Pseudoscalar glueball mass: a window on three-gluon interactions

TL;DR

This paper investigates the mass of the pseudoscalar glueball in pure-glue QCD, revealing that an infrared suppression in the three-gluon vertex is crucial for matching lattice-QCD results, thus providing insights into three-gluon interactions.

Contribution

It demonstrates that an infrared suppressed three-gluon vertex is necessary to accurately predict the pseudoscalar glueball mass in pure-glue QCD, linking vertex behavior to observable spectra.

Findings

Infrared suppression of the three-gluon vertex is essential for matching lattice-QCD glueball masses.

Calculations show the vertex's behavior significantly influences glueball properties.

Results suggest observable implications for QCD bound-states and their interactions.

Abstract

In pure-glue QCD, gluon-gluon scattering in the $J^{PC}=0^{-+}$ channel is described by a very simple equation, especially if one considers just the leading contribution to the scattering kernel. Of all components in this kernel, only the three-gluon vertex, $V_{\mu\nu\rho}$, is poorly constrained by contemporary analyses; hence, calculations of $0^{-+}$ glueball properties serve as a clear window onto the character and form of $V_{\mu\nu\rho}$. This is important given that many modern calculations of $V_{\mu\nu\rho}$ predict the appearance of an infrared suppression in the scalar function which comes to modulate the bare vertex after the nonperturbative resummation of interactions. Such behaviour is a peculiar prediction; but we find that such suppression is essential if one is to achieve agreement with lattice-QCD predictions for the $0^{-+}$ glueball mass. It is likely, therefore, that this novel feature of $V_{\mu\nu\rho}$ is real and has observable implications for the spectrum, decays and interactions of all QCD bound-states.