arXiv subjects

M. Abu-Shady

Publications and source records attributed to M. Abu-Shady.

At least 19 recordsLinked to original sources

arXiv2026

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.

hep-ph↗

arXiv2026

The Effect of Topological Defects and Magnetic Flux on Tetraquarks Using the Analytical Exact Iteration Method

Investigating the non-perturbative behavior of QCD and the dynamics of strong interaction is crucial for the study of heavy quarkonia and the understanding of exotic fully-heavy tetraquarks. In this work, using the analytical exact iteration method (AEIM), the analytical eigenvalue solutions of the non-relativistic Schrödinger equation are obtained in the presence of topological defects and external magnetic flux. The interactions are modelled using a modified Cornell potential supplemented by harmonic and inverse quadratic terms. We demonstrate that the energy levels are distinctly shifted by the topological defect parameter ($α$). The mass spectra of heavy quarkonia ($c\bar{c}$ and $b\bar{b}$) and fully-heavy tetraquarks ($cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$) across several radial and orbital excitation states are successfully calculated using this approach. The computed masses of bottomonium and charmonium accord well with current theoretical predictions and experimental findings. Our findings for the heavy tetraquarks are in line with previous theoretical investigations that consider tetraquarks as configurations of diquarks and antidiquarks. The numerical results demonstrate that a nontrivial interaction between the confining potential and the background space-time geometry governs the mass hierarchy of these exotic hadronic states, providing high-precision data with excellent agreement with established theoretical models and experimental benchmarks.

hep-ph↗

arXiv2024

The Influence of Fractional Derivatives on Thermodynamic Properties by Studying the CPSEHP Interaction

The parametric Nikiforov-Uvarov (N-U) method is employed in conjunction with a generalized fractional derivative (GFD) to investigate the energy eigenvalues and the total normalized wave function associated with the Coulomb plus screened exponential hyperbolic potential (CPSEHP) in terms of Jacobi polynomials. This potential exhibits maximum effectiveness at lower values of the screening parameter. To explore the thermal and superstatistical characteristics, the derived energy eigenvalues are directly incorporated into the partition function (Z) and subsequently used to determine other thermodynamic quantities, including vibrational mean energy (U), specific heat capacity (C), entropy (S), and free energy (F). Comparisons with previous studies are conducted. The classical case is recovered from the fractional case by setting alpha = beta = 1, consistent with prior work. Our results demonstrate that the fractional parameter plays a crucial role in governing the thermal and superstatistical properties within the framework of this model.

cond-mat.stat-mech↗

arXiv2024

Impact of global monopole on heavy mesons in hot-dense medium

This research study is primarily focus on investigating how the topological effects influence the eigenvalue solutions in the presence of a hot-dense medium. To accomplish this, we employ the non-relativistic Schrödinger wave equation, taking into consideration both the quantum flux field and an interaction potential. Through this approach, we determine the energy eigenvalues and their corresponding wave functions using the Nikiforov-Uvarov method. Our findings indicate that when we consider both the topological effects and the magnetic flux, $Φ$, there is a noticeable reduction in the binding energy within the hot-dense medium. Additionally, we analyze the role of the baryonic potential in shaping the binding energy within the $(T, u_b)$ plane. Interestingly, it is evident that the influence of the baryonic potential becomes more pronounced as its values decrease

hep-th↗

arXiv2024

On the Fractional Quark-Antiquark Confinement and Symplectic Quantum Mechanics

Using the formalism of generalized fractional derivatives, a two-dimensional non-relativistic 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 $α$ and $β$ with the ground state solution is analyzed through the Wigner function for the charm-anticharm, bottom-antibottom and $b\overline{c}$ 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

hep-ph↗

arXiv2023

Approximate Bound State Solutions of the Fractional Schrödinger Equation under the Spin-Spin-Dependent Cornell Potential

In this work, the approximate bound state solutions of the fractional Schrödinger 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 Schrödinger equation improves the mass spectra compared to the masses obtained in the existing literature. The bottomonium masses agree with the experimental data of the Particle Data Group where percentage errors for fractional parameters of \b{eta}=1,α=0.97 and \b{eta}=1,α=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 \b{eta}=1,α=0.97 and \b{eta}=1,α=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

hep-ph↗

arXiv2023

Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics

We investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the context of generalized fractional derivatives. For this purpose, it was solved the Schrödinger equation in phase space with the linear potential. The solution (ground state) is obtained, analyzed through the Wigner function comparing with the original solution, the Airy function for the meson $c\overline{c}$. The identified eigenfunctions are connected to the Wigner function via the Weyl product and the Galilei group representation theory in phase space. In some ways, compared to the wave function, the Wigner function makes it simpler to see how the meson system is non-classical.

hep-th↗

arXiv2023

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

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.

hep-ph↗

arXiv2023

The Fractional Schrodinger Equation with the Generalized Woods-Saxon Potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential reported in [Phys. Rev. C 72, 027001 (2005)] is extended to the fractional forms using the generalized fractional derivative and the fractional Nikiforov-Uvarov (NU) technique. Analytical solutions of bound states of the Schrodinger equation for the present potential are obtained in the terms of fractional Jacobi polynomials. It is demonstrated that the classical results are a special case of the present results at Elfa=Beta=1 Therefore, the present results play important role in molecular chemistry and nuclear physics.

quant-ph↗

arXiv2022

The Generalized Fractional NU Method for the Diatomic Molecules in the Deng-Fan Model

A solution of the fractional N-dimensional radial Schrodinger equation with the Deng-Fan potential is investigated by the generalized fractional NU method. The analytical formulas of energy eigenvalues and corresponding eigen functions for the Deng-Fan potential are generated. Furthermore, the current results are applied to several diatomic molecules for the Deng-Fan potential as well as the shifted Deng Fan potential. For both the Deng-Fan potential and its shifted potential, the effect of the fractional parameter on the energy levels of various diatomic molecules is examined numerically and graphically. We found that the energy eigenvalues are gradually improved when the fractional parameter increases. The energy spectra of various diatomic molecules are also evaluated in three-dimensional space and higher dimensions. It is worthy to note that the energy spectrum raises as the number of dimensions increases. In addition, the dependence of the energy spectra of the Deng-Fan potential and its shifted potential on the reduced mass, screening parameter, equilibrium bond length, rotational and vibrational quantum numbers is illustrated. To validate our findings, we estimate the energy levels of the Deng-Fan potential and shifted Deng-Fan potential at the classical case for various diatomic molecules and found that they are entirely compatible with earlier studies.

quant-ph↗

arXiv2022

Heavy-Meson Masses in the Framework of Trigonometric Rosen-Morse Potential Using the Generalized Fractional Derivative

Trigonometric Rosen-Morse Potential is employed as a mesonic potential interaction. The extended Nikiforov-Uvarov method is used to solve the N-radial Fractional Schrodinger equation analytically. Using the generalized fractional derivative, the energy eigenvalues are obtained in the fractional form. The current findings are used to calculate the masses of mesons such as charmonium, bottomonium, and heavy-light mesons. The current findings are superior to those of other recent studies and show good agreement with experimental data as a result, the fractional parameter is crucial in optimizing meson masses.

hep-ph↗

arXiv2021

A Generalized Definition of Fractional Derivative with Applications

A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function that can be expanded by Taylor series, we show that D^Elafa*D^Beta f(t)=D^(Elafa+Beta)f(t). GFD is applied for some functions in which we investigate that GFD coincides with Caputo and Riemann-Liouville fractional derivatives' results. The solutions of Riccati fractional differential equation are simply obtained via GFD. A comparison with other definitions is also discussed. The results show that the proposed definition in this work gives better accuracy than the commonly known conformable derivative definition. Therefore, GFD has some advantages in comparison with other definitions in which a new path is provided for simple analytical solutions of many problems in the context of fractional calculus.

math.CA↗

arXiv2019

Dissociation of Nucleon and Heavy-Baryon in an Anisotropic Hot and Dense QCD Media Using Nikiforov-Uvarov Method

By using the Nikiforov-Uvarov method, the hyper-radial Schrodinger equation is analytically solved, in which the real modified potential is employed at finite temperature and baryon chemical potential. The eigenvalue of energy and corresponding wave function are obtained in the isotropic and anisotropic media in hot and dense media. The present results show that the binding energy of nucleon and some heavy baryon decrease strongly in hot medium and decreases slightly with increasing baryon chemical potential. In addition, binding energy for each baryon is more bound in an anisotropic medium in comparison with its value in an isotropic medium. The dissociation of temperature of each baryon is above a critical temperature and it increases in the anisotropic medium. The dissociation of temperature is slightly decreased in the hot medium when the baryon of chemical potential is considered. A comparison is studied with the available studies. We conclude that the present study provides a good description of the nucleon and some heavy baryon in hot and dense media in the isotropic and anisotropic systems.

hep-ph↗

arXiv2019

Mid-Point Technique for Calculating Divergent integrals

A mid-point technique is suggested to overcome the difficulties in other techniques. The modified effective interaction quark potential which uses to calculate different properties of the NJL model such as the constituent quark mass, the pressure, and the energy density is solved using the present technique. The present method gives good accuracy for the mathematical problem and avoids the physical difficulty in the previous works.

nucl-th↗

arXiv2019

Radial dose distribution and effective delta ray radius (Penumbra radius): Determination for some ions passing through water

An analytical equation for calculating radial dose of heavy ions in water is introduced by Awad et al. (Applied Radiation and Isotopes, 142 (2018) 135-142. It is simple alternative to Monte Carlo code and is a promising code, however, still needs refinement. Refinement was added through adjusting radial dose integration upper limit which gives the effective delta-ray range, rmax and ions penumbra radius in water as well. Radial dose distributions for 85 ions forming fifteen energy groups from 0.25 to 24 MeV/n were studied. By employing the effective delta-ray range, it was possible to get more consistent radial dose distribution in comparison to experimental and Monte Carlo simulation data. The corresponding LET values of those ions were estimated and compared with SRIM program. Penumbra radii for 85 ions were determined. Good description for the penumbra radii was obtained using a proposed new equation which fits experimental data as well.

physics.ins-det↗

arXiv2019

Quarkonium Masses in a hot QCD Medium Using Conformable Fractional of the Nikiforov-Uvarov Method

By using conformable fractional of the Nikiforov-Uvarov (CF-NU) method, the radial Schrodinger equation is analytically solved. The energy eigenvalues and corresponding functions are obtained, in which the dependent temperature potential is employed. The effect of fraction-order parameter is studied on heavy-quarkonium masses such as charmonium and bottomonium in a hot QCD medium in the 3D and the higher dimensional space. A comparison is studied with recent works. We conclude that the fractional-order plays an important role in a hot QCD medium in the 3D and higher-dimensional space.

hep-ph↗

arXiv2019

Trigonometric Rosen-Morse Potential as the Quark-Antiquark Interaction Potential for Meson Properties in the Non-Relativistic Quark Model Using EAIM

Trigonometric Rosen-Morse potential is suggested as the quark-antiquark interaction potential for studying the thermodynamic properties and the masses of heavy and heavy-light mesons. For this purpose, N-radial Schrodinger equation is analytically solved using an exact analytical iteration method (EAIM). The eigenvalues of energy and corresponding wave functions are obtained in the N-dimensional space. The present results are applied for calculating the mass of heavy mesons such as charmonium, bottomonium, bc, and cs mesons and thermodynamic properties such as the mean-internal energy, the specific heat, the free energy, and the entropy. The effect of dimensional number is studied on the meson masses. A comparison is studied with other works and experimental data. The present potential provides satisfying results in comparison with other works and experimental data.

hep-ph↗

arXiv2019

Effect of an External Magnetic Field on Some Statistical Properties of the 2+1 Dirac-Moshinsky Oscillator

The 2+1 Dirac-Moshinsky oscillator ( 2+1 DMO ) is mapped into the generalized Jaynes-Cummings model (GJCM), in which an external magnetic field is coupled to an external isospin field. The basic equations of model are analytically solved, where the coherent state is considered as an initial state. The obtained results show that the strength of the magnetic field and the coupling parameter of the isospin field play important roles on some statistical properties such as entanglement, population inversion and degree of coherence. It has been shown that these parameters play a rule to increase entanglement and show the collapses and revivals phenomenon.

quant-ph↗