Theoretical Estimations of the Spin – Averaged Mass Spectra of Heavy Quarkonia and Bc Mesons

S. M. Kuchin,N.V. Maksimenko

doi:10.13189/ujpa.2013.010310

Abstract

In this work, the spin-averaged mass spectra of heavy quarkonia and Bc mesons in a Cornell potential is studied within the framework of nonrelativistic Schrodinger equation. The energy eigenvalues and eigenfunctions are obtained in compact forms for any l-value using Nikiforov-Uvarov method. Based on the results determined the mass spectra of charmonium, bottomonium and Bc mesons. Our results are in good correspondence with other experimental and theoretical studies.

Highlights

Among the modern methods of study strongly conditions, such as lattice QCD, QCD sum rules, and others, still remains urgent study of such systems in the quark potential models for theoretical studies of the properties of the constituent particles and the dynamics of their interaction
Properties quarkoniums consisting of heavy quark and antiquark are well described by the Schrödinger equation, so the solution of this equation with a spherically - symmetric potentials is one of the most important problems in physics quar
The mass spectra for some charmonium, bottomonium and BBcc mesons states are given in comparison with experimental data and other theoretical calculations in Table 1, Table 2 and Table 3, where standard notations are used for the centers of gravity of the (n +1)l th levels, where n is the radial quantum number

Summary

Introduction

Among the modern methods of study strongly conditions, such as lattice QCD, QCD sum rules, and others, still remains urgent study of such systems in the quark potential models for theoretical studies of the properties of the constituent particles and the dynamics of their interaction. Enjoy a direct numerical solution of the given boundary conditions on the wave functions, and various approximate methods for finding analytical solutions of this equation The preparation of such decisions as necessary to describe the mass spectrum of the quark - antiquark systems, and to describe the characteristics of other mesons. As ππ(rr) is a polynomial, the radicand should be represented in the form of a quadratic polynomial This is possible only if the discriminant of the polynomial of degree two under the root is equal to zero. From this condition we obtain, generally speaking, a quadratic equation for the constant kk. The polynominal solution of equation (1.3) is determined by the Rodrigues formula yynn (rr)

The Solution of the Schrödinger Equation

Conclusions