  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.
