Spin Splitting Spectroscopy of Heavy Quark and Antiquarks Systems

Hesham Mansour,Ahmed Gamal,M. Abolmahassen,Smarajit Triambak

doi:10.1155/2020/2356436

Abstract

Phenomenological potentials describe the quarkonium systems likecc¯,bb,¯ and b¯cwhere they give a good accuracy for the mass spectra. In the present work, we extend one of our previous works in the central case by adding spin-dependent terms to allow for relativistic corrections. By using such terms, we get better accuracy than previous theoretical calculations. In the present work, the mass spectra of the bound states of heavy quarks cc¯,bb¯,and 𝐵𝑐 mesons are studied within the framework of the nonrelativistic Schrödinger equation. First, we solve Schrödinger’s equation by Nikiforov-Uvarov (NU) method. The energy eigenvalues are presented using our new potential. The results obtained are in good agreement with the experimental data and are better than the previous theoretical estimates.

Highlights

In the twentieth century, quarkonium systems have been discovered
Theorists have been trying to explain some aspects of those systems like mass spectra and decay mode properties. [1,2,3,4,5]
Some of them used lattice quantum chromodynamics view [6,7,8,9,10,11,12], effective field theory [13], relativistic potential models [14, 15], semirelativistic potential models [16], and nonrelativistic potential models [17,18,19] which have shared in common the Coulomb and linear potentials

Summary

Introduction

Theorists have been trying to explain some aspects of those systems like mass spectra and decay mode properties. Some of them used lattice quantum chromodynamics view [6,7,8,9,10,11,12], effective field theory [13], relativistic potential models [14, 15], semirelativistic potential models [16], and nonrelativistic potential models [17,18,19] which have shared in common the Coulomb and linear potentials. There are other groups which use confinement power potential rn [20,21,22], the Bethe-Salpeter approach [23,24,25]. We use mixed potential: nonrelativistic potential models (Coulomb+linear) and confinement power potentials plus spin-dependent splitting terms as a correction. Schrödinger’s equation is solved by the NikiforovUvarov (NU) method [26,27,28,29,30,31,32,33,34], which gives asymptotic expressions for the eigenfunctions and eigenvalues of the Schrödinger equation

Methodology

Numerical Results and Discussions

Conclusions