Scalar model of glueball in nonperturbative quantisation \`a la Heisenberg

TL;DR

This paper develops a nonperturbative scalar model of glueballs using two scalar fields to approximate SU(3) non-Abelian dynamics, providing numerical profiles and mass predictions that align with other models and experimental data.

Contribution

It introduces a novel two-scalar field approximation for modeling glueballs nonperturbatively, enabling detailed numerical analysis of glueball properties.

Findings

Derived asymptotic behavior of scalar fields

Calculated glueball mass dependence on model parameters

Compared model predictions with experimental data

Abstract

A scalar model of glueball is considered. The model is based on two scalar fields approximation for SU(3) non-Abelian Lagrangian. The approach to approximation makes use of the assumption that 2 and 4-points Green's functions are described in terms of some two scalar fields. The model is described via non-perturbative method due to value of coupling constant, which does not permit us using of Feynman diagrams and therefore of perturbative methods. Asymptotical behaviour of the scalar fields are obtained. Profiles of these fileds calculated for a range of values of a parameter of the problem is given. Detailed numerical investigation of corresponding equations describing this model is performed. The dependence of the glueball mass vs parameters of scalar fields is shown. Comparison of characteristics of glueball obtained in our two-scalar model and predictions of other models and experimental data for glueball is performed.