Use of a non-relativistic basis for describing the low energy meson spectrum

D A Amor-Quiroz,P O Hess,O Civitarese,T Yepez-Martinez

doi:10.1088/1742-6596/912/1/012028

Abstract

We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an effective field theory and evaluate its utility for solving a Hamiltonian inspired by the QCD formalism in the Coulomb Gauge. Since the functions involved in such expansion are non-relativistic, the Talmi-Moshinsky transformations can be used to recover the translational invariance of the center of mass of the mesonic states. Finally, many-body methods and an a posteriori flavor mixing procedure are used to compute a preliminary spectrum for the mesons below 1 GeV.

Highlights

In the low energy regime the strong interaction coupling constant αs is of the order of the unit and it is impossible to model the color interaction as a perturbation
We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an effective field theory and evaluate its utility for solving a Hamiltonian inspired by the QCD formalism in the Coulomb Gauge
Since the functions involved in such expansion are non-relativistic, the Talmi-Moshinsky transformations can be used to recover the translational invariance of the center of mass of the mesonic states

Summary

Introduction

In the low energy regime (below 1 GeV ) the strong interaction coupling constant αs is of the order of the unit and it is impossible to model the color interaction as a perturbation. Due to confinement, the fermionic fields are expected to be restricted to a finite volume, forming localized hadrons This is why the oscillator basis is intuitively more adequate than plane waves, since it establishes a characteristic lenght for the fields in the position space: By expanding the fields in such basis, the color charge distribution functions are suppressed over long distances by an exponential e−. The 3D-h.o. basis is not Lorentz invariant, it is possible to recover the Galilean invariance of the mesons’ CM by using the TM transformations [14] This means that the individual quarks will not be invariant under spatial translations, the important degrees of freedom to be considered in QCD at low energies are light mesons and not their constituent components. This basis seems to be suitable in order to extend the analysis in many directions, like adding gluonic degrees of freedom or evaluating other hadronic states

Construction of the effective Hamiltonian

The diagonalization method

Results

Conclusions