Charmonium Spectra and Decays in a Semirelativistic Model

Abstract

We investigate the spectra and decays of charmonium [Formula: see text] system in a semirelativistic potential model. The Hamiltonian of our model consists of a relativistic kinetic energy term, a vector Coulomb-like potential and a scalar confining potential. From this Hamiltonian a spinless wave equation is obtained. The wave equation is then reduced to the form of a single particle Schrödinger equation. The spin dependent potentials are introduced as a perturbation. The three-dimensional harmonic oscillator wave function is employed as a trial wave function and the [Formula: see text] mass spectra is obtained by the variational method. The model parameters and the wave function that reproduce the mass spectra of the [Formula: see text] mesons are then used to investigate some of the decay properties. The results obtained are then compared with the experimental data and with the predictions of other theoretical models. We also propose possible [Formula: see text] assignments for the recently observed charmonium or charmonium-like states.

Properties of Charmonium States in a Phenomenological Approach

“…is the reduced mass of the Q Q system, where m Q and m Q are the masses of the individual quark and anti quark respectively and M is the total mass of quark and antiquark. [39] The potential energy V is the sum of the heavyquark potential…”

“…Here p is the relative momentum, µ = mQm Q mQ+m Q is the reduced mass of the Q Q system, where m Q and m Q are the masses of the individual quark and anti quark respectively and M is the total mass of quark and antiquark [39].…”

“…with the strong coupling constant α s and inter quark distance r. The confinement term represents the non perturbative effect of QCD which includes the spin-independent linear confinement term [39] V…”

Properties of bottomonium in a semi-relativistic model

“…It is also suggested [28,34] that the conventional potential models with linear con-finement overestimate the masses of quarkonia in the energy region above the open-flavor thresholds. With these points in mind, in the present work, we investigate the bottomonium spectrum and decays in a semi-relativistic quark model [35]. Using the relativistic kinetic energy for the quarks, we derive a wave equation for the mesons.…”

Charmonium Properties

“…There are many potential models commonly used to study heavy quarkonium spectra [6][7][8][9]. One of the most successful potential for such systems is the non-relativistic potential model [10][11][12][13]. We adopt the Cornell plus hyperfine correction plus spin-dependent terms model [14] to accurately obtain the ̅ spectrum of quark interactions for S and P states.…”