Generalized linear sigma model with two glueballs

TL;DR

This paper develops a comprehensive linear sigma model incorporating scalar and pseudoscalar glueballs alongside quark-based mesons, aiming to understand glueball interactions and properties within QCD-inspired effective field theory.

Contribution

It introduces the most general Lagrangian structure for mesons and glueballs based on QCD anomalies, including a decoupling analysis of scalar glueballs to study their properties.

Findings

Determined properties of the pure scalar glueball.

Established a framework for parameter determination with glueball interactions.

Analyzed the impact of scalar glueballs on the vacuum structure.

Abstract

We present a generalized linear sigma model that includes both scalar and pseudoscalar glueballs in addition to a quark-antiquark as well as a four-quark chiral nonet. Utilizing the axial and trace anomalies of QCD (at the effective mesonic level), we aim to develope the most general structure of the Lagrangian which can be used to study the interaction of quarkonia with glueballs. We then study the effect of scalar glueball on the vacuum of the model by considering a decoupling limit in which the glueball fields are decoupled from quarkonia. This determines the properties of the pure scalar glueball and builds a practical foundation for determining the model parameters when the interactions are turned on.