A Gaussian Sum-Rules Analysis of Scalar Meson-Glueball Mixing

Gaussian QCD sum-rules (GSRs) are well-suited to a study of meson-glueball mixing due to their balanced sensitivity to ground and excited states. The GSRs corresponding to both diagonal and non-diagonal (crossed) two-point correlators between scalar-isoscalar (non-strange) quark currents and gluonic currents will be presented. For the crossed correlator, we show that perturbative and gluon condensate contributions are chirally-suppressed as compared to non-perturbative effects of the quark condensate, mixed condensate, and instantons, implying that the mixing of quark mesons and gluonium is of a non-perturbative origin. Independent predictions of the masses and relative coupling strengths stemming from the three GSRs (two diagonal and one non-diagonal) are remarkably consistent with a scenario of two states with masses of approximately $ 1\;{\rm GeV}$ and $1.4\;{\rm GeV}$ that couple to significant mixtures of quark and gluonic currents. The mixing is nearly maximal with the heavier mixed state having a slightly larger gluonium content than the lighter state.