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Register a new userNear-Maximal Mixing of Scalar Gluonium and Quark Mesons: A Gaussian Sum-Rule Analysis
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Gaussian QCD sum-rules are ideally suited to the study of mixed states of gluonium (glueballs) and quark ($qbar q$) 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 $qbar q$ 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.
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Gaussian QCD sum-rules are used to analyze all possible two-point correlation functions of scalar gluonic and quark currents. The independent predictions of the masses and relative coupling strengths from the different correlators are remarkably consistent with a scenario of two scalar states that couple to nearly-maximal mixtures of quark and gluonic currents.
We revisit, improve and confirm our previous results [1-3] from the scalar digluonium sum rules within the standard SVZ-expansion at N2LO {it without instantons} and {it beyond the minimal duality ansatz} : one resonance $oplus$ QCD continuum parametrization of the spectral function. We select different unsubtracted sum rules (USR) moments of degree $leq$ 4 for extracting the two lowest gluonia masses and couplings. We obtain in units of GeV: $(M_{G},f_G)=[1.04(12),0.53(17)]$ and $[1.52(12),0.57(16)]$. We attempt to predict the masses of their first radial excitations to be $M_{sigma} simeq 1.28(9)$ GeV and $M_{G_2}simeq 2.32(18)$ GeV. Using a combination of the USR with the subtracted sum rule (SSR), we estimate the conformal charge (subtraction constant $psi_G(0)$ of the scalar gluonium two-point correlator at zero momentum) which agrees completely with the Low Energy Theorem (LET) estimate. Combined with some low-energy vertex sum rules (LEV-SR), we confront our predictions for the widths with the observed $I=0$ scalar mesons spectra. We confirm that the $sigma$ and $f_0(980)$ meson can emerge from a maximal (destructive) ($bar uu+bar dd$) meson - $(sigma_B$) gluonium mixing [10]. The $f_0(1.37)$ and $f_0(1.5)$ indicate that they are (almost) pure gluonia states (copious decay into $4pi$) through $sigmasigma$, decays into $etaeta$ and $etaeta$ from the vertex $U(1)_A$ anomaly with a ratio $div$ to the square of the pseudoscalar mixing angle sin$^2theta_P$.
We study $bar qq$-hybrid mixing for the light vector mesons and $bar qq$-glueball mixing for the light scalar mesons in Monte-Carlo based QCD Laplace sum rules. By calculating the two-point correlation function of a vector $bar qgamma_mu q$ (scalar $bar q q$) current and a hybrid (glueball) current we are able to estimate the mass and the decay constants of the corresponding mixed physical state that couples to both currents. Our results do not support strong quark/gluonic mixing for either the $1^{--}$ or the $0^{++}$ states.
This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.
This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.
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