Masses of Single, Double, and Triple Heavy Baryons in the Hyper-Central Quark Model by Using GF-AEIM

Abu‐Shady, M.; Fathallah, Hamdi

doi:10.1155/2022/4539308

Cited by 7 publications

(7 citation statements)

References 61 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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“…The generalized fractional analytical iteration method is used as in Ref. [23] to solve the hyper-central Schrödinger equation and studied its applications on the theory baryons with single, double, and triple in the ground state. In addition, the SE can be exactly solved, the system can be fully described as in [24,25,26] using the Nikiforov Uvarov method.…”

Section: Introductionmentioning

confidence: 99%

The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications

Abu-Shady,

Fath-Allah

2023

East Eur. J. Phys.

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By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The obtained results are applied on the extended Cornell potential, the pesudoharmonic potential, the Mie potential, the Kratzer-Fues potential, the harmonic oscillator potential, the Morse potential, the Woods-Saxon potential, the Hulthen potential, the deformed Rosen-Morse potential and the P schl-Teller potential which play an important role in the fields of molecular and atomic physics. The special of classical cases are obtained from the fractional cases at which are agreement with recent works.

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“…Fractional-order derivative is basically a natural extension of ordinary derivatives, which has become a popular research topic in applied sciences [1][2][3][4] and engineering [5,6]. The nonlocality plays a significant role in fractional derivative models.…”

Section: Introductionmentioning

confidence: 99%

On a Relativistic Quark Model Description via the Fractional Nikiforov-Uvarov Method

Abu-Shady¹,

Kaabar²

2023

Preprint

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The Dirac equation plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrodinger equation when a certain potential's type is selected as the Cornell potential. By choosing the generalized fractional derivative, the fractional Nikiforov-Uvarov method is applied as a good efficient tool. The energy eigenvalues and corresponding wave functions are obtained in the sense of fractional forms by solving Dirac equation analytically. The special case is obtained, which is compatible with the classical model. Solving the fractional Dirac equation will open a new path to solve and improve results in the classical relativistic quantum systems.

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Masses of Single, Double, and Triple Heavy Baryons in the Hyper-Central Quark Model by Using GF-AEIM

Cited by 7 publications

References 61 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

The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications

On a Relativistic Quark Model Description via the Fractional Nikiforov-Uvarov Method

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