Near-maximal mixing of scalar gluonium and quark mesons: A Gaussian sum-rule analysis

Gaussian QCD sum-rules are ideally suited to the study of mixed states of gluonium (glueballs) and quark () 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 (JPC=0++) currents is discussed. For the non-diagonal sum-rule of gluonic and 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.