${\eta }_{\mathrm{c}}$- and $J\mathrm{/}\psi$-isoscalar meson bound states in the hadro-charmonium picture

We study ${\eta }_{\mathrm{c}}$- and $J\mathrm{/}\psi$-isoscalar meson bound states in the hadro-charmonium picture. In the hadro-charmonium, the four $q\bar{q}c\bar{c}$ quarks are arranged in terms of a compact charm-anticharm pair, $c\bar{c}$, embedded in light hadronic matter, $q\bar{q}$, with $q=u$, $d$ or $s$. The interaction between the charmonium core and the light matter can be written in terms of the multipole expansion in QCD, with the leading term being the $E1$ interaction with chromo-electric field ${\mathbf{E}}^a$. The spectrum of $\eta_{\rm c}$-and$J/\psi$-isoscalar meson bound states is calculated and the results compared with the existing experimental data.