The coulomb plus linear (Cornell) potential is used to investigate the mass spectrum of bottomonium. Gaussian wave function is used in position and momentum space to estimate values of potential and kinetic energies, respectively. Based on our calculations, we study newly observed ${{\mathit Υ}{(10860)}}$ as an admixture of $4^{3}S_{1}$ with $4^{3}D_{1}$, and ${{\mathit Υ}{(10753)}}$ as an admixture of $6^{3}S_{1}$ with $4^{3}D_{1}$ also, we try to assign ${{\boldsymbol Υ}{(11020)}}$ as a pure $4^{3}D_{1}$ bottomonium state. We also study the Regge trajectories in the $(J,M^{2})$ and $(n_r,M^{2})$ planes to help prove our association. We estimate the pseudoscalar and vector decay constants, the radiative (Electric and Magnetic Dipole) transition rates, and the annihilation decay width for bottomonium states.
The effect of an extended Cornell potential on mass spectra of heavy and heavy-light mesons is studied. The Cornell potential is extended to include quadratic potential and inverse quadratic potential. The N-radial Schrodinger equation is solved by using series method. The results for charmonium and bottomonium, and light-heavy meson masses are obtained. A comparison with other recent works is discussed. The present results are improved in comparison with other recent works and are in good agreement with experimental data.
The typical binding energy of heavy hadron spectroscopy makes the system accessible to perturbative calculations in terms of non-relativistic QCD. Within NRQCD the predictions of heavy quarkonium energy levels rely on the accurate description of the static QCD potential $V_{\rm QCD}(r)$. Historically, heavy quarkonium spectroscopy was studied using phenomenological approaches such as the Cornell model $V_{\rm Cornell}=-κ/r+σ\, r$, which assumes a short-distance dominant Coulomb potential plus a liner rising potential that emerges at long distances. Such model works reasonably well in describin…
The exact solution of N- dimensional radial Schrödinger equation with the generalized Cornell potential has been obtained using the Laplace transformation (LT) method. The energy eigenvalues and the corresponding wave functions for any state have been determined. The eigenvalues for some special cases of the generalized Cornell potential are obtained. The present results are applied to calculate the mass spectra of heavy quarkonium systems such as charmonium and bottomonium and the bc meson. A comparison is discussed with the experimental data and recent works. The present results are improved…
Heavy quarkonia, Bc-meson, and CS-meson masses are calculated within the framework of the N-dimensional radial Schrodinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The energy eigenvalues are obtained in the three-dimensional space. The mass of spectra of charmonium, bottomonium, and mesons are calculated. The effect of dimensionality number on the mass of quarkonium is investigated. A comparison with oth…
The N-dimensional radial Schrodinger equation with an extended Cornell potential is solved. The analytical exact iteration method is applied. The energy eigenvalues are calculated in the N-dimensional space. The charmonium meson, the bottomonium meson and the bc meson masses are calculated in the N-dimensional space. The special cases are obtained from the general case. The study of the effect of dimensionality number is studied. The mean value of the radius and the mean square velocity of charmonium meson, bottomonium meson, and bc meson are calculated. The present results are improved in com…
Along the years, the Cornell Model has been extraordinarily successful in describing hadronic phenomenology, in particular in physical situations for which an effective theory of the strong interactions such as NRQCD cannot be applied. As a consequence of its achievements, a relevant question is whether its model parameters can somehow be related to fundamental constants of QCD. We shall give a first answer in this article by comparing the predictions of both approaches. Building on results from a previous study on heavy meson spectroscopy, we calibrate the Cornell model employing NRQCD predic…
We solved the radial Schr"odinger equation analytically using the Exact Quantization Rule approach to obtain the energy eigenvalues with the Extended Cornell potential ECP. The present results are applied for calculating the mass spectra of heavy mesons such as charmonium cc and bottomonium bb, and heavylight mesons such as bottom-charm bc and charm-Strange cs for different quantum states. Two special cases were considered when some of the potential parameters were set to zero, resulting into Coulomb potential, and Cornell potential, respectively. The present potential provides excellent resul…
The bottomonium mass spectra is computed in the framework of potential non-relativistic quantum chromodynamics. The potential consists of a static term incorporating Coulombic plus confinement part along with a correction term added non-perturbatively from pNRQCD, which is classified in powers of the inverse of heavy quark mass \textit{O}$(1/m)$. The masses of excited bottomonia are calculated by perturbatively adding spin-hyperfine, spin-orbit and tensor components of one gluon exchange interactions in powers of \textit{O}$(1/m^2)$. Calculated masses are found to be consistent with other theo…
We derive and analyze the confinement potential of the Cornell type within the framework of the generalized Soft Wall holographic model that includes a parameter controlling the intercept of the linear Regge spectrum. In the phenomenology of Regge trajectories, this parameter is very important for the quantitative description of experimental data. Our analysis shows that the ''linear plus Coulomb'' confinement potential obtained in the scalar channel is quantitatively consistent with the phenomenology and lattice simulations while the agreement in the vector channel is qualitative only. This r…
$Q\bar{Q}$ potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci-Ferrari type, the possibility of a gluon condensation $\langle A_μ^+A_μ^-\rangle$ in low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales…
It is well known that the Soft-Wall holographic model for QCD successfully reproduces not only the linear Regge spectrum, but also, via the holographic Wilson confinement criterion, the ''linear plus Coulomb'' confinement potential similar to the Cornell potential. This property could be interpreted as a holographic counterpart of the hadron string picture, where the linearly rising potential and Regge-like spectrum are directly related. However, such a relation does not take place in the bottom-up holographic approach. Namely, the Cornell-like potentials arise in a broad class of bottom-up ho…
The mass spectra of charmonium are investigated using a Coulomb plus linear (Cornell) potential. Gaussian wave function in position space as well as in momentum space are employed to calculate the expectation value of potential and kinetic energy respectively. Various experimental states ($X(4660)(5^{3}S_{1})$, $X(3872)(2^{3}P_{1})$, $X(3900)(2^{1}P_{1})$, $X(3915)(2^{3}P_{0})$ and $X(4274)(3^{3}P_{1})$ etc.) are assigned as charmonium states. We also study the Regge trajectories, pseudoscalar and vector decay constants, the Electric and Magnetic dipole transition rates and the annihilation de…
Improved analysis of rare $Z$-boson decays into a heavy vector quarkonium plus lepton pair
University of Science and Technology of China（中国科学技术大学）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论交叉中心）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论研究中心）
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 and bottomonium , 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.
Hulthén plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. 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 and bottomonium . Four special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, Yukawa potential, Coulomb potentia…
We explore the phenomenology of a model of monopolium based on an electromagnetic dual formulation of Zwanziger and lattice gauge theory. The monopole is assumed to have a finite-sized inner structure based on a 't Hooft-Polyakov like solution, with the magnetic charge uniformly distributed on the surface of a sphere. The monopole and anti-monopole potential becomes linear plus Coulomb outside the sphere, analogous to the Cornell potential utilised in the study of quarkonium states. Discovery of a resonance feature in the diphoton channel as well as in a higher multiplicity photon channel woul…
Comprehensive study of spectroscopic properties of $D_{(s)}$ mesons
The Maharaja Sayajirao University of Baroda（巴罗达马哈拉贾·萨亚吉拉奥大学）；Government Science College, Jasdan（贾斯丹政府科学学院）；Institute of Advanced Research, Gandhinagar（甘地纳加尔高级研究所）；Sardar Patel University, Vallabh Vidyanagar（瓦拉布·维德亚纳加尔萨达尔·帕特el大学）
