On tetraquarks with hidden charm and strangeness as phi-psi(2S) hadrocharmonium

In the hadrocharmonium picture a $\bar cc$ state and a light hadron form a bound state. The effective interaction is described in terms of the chromoelectric polarizability of the $\bar cc$ state and energy-momentum-tensor densities of the light hadron. This picture is justified in the heavy quark limit, and may successfully account for a hidden-charm pentaquark state recently observed by LHCb. In this work we extend the formalism to the description of hidden-charm tetraquarks, and address the question of whether the resonant states observed by LHCb in the $J/\psi$-$\phi$ spectrum can be described as hadrocharmonia. This is a non-trivial question because nothing is known about the $\phi$ meson energy-momentum-tensor densities. With rather general assumptions about energy-momentum-tensor densities in the $\phi$-meson we show that a $\psi(2S)$-$\phi$ bound state can exist, and obtain a characteristic relation between its mass and width. We show that the tetraquark $X(4274)$ observed by LHCb in $J/\psi$-$\phi$ spectrum is a good candidate for a hadrocharmonium. We make predictions which will allow testing this picture. Our method can be generalized to identify other potential hadrocharmonia.