Investigating heavy quarkonia binding in an anisotropic-dense quark-gluon plasma with topological defects in the framework of fractional non-relativistic quark model

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Abstract The quark-gluon plasma analysis relies on the heavy quark potential, which is influenced by the anisotropic plasma parameter $$(\xi ),$$ ( ξ ) , temperature (t), and baryonic chemical potential (μ). Employing the generalized fractional derivative Nikiforov-Uvarov (GFD-NU) method, we solved the topologically-fractional Schrödinger equation. Two scenarios were explored: the classical model (α = β = 1) and the fractional model (α, β < 1). This allowed us to obtain the binding energy of charmonium $$(c\bar{c})$$ ( c c ¯ ) and bottomonium $$(b\bar{b})$$ ( b b ¯ ) in the 1p state. The presence of the topological defect leads to a splitting between the np and nd states. While increasing the temperature reduces the binding energy, increasing the anisotropic parameter has the opposite effect. Compared to the classical model, the fractional model yields lower binding energies. Additionally, the binding energy further decreases with increasing topological defect parameter, and the influence of the baryonic chemical potential is negligible. We also obtained the wave function for the p-state of charmonium and bottomonium. Here, increasing the anisotropic parameter shifts the wave function to higher values. Moreover, the wave function is lower in the fractional model compared to the classical model. Increasing the topological defect parameter again increases the wave function, while the baryonic chemical potential has no discernible effect.

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