Variational Constraints of Masses and Radii of cc�-Mesons

Charmonium Properties

“…In Figure (3), the present potential has been plotted for S and P states of charmonium. The predictions about the values of momentum width (Coefficient β) for charmonium S and P States in comparison between our results and those obtained in previous calculations [20,21] are reported in Tables (3, 4…”

“…Momentum width parameter β can be used to calculate the decay widths [18], and differential cross sections [19] for quarkonium states. The produced calculations of the momentum width parameter β are compared with published theoretical calculations from [20,21]. The main aim of this research is to study the spectrum of charmonium meson using the matrix method [22].…”

A new variational approach and its application toheavy quarkonia

“…This definition is in accordance with the momentum width of known botommonium and charmonium states (see, for instance, Refs. [25,26,67]) and is convenient for the discussion below, as we shorty explain. By keeping in mind the quantum indeterminacy in position and momentum of quark in a meson, let us define the notation in which ∆x isx-the mean of the position coordinate of quark relative to center of mass of the meson, and similarly ∆p x by the mean quark momentum widthβ x about center of mass.…”

“…To that end, a vast number of numerical strategies have been implemented in literature among which, to count a few, we find the shooting method [22], the Asymptotic Iteration Method (AIM) [23] and many others such as different forms of Runge-Kutta methods. Most numerical strategies implemented for solving the SWE are as precise as going up to O(d 2 ) of grid spacing d. The Matrix Numerov Method (MNM) (see, for instance [24]) which in the context of meson physics has been put forward by the Qena group [25] and extended by our group [26], departs from a discretization of the kinetic term in the SWE in such a manner that the problem of solving the radial SWE is cast in the form of a matrix eigenvalue problem. In this form, its accuracy is of O(d 6 ).…”

“…After preparing the firm ground from MNM we obtain the charmonium and bottomonium spin averaged masses and radii, in order to circumvent the struggle for numerical accuracy in the numerical solution, we introduce a variatonal approach combining the Heisenberg uncertainty principle and the variational principle in the Hamiltonian of the SWE. Such an approach, which we refer to simply as the variational principle (VP), imposes an algebraic transcendental relation between the masses and the radii of these states and is partially based in our previous work in [26]. The results from our VP are less uncertain than those from MNM.…”