# Tetraquarks with hidden charm and strangeness as $\varphi \text{−}\psi \left(2S\right)$ hadrocharmonium

Panteleeva, Julia Yu. (Physics Department, Irkutsk State University, Karl Marx Street 1, 664003 Irkutsk, Russia) ; Perevalova, Irina A. (Physics Department, Irkutsk State University, Karl Marx Street 1, 664003 Irkutsk, Russia) ; Polyakov, Maxim V. (Petersburg Nuclear Physics Institute, Gatchina, 188300 St. Petersburg, Russia) (Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany) ; Schweitzer, Peter (Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA) (Institute for Theoretical Physics, Tübingen University, Auf der Morgenstelle 14, 72076 Tübingen, Germany)

19 April 2019

Abstract: In the hadrocharmonium picture a $\overline{c}c$ state and a light hadron form a bound state. The effective interaction is described in terms of the chromoelectric polarizability of the $\overline{c}c$ 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 the LHCb Collaboration. 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 $J/\psi \text{−}\varphi$ spectrum can be described as hadrocharmonia. This is a nontrivial question because nothing is known about the $\varphi$ meson energy-momentum-tensor densities. With rather general assumptions about energy-momentum-tensor densities in the $\varphi$ meson we show that a $\psi \left(2S\right)\text{−}\varphi$ bound state can exist, and we obtain a characteristic relation between its mass and width. We show that the tetraquark $X\left(4274\right)$ observed by LHCb in the $J/\psi \text{−}\varphi$ 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.

Published in: Physical Review C 99 (2019)