Eur. Phys. J. C (2022) 82: 1024
https://doi.org/10.1140/epjc/s10052-022-11006-4

Regular Article - Theoretical Physics

The two-channel exotic charmonium-like resonances in the mass region (3900–4700) MeV

NRC “Kurchatov Institute”, Moscow, Russia

^b simonov@itep.ru

Received: 3 June 2022
Accepted: 5 November 2022
Published online: 15 November 2022

Abstract

Numerous resonances in the $c\overline{c}$ and 4q systems, containing $c\overline{c}$ plus $s\overline{s}$ quarks (or light $q\overline{q}$) were observed during last decades and recently the LHCb has found a remarkable narrow peak $T_{\mathit{cc}}(3875)$ in the $D{D}^{\ast }$ system. Besides there are several highly excited charmonium-like resonances, which can be treated as the shifted standard charmonium states. We analyze all these groups of the resonances in the mass region (3900–4700) MeV, using relativistic strong coupling theory with possible channel coupling phenomena. For the shifted charmonium states conventional charmonium spectrum is presented, being calculated with the relativistic string Hamiltonian, which does not contain fitting parameters, while for high excitations the universal flattened confining potential is used. It is shown that X(4274), X(4500), X(4700) can be identified as $3{}^3{P}_1,4{}^3{P}_0,5{}^3{P}_0$ states. The group of exotic states are considered using the Extended Recoupling Model, where two mesons $m_1,m_2$ transfer into another pair of mesons $m_3,m_4$ and back (infinite number of times), creating the four-quark resonance. Within this approach the resonances – $T_{\mathit{cc}}(3875),Z_c(3900),X(3915),Z_{\mathit{cs}}(3985),X(4014)$, and X(4140) – can be explained as the exotic four-quark states in the S-wave decay channels.