Analysis of Fully-Heavy and Hidden-Heavy Tetraquarks in Anisotropic Plasma Using the Generalized Fractional Derivatives
Investigating the spectroscopy and thermal stability of exotic multiquark states provides crucial insights into the fundamental confinement mechanisms of quantum chromodynamics (QCD) under extreme regimes. This work presents an innovative study of the spectroscopy and dissociation of fully-heavy tetraquarks in an anisotropic plasma via the generalized fractional derivative (GFD) structure. The radial Schrödinger equation (SE) with an extended Cornell potential that includes Debye screening and plasma anisotropy into account is solved by applying the parametric generalised fractional Nikiforov-Uvarov (PGFNU) technique. The analysis of systems consisting of $cc\bar c\bar c$ and $bb\bar{b}\bar{b}$ shows that the binding potential of the systems and the dissociation energy increase with the anisotropy parameter and decrease with temperature. The fractional paradigm also shows that when the fractional orders are lower, the systems will be more strongly bound than in classical quantum mechanics. Furthermore, the mass spectra for all considered tetraquark configurations, including the $cc\bar{c}\bar{c}$, $bb\bar{b}\bar{b}$, $c\bar{q}c\bar{q}$, and $b\bar{q}b\bar{q}$ systems, are calculated for both ground and excited states. These calculations were performed across both the fractional and classical regimes. The findings indicate that the GFD framework provides an effective mathematical basis for modelling hadronic systems in complex contexts, and they demonstrate significant agreement with earlier theoretical studies.