Vol.2, No.11, 1292-1297 (2010) Natural Science

http://dx.doi.org/10.4236/ns.2010.211156

Copyright © 2010 SciRes. OPEN ACCESS

Light D wave meson spectrum in a relativistic harmonic

model with instanton induced interaction

Antony Prakash Monteiro, Kanti Basavarajappa Vijaya Kumar*

Department of Physics, Mangalore University, Mangalagangothri, Mangalore, India; *Corresponding author: kbvijaya kumar@

yahoo.com

Received 20 July 2010; revised 25 August 2010; accepted 28 August 2010.

ABSTRACT

The mass spectrum of the D wave mesons is

considered in the frame work of relativistic

harmonic model (RHM). The full Hamiltonian

used in the investigation has the Lorentz scalar

plus a vector harmonic-oscillator potential, the

confined-one-gluon-exchange potential (COGEP)

and the instanton-induced quark-antiquark in-

teraction (III). A good agreement between calcu-

lated D wave meson masses with experimental

D wave meson masses is obtained. The respec-

tive role of III and COGEP in the D wave meson

spectrum is discussed.

Keywords: Quark Model; Confined-One-Gluon-

Exchange Potential; Instanton Induced Interaction;

D Wave Meson Spectra

1. INTRODUCTION

The Quantum Chromodynamics (QCD), the theory of

strong interactions, is not exactly solvable in the

non-perturbative regime which is required to obtain the

physical properties of the hadrons. Hence various ap-

proximation methods like lattice gauge theories are em-

ployed to solve QCD in the non-perturbative regime. In

the constituent quark model, conventional mesons are

bound states of a spin ½ quark and spin ½ antiquark

bound by a phenomenological potential. The phenome-

nological models developed to explain the observed

properties of mesons are either non-relativistic quark

models (NRQM) with suitably chosen potential or rela-

tivistic models where the interaction is treated pertur-

batively [1-3]. In most of the works that use NRQM, it is

assumed that the quark interaction is dominated by a

linear or quadratic confinement potential and is supple-

mented by a short range potential stemming from the

one-gluon exchange mechanism. The Hamiltonian of

these quark models usually contains three main ingredi-

ents: the kinetic energy, the confinement potential and a

hyperfine interaction term, which has often been taken

as an effective one-gluon-exchange potential (OGEP) [4].

Other types of hyperfine interaction like Instanton-

Induced Interaction (III) deduced by a non-relativistic

reduction of the ‘t Hooft interaction [5-12] have also

been introduced in the literature.

The success of the NRQM in describing the hadron

spectrum is somewhat paradoxical, as light quarks

should in principle not obey a non-relativistic dynamics.

This paradox has been avoided in many works based on

the constituent quark models by using for the kinetic

energy term of the Hamiltonian a semi-relativistic or

relativistic expression [9-12]. Even in the existing rela-

tivistic models though the effect of confinement of

quarks has been taken into account, the effect of con-

finement of gluons has not been taken into account

[13-15]. Therefore in our present work, we have inves-

tigated the effect of exchange of confinement of gluons

on the masses of light D wave mesons and their radially

excited states in the frame work of RHM with III

[6,11-12,16]. The essential new ingredient in our inves-

tigation of the light D wave mesonic states is to take into

account the confinement of gluons in addition to the

confinement of quarks. In the existing quark models,

Fermi-Breit interaction which gives rise to π- and N-

splitting is treated as perturbation. The OGEP being at-

tractive for π, and for a nucleon a naïve perturbative

treatment of one gluon hyperfine interaction is incorrect

and hence one obtains a high value for the pion mass. This

leads to further renormalization of strength of interaction

for a better fit. Also, the most prominent flaw of NRQM is

the neglect of relativistic effects and gluon dynamics. In

our present work, for the confinement of quarks we are

making use of the RHM which has been successful in

explaining the properties of light hadrons. For the con-

finement of gluons, we have made use of the current con-

finement model (CCM) which was developed in the spirit

of the RHM [13-15]. The CCM has been quite successful

in describing the glue-ball spectra. The confined gluon