Exploring the Interpretations of Charmonia and ccc–c– Tetraquarks in the Relativistic Flux Tube Model

Incited by the scant understanding of unsettled charmonia and newly observed ccc–c– tetraquarks, this work aims to explore the canonical interpretations and spectroscopic properties of these fully hidden-charm states. In the framework of a relativistic flux tube model, the centroid masses of the low-lying nL-wave states with 1≤n+L≤4 are unraveled. In order to pin down the complete mass spectra, the hyperfine splittings induced by the spin-dependent interactions are incorporated into the final predictions. Accordingly, fourteen charmonia are well identified, including the ηc(1S), J/ψ(1S), χc0(1P), hc(1P), χc1(1P), χc2(1P), ηc(2S), ψ(2S), ψ(3770), ψ2(3823), ψ3(3842), χc0(3915), χc2(3930), and ψ(4040) states. Additionally, the exotic Tψψ(6400), Tψψ(6600), Tψψ(6900), and Tψψ(7300) states are interpreted as the 1S-wave, 1P/2S-wave, 1D/2P-wave, and 2D/3P/4S-wave ccc–c– tetraquarks, respectively. Based on the achieved outcomes, the spin-parity quantum number is imperative to discriminate the nature of the ccc–c– structures, pending further experimental measurement in the future.