Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics

Luz, R. R.; Abu‐Shady, M.; Dessano, H.; Santana, A. E.; Amorim, R. G. G.

doi:10.1155/2023/8366154

Cited by 2 publications

(1 citation statement)

References 39 publications

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“…This new definition coincides with the classical fractional derivative and has become a useful tool for solving fractional differential equations. It has been successfully applied in heavy meson and molecular physics, as can be seen in the references [44][45][46][47][48]. The GFD is a novel formula for a fractional derivative.…”

Section: The Generalized Fractional Derivativementioning

confidence: 99%

Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential

Omugbe,

Abu-Shady,

Inyang

2024

J. Nig. Soc. Phys. Sci.

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In this work, the approximate bound state solutions of the fractional Schr\"{o}dinger equation under a spin-spin-dependent Cornell potential are obtained via the convectional Nikiforov-Uvarov approach. The energy spectra are applied to obtain the mass spectra of the heavy mesons such as bottomonium, charmonium and bottom-charm. The masses for the singlet and triplet spin numbers increase as the quantum numbers increase. The fractional Schr\"{o}dinger equation improves the mass spectra compared to other theoretic masses. The bottomonium masses agree with the experimental results where percentage errors for fractional parameters of $\beta =1,\alpha =0.97$ and $\beta =1,\alpha =0.50$ were found to be 0.67\% and 0.49\% respectively. The respective percentage errors of 1.97\% and 1.62\% for fractional parameters of $\beta =1,\alpha =0.97$ and $\beta =1,\alpha =0.50$ were obtained for charmonium meson. The results indicate that the potential curves coupled with the fractional parameters account for the short-range gluon exchange between the quark-antiquark interactions and the linear confinement phenomena which is associated with the quantum chromo-dynamic and phenomenological potential models in particle and high-energy physics.

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Section: The Generalized Fractional Derivativementioning

confidence: 99%

Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential

Omugbe,

Abu-Shady,

Inyang

2024

J. Nig. Soc. Phys. Sci.

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show abstract

On the fractional quark–antiquark confinement and symplectic quantum mechanics

Abu-Shady,

Luz,

Petronilo

et al. 2024

Int. J. Mod. Phys. A

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Using the formalism of generalized fractional derivatives, a two-dimensional nonrelativistic meson system is studied. The mesons are interacting by a Cornell potential. The system is formulated in the domain of the symplectic quantum mechanics by means of the generalized fractional Nikiforov–Uvarov method. The corresponding Wigner function and the energy eigenvalues are then derived. The effect of fractional parameters [Formula: see text] and [Formula: see text] with the ground state solution is analyzed through the Wigner function for the charm–anticharm, bottom–antibottom and [Formula: see text] mesons. One of the fundamental achievements of such Cornell model is the determination of heavy quarkonia mass spectra. We have computed these masses and the present results are in agreement with the experimental data, improving previous theoretical results.

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Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics

Cited by 2 publications

References 39 publications

Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential

Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential

On the fractional quark–antiquark confinement and symplectic quantum mechanics

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