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.
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