 0.54 GeV, identified with the X(6600) structure.
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Two-pion exchange for coupled-channel scattering of two heavy mesons
The authors derive the next-to-leading-order two-pion-exchange potentials for heavy meson and heavy antimeson scattering and show the results are close to simple momentum-dependent contact terms.
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$\eta_c\eta_c$ and $J/\psi J/\psi$ scatterings from lattice QCD
Lattice QCD predicts a broad J/psi J/psi 2++ resonance with mass about 6.54 GeV and width about 0.55 GeV, compatible with X(6600) and X(6400), plus a 0++ virtual state near threshold.
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Fully charmed P-wave tetraquark resonant states in the quark model
A quark-model calculation predicts compact fully charmed P-wave tetraquark resonances near 7.0 to 7.2 GeV, including exotic J^PC = 0^-- and 1^-+ states, and finds no narrow tetraquark candidates below 7 GeV for X(6400...
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Lattice calculation of the $\eta_c\eta_c$ and $J/\psi J/\psi$ s-wave scattering length
A continuum-extrapolated lattice calculation gives a^{0+}_{eta_c eta_c} = -0.104(09) fm and a^{2+}_{J/psi J/psi} = -0.165(16) fm, indicating repulsive interactions.
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Low-energy scattering of the $J/\psi \pi$ and $J/\psi K$ system
First dispersive upper-bound estimates for J/ψπ and J/ψK scattering lengths, with soft-gluon exchange dominating the coupled-channel mechanism.
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Role of electromagnetic corrections in the $\pi\pi$ distributions of $\psi^\prime \to J/\psi \pi \pi$
Electromagnetic corrections alter the π⁺π⁻-threshold cusp magnitude by ~2–3% in ψ′→J/ψπ⁰π⁰, so they must be included for precision extraction of S-wave ππ scattering lengths.
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