Study of Heavy Quarkonium with Energy Dependent Potential

Pramila Gupta,Indira Mehrotra

doi:10.4236/jmp.2012.310189

Abstract

Heavy quark systems (c and b ) have been studied in the nonrelativistic framework using energy dependent interquark potential of the form harmonic oscillator with a small linear term as energy dependent as perturbation plus a inverse square potential. This potential admits exact analytical solution of the Schrodinger equation. Mass spectra, leptonic decay width, root mean square radii (), the expectation value of the radius (r) and have been estimated for different quantum mechanical states for and systems. It is observed that energy dependent term in the potential leads to saturation of the mass spectra and degree of saturation is governed by the magnitude of perturbation. The calculated values of leptonic decay widths for 1s state are in very good agreement with the experimental data both for c and b systems.

Highlights

Energy spectrum of heavy quarkonium are a rich source of information on the nature of the interquark force at distances 1.0 fm
The combination of harmonic oscillator and inverse square potential was first of all adopted by Joshi and Mitra [14] in a theory based on the Schrodinger equation for studying the heavy meson spectroscopy
The interquark potential used in the present work is of harmonic oscillator plus inverse square form with a small energy dependent term in harmonic oscillator part

Summary

Introduction

Energy spectrum of heavy quarkonium are a rich source of information on the nature of the interquark force at distances 1.0 fm. The combination of harmonic oscillator and inverse square potential was first of all adopted by Joshi and Mitra [14] in a theory based on the Schrodinger equation for studying the heavy meson spectroscopy. Later it has been used by Iyer et al [15] and Ryes et al [16] in the study of hadron spectroscopy. This is a great advantage in view of the high nonlinearity of the differential equation to be solved Using this potential we have calculated the mass spectrum, the root mean square radii, average radii, leptonic decay width and 1 r for cc and bb systems. The aim is to study the effect of energy dependence on the low as well as high excitation states of the system

Details of Calculation

Results and Discussion

Summary and Conclusion