Heavy quarkonium spectra and its decays in a nonrelativistic model with Hulthen potential

Abstract

In this paper, we have made a comprehensive study of S wave quarkonium spectra in the general framework of a nonrelativistic potential model. The full Q Q potential used in our model consists of a Hulthen potential and a confining linear potential. The spin hyperfine interaction is introduced to obtain the masses of the pseudoscalar and vector mesons. The three-dimensional harmonic oscillator wavefunction is used as a trial wavefunction to obtain the mass spectra. The model parameters and the wavefunction that reproduce the mass spectra of cc and b b mesons are used to investigate the decay constants, leptonic decay widths, two-photon and two-gluon decay widths, and radiative decay widths of the S wave cc and b b mesons. The obtained values are compared with the experimental results and with the values obtained from other theoretical models. The predictions from our model are found to be in good agreement with the experimental results.

Study of Heavy Quarkonium with Energy Dependent Potential

“…The parameters  , g and  are obtained from fit to the experimental energies of triplet states of 2s and 3s and center of gravity of 1p with respect to 1S in Equation (9). In the case of energy independent potential ( E  = 0) the two parameters  and g are obtained from fitting to the theoretically estimated values of 2s and 1p to the corresponding experimental data.…”

“…In the case of energy independent potential ( E  = 0) the two parameters  and g are obtained from fitting to the theoretically estimated values of 2s and 1p to the corresponding experimental data. These in turn are used to predict eigenvalues of higher excited levels from the energy eigenvalue Equation (9). All the experimental data for cc and bb are taken from recent compilation of Particle Data Group 2008 [18].…”

“…These can be broadly classified as 1) QCD motivated potential [1][2][3][4][5] and 2) purely phenomenological potential [6][7][8][9]. A comprehensive list of potential models is described in the work of Lichtenberg [10].…”

Orbitally Excited States of Quarkonia in a Nonrelativistic Model

“…The wave functions and masses for the S-wave states were taken from Ref. 1. In calculating the radiative decay widths, we assumed that, in the nonrelativistic limit, the dipole radial matrix elements are independent of J.…”

“…Our model is very successful in predicting the S-wave quarkonium spectrum and its decays. 1 To obtain the P -and D-wave spectrum, we have added the spin-dependent terms (spin-spin, spin-orbit and tensor) to the Hamiltonian by applying the first-order perturbation theory. The spin-spin interaction term determines the masses of the singlet states ( 1 P 1 and 1 D 2 ), while the mass splitting among the triplet states ( 3 P J or 3 D J ) is provided by the spin-orbit and tensor interactions.…”