Scalar model of glueball in nonperturbative quantisation à la Heisenberg

Abstract

A scalar model of glueball is considered. The model is based on two calar 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 arameter of the problem is given. Detailed numerical investigation of corresponding equations describing this model is performed. The pendence 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.

Keywords

• glueball
• scalar field approximation
• quantum chromodynamics
• non-perturbative methods
• gluonic fields