Spectroscopy of $cc\bar{c}\bar{c}$ and $ss\bar{c}\bar{c}$ Tetraquarks within the Framework of Regge Phenomenology
Vandan Patel, Juhi Oudichhya, Ajay Kumar Rai
TL;DR
The paper investigates $cc\bar{c}\bar{c}$ and $ss\bar{c}\bar{c}$ tetraquarks through Regge phenomenology, deriving linear and quadratic mass relations and fitting Regge slopes to $(J,M^{2})$ trajectories. By treating tetraquarks as diquark–antidiquark bound states, it predicts ground- and excited-state masses in both orbital and radial channels, producing $M$–ranges like $M_{cc\bar{c}\bar{c}}\in[5.712,6.411]$ GeV for $0^{+}$ and analogous ranges for other quantum numbers, and extending to $(n,M^{2})$ spectra with $M_{J+k}=\sqrt{M_{J}^{2}+k/\beta'}$. The results are compared with various theoretical approaches and show good agreement, reinforcing Regge phenomenology as a robust, economical tool for heavy multiquark spectroscopy. Potential identifications of observed resonances, notably $\psi(4660)$ and $\chi_{c0}(4700)$, with $ss\bar{c}\bar{c}$ states are discussed, highlighting the framework’s relevance for guiding future experiments and spin–parity assignments in exotic hadrons.
Abstract
In this work, we investigate the mass spectra of all-charm ($cc\bar{c}\bar{c}$) and doubly strange- doubly charm ($ss\bar{c}\bar{c}$) tetraquark states using the framework of Regge phenomenology. Employing a quasi-linear Regge trajectory ansatz, we derive linear and quadratic mass inequalities for hadrons, which provide constraints on the masses of tetraquark states. We estimate the range of ground state masses of $cc\bar{c}\bar{c}$ tetraquarks and determine the Regge slope parameters by fitting the corresponding $(J, M^2)$ trajectories. These parameters are then utilized to predict the mass spectra of orbital excited states of both $cc\bar{c}\bar{c}$ and $ss\bar{c}\bar{c}$ systems in the $(J, M^2)$ plane. Furthermore, we extend our analysis to radial excitations by exploring Regge trajectories in the $(n, M^2)$ plane. The obtained mass predictions are compared with existing theoretical results from various models. Additionally, we discuss the possible identification of the experimentally observed $ψ(4660)$ and $χ_{c0}(4700)$ resonances as tetraquark candidates. The results presented in this study offer useful benchmarks for future experimental investigations and may assist in the spin-parity assignment of exotic hadronic states. Our findings contribute to a deeper understanding of multiquark dynamics and the spectroscopy of exotic hadrons within the framework of Quantum Chromodynamics.