The pseudoscalar glueball in a chiral Lagrangian model with instanton effect

TL;DR

This paper investigates pseudoscalar glueball candidates within a chiral Lagrangian model incorporating instanton effects, analyzing parameter spaces and potential experimental candidates based on different assumptions about the lightest scalar glueball mass.

Contribution

It introduces a model that accounts for instanton effects in describing pseudoscalar glueballs and explores the parameter space constraints and candidate states.

Findings

Three eta states could be glueball candidates if the scalar glueball is 1710 MeV.

No pseudoscalar glueball candidates are found if the scalar glueball is 660 MeV.

Parameter space sensitivity depends on the scalar sector assumptions.

Abstract

We study the pseudoscalar glueball candidates in a chiral effective Lagrangian model proposed by 't hooft, motived by taking into account the instanton effects, which can describe not only the chiral symmetry breaking, but also the solution of $U_A(1)$. We study the parameter space allowed by constraints from vacuum conditions and unitary bounds. By considering two scenarios in $0^{++}$ sector, we find that parameter space which can accommodate the $0^{-+}$ sector is sensitive to the conditions in $0^{++}$ sector. From our analysis, it is found that three $\eta$ states, i.e. $\eta(1295)$, $\eta(1405)$, $\eta(1475)$, can be glueball candidates if we assume that the lightest $0^{++}$ glueball has a mass 1710 MeV. While there is no $0^{-+}$ glueball candidate found in experiments if we assume that the lightest $0^{++}$ glueball has a mass 660 MeV.