Studies of meson mass spectra in the context of quark-antiquark bound states

Mallika Dhar

Abstract

This dissertation deals with the computation of meson mass spectra in the context of quark-antiquark (qq ) bound-state. Traditionally the qq bound-state problem is treated by solving the non-relativistic Schrödinger equation in position representation with a linear confining potential and a Coulomb-like attractive potential. For high energy, relativistic kinematics is necessary. It is well known that relativistic kinematics cannot be treated properly in position representation, but it can easily be handled in momentum representation. On the other hand, the linear potential and Coulomb-like potential have singularities in momentum-space and complicated subtraction procedure is necessary to treat the singularities properly. In order to deal with the double conflict, we have developed a method to solve any Schrödinger-like wave equation with/without relativistic kinematics in the mixed-space representation. In this representation, the kinematic term is treated in momentum-space and the potential term is treated in position-space. The results obtained from the mixed representation are in excellent agreement with the results obtained from the position-space and momentum space representations of the nonrelativistic Schrödinger equation without the spin-dependent terms in potential. The success of our computational scheme encouraged us to extend the investigation towards relativistic treatment of the mesonic systems along with the spin-dependent interactions in potential. We have included relativistic kinematics and spin-dependent potentials along with the regular linear and Coulomb-type potentials in our equation. Our predicted results of meson masses are in excellent agreement with the experimental data.