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Gaussian QCD sum-rules are ideally suited to the study of mixed states ofgluonium (glueballs) and quark ($q\bar q$) mesons because of their capabilityto resolve widely-separated states of comparable strength. The analysis of theGaussian QCD sum-rules (GSRs) for all possible two-point correlation functionsof gluonic and non-strange ($I=0$) quark scalar ($J^{PC}=0^{++}$) currents isdiscussed. For the non-diagonal sum-rule of gluonic and $q\bar q$ currents weshow that perturbative and gluon condensate contributions are chirallysuppressed compared to non-perturbative effects of the quark condensate, mixedcondensate, and instantons, implying that the mixing of quark mesons andgluonium is of non-perturbative origin. The independent predictions of themasses and relative coupling strengths from the non-diagonal and the twodiagonal GSRs are remarkably consistent with a scenario of two states withmasses of approximately 1 GeV and 1.4 GeV that couple to significant mixturesof quark and gluonic currents. The mixing is nearly maximal with the heaviermixed state having a slightly larger coupling to gluonic currents than thelighter state.

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