Spectroscopy of the Quarkonium Systems for Heavy Quarks

Journal of Radiation Research and Applied Sciences, 2020

Through the introduced work a viable numerical scheme has been developed, using Numerov's method, to study the energy spectra of mesons and hadronic interactions. Upon the implementation of the non-relativistic quark model and the Quantum Chromodynamics theory elements which describe the phenomenological interactions between the charm-anticharm quarks via two proposed potentials, our model accurately predicts the mass spectra of charmed quarkonium as an example of mesonic systems. It was found that our results agree well with the experimental charmonium masses that were published via the Particle Data Group (PDG). The proposed model has been tested for numerical instabilities and found that it works well for both proposed potentials. Although this model is suited to study the dynamics of charmonium interactions, we found that the results for one of the potentials are in better agreement with the published data. In addition, we predicted the mass spectrum of new charmed multiplets using the same previously mentioned potentials.

2021

In this work, we obtain the Schrödinger equation solutions for the Kratzer potential plus screened Coulomb potential model using the series expansion method. The energy eigenvalues is obtained in non-relativistic regime and the corresponding unnormalized eigenfunction. Three special cases were obtained. We applied the present results to calculate heavy-meson masses of charmonium cc and bottomonium bb , and we got the numerical values for 1S, 2S, 1P,2P, 3S, 4S ,1D,2D and 1F states. The results are in good agreement with experimental data and the work of other researchers.

Indian Journal of Pure & Applied Physics, 1999

A phenomenological quark-antiquark potential is constructed from the spectroscopic data of charmonium states within an overall non-relativistic framework. Employing a general power-law-type potential, we study the mass variation of charmonium W.r.t. the parameters of the confming part of the interaction potential. Use of the short-distance part as ' Coulombic' type, as given by the perturbative QCD, is shown to be inconsistent with the data. And thereafter, analysis is repeated employing the short distance part as having an inverse square root behaviour, leading to the conclusion that the experimental data favour a potential of the type : V(r)= k/-Yr + p-Yr . With this potential, the numerical results of masses and leptonic decay widths of cc , bb, as well as those of cb states are presented. Variation of wavefunction overlap at origin, 1\If(0)1 2 , W.r. t. the parameters of the confming part of the potential is also investigated .

Bulletin of Pure & Applied Sciences- Physics, 2021

In this work, we obtain the Schrödinger equation solutions for the Kratzer potential plus screened Coulomb potential model using the series expansion method. The energy eigenvalues is obtained in non-relativistic regime and the corresponding unnormalized eigenfunction. Three special cases were obtained. We applied the present results to calculate heavy-meson masses of charmonium cc and bottomonium bb , and we got the numerical values for 1S, 2S, 1P,2P, 3S, 4S ,1D,2D and 1F states. The results are in good agreement with experimental data and the work of other researchers.

Communication in Physical Sciences, 7(2) 97-114, 2021

We solved the N-dimensional Klein-Gordon equation analytically using the Nikiforov-Uvarov method to obtain the energy eigenvalues and corresponding wave function in terms of Laguerre polynomials with the ultra-generalized exponential-hyperbolic potential. The results were applied for calculating the mass spectra of heavy mesons including charmonium (cc) and bottomonium (bb) for different quantum states. Also, the thermodynamic properties such as free energy, mean energy, entropy, and specific heat were obtained. The data obtained in the study was in excellent agreement with experimental results and with results obtained from others with a maximum error of 0.0059 GeV .

Physical review, 1982

cc and bb spectra, including fine and hyperfine structures, are investigated with the use of a recently derived quantum-chromodynamic potential supplemented by a phenomenological longrange confining potential. Our theoretical results for all energy levels below the charm and bottom thresholds as well as their leptonic widths are in excellent agreement with experiments. We also give unambiguous theoretical predictions for unobserved bb energy levels, and present reasonable estimates for energy levels of tt. Our values of the strong coupling constant n, and the QCD scale parameter A are consistent with those extracted from high-energy positronelectron annihilation. (i) Introduction. Recently the quark-antiquark potential to the fourth order in perturbative quantum chromodynamics was obtained' with special emphasis on a precise determination of the spin-dependent interaction terms. We shall now investigate the cc, bb, and tt spectra, including their fine and hyperfine structures, with the use of this quantum-chromodynamic potential supplemented by a phenomenological long-range confining potential.

2010

This dissertation deals with the computation of meson mass spectra in the context of quarkantiquark (q q) bound-state. Traditionally the q q bound-state problem is treated by solving the non-relativistic Schrödinger equation in position representation with a linear confining potential and a Coulomb-like attractive potential. For high energy, relativistic kinematics is I would like to thank all of those who have assisted me in this effort. I am forever thankful to my adviser, Dr. Khin Maung Maung, who taught me with great patience and helped me in many ways to complete my dissertation. He taught me with great care and helped me to understand the nature of research in the field of theoretical physics and computations. I have gained considerable amount of knowledge and experience while working under his supervision. I would like to thank my other committee members, Dr. John Norbury, Dr. Lawrence Mead, Dr. Sung Lee and Dr. Christopher Sirola, whose active support made it possible for me to complete my dissertation. I would like to thank my friend Charles Werneth with all my heart; without his active support, both academically and emotionally, it would not have been possible for me to carry on. I would like to thank my parents, Sarashi Ranjan Dhar and Manju Dhar, for their kindness, love and care. They are always very supportive. I would like to thank my brother, Tanmay Dhar, for his continuous support and care.

European Journal of Applied Physics

In this work, we obtain solutions of the Schrödinger equation with Kratzer-screened Coulomb potential (KSCP) model using the series expansion method. Explicitly, we compute the bound state energy eigenvalues for selected diatomic molecules of N2, CO, NO, and CH, respectively, for the various vibrational and rotational quantum states and the numerical energy eigenvalues agree with the existing literature. Three special cases were considered. The energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium system such as charmonium and bottomonium. The results agree with the experimental data and other recent theoretical studies.

Canadian Journal of Physics, 2021

Hulthen plus Hellmann potentials are adopted as the quark–antiquark interaction potential for studying the thermodynamic properties and the mass spectra of heavy mesons. The potential was rendered temperature dependent by replacing the screening parameter with Debye mass. We solved the radial Schrödinger equation analytically using the Nikiforov–Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons, such as charmonium [Formula: see text] and bottomonium [Formula: see text], and thermodynamic properties, such as the mean energy, the specific heat, the free energy, and the entropy. Four special cases were considered when these potential parameters were set to zero, resulting in Hellmann potential, Yukawa potential, Coulomb potential, and Hulthen potential, respectively. The present potential provides satisfying results in comparison with experimental...

Journal of Physics G: Nuclear and Particle Physics, 2006

A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of our results is verified by comparing them both with the literature on the subject and with the numerical results obtained with a Fortran code. As an application of the method that we propose, we consider the meson spectroscopy with various phenomenological potentials.