Spectroscopy of $cc\bar{c}\bar{c}$ and $ss\bar{c}\bar{c}$ Tetraquarks within the Framework of Regge Phenomenology

TL;DR

This paper predicts the mass spectra of $cc\bar{c}\bar{c}$ and $ss\bar{c}\bar{c}$ tetraquarks using Regge phenomenology, providing theoretical benchmarks and potential identification of experimental candidates.

Contribution

It introduces a novel application of Regge trajectories to estimate masses and excited states of heavy tetraquarks, extending previous models with new mass inequalities and trajectory analyses.

Findings

Predicted ground state masses for $cc\bar{c}\bar{c}$ tetraquarks.

Estimated Regge slope parameters from trajectory fits.

Suggested possible identification of $\psi(4660)$ as a tetraquark.

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 $\psi(4660)$ and $\chi_{c0}(4700)$ 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.