Near-Maximal Mixing of Scalar Gluonium and Quark Mesons: A Gaussian Sum-Rule Analysis

TL;DR

This paper uses Gaussian QCD sum-rules to analyze the mixing of scalar gluonium and quark mesons, revealing nearly maximal mixing and two states around 1 and 1.4 GeV with significant quark-gluon mixture.

Contribution

It introduces a Gaussian sum-rule approach to study non-perturbative mixing of gluonium and quark mesons, providing new insights into their mass spectrum and coupling strengths.

Findings

Identifies two mixed states at approximately 1 and 1.4 GeV.

Shows mixing is predominantly non-perturbative in origin.

Finds the mixing is nearly maximal with a slight gluonic dominance in the heavier state.

Abstract

Gaussian QCD sum-rules are ideally suited to the study of mixed states of gluonium (glueballs) and quark ($q\bar q$) mesons because of their capability to resolve widely-separated states of comparable strength. The analysis of the Gaussian QCD sum-rules (GSRs) for all possible two-point correlation functions of gluonic and non-strange ($I=0$) quark scalar ($J^{PC}=0^{++}$) currents is discussed. For the non-diagonal sum-rule of gluonic and $q\bar q$ currents we show that perturbative and gluon condensate contributions are chirally suppressed compared to non-perturbative effects of the quark condensate, mixed condensate, and instantons, implying that the mixing of quark mesons and gluonium is of non-perturbative origin. The independent predictions of the masses and relative coupling strengths from the non-diagonal and the two diagonal GSRs are remarkably consistent with a scenario of two states with masses of approximately 1 GeV and 1.4 GeV that couple to significant mixtures of quark and gluonic currents. The mixing is nearly maximal with the heavier mixed state having a slightly larger coupling to gluonic currents than the lighter state.