Di-gluonium sum rules, I = 0 scalar mesons and conformal anomaly

Abstract We revisit, scrutinize, improve, confirm and complete our previous results [1] , [2] , [3] from the scalar di-gluonium sum rules within the standard SVZ-expansion at N2LO without instantons and beyond the minimal duality ansatz: “one resonance ⊕ QCD continuum” parametrization of the spectral function which is necessary for a better understanding of the complex spectra of the I = 0 scalar mesons. We select different (un)subtracted sum rules (USR) moments of degree ≤ 4 for extracting the two lowest gluonia masses and couplings. We obtain: [ M σ B , f σ B ] = [ 1.07 ( 13 ) , 0.46 ( 16 ) ] , [ M G 1 , f G 1 ] [ 1.55 ( 12 ) , 0.37 ( 11 ) ] GeV and the corresponding masses of the radial excitations: M σ B ′ = 1.12 ( 12 ) and M G 1 ′ = 1.56 ( 14 ) GeV which are (unexpectedly) almost degenerated with the ground states. The 2nd radial excitation is found to have a much heavier mass: M G 2 ≃ 2.99(22) GeV. Combining these results with some Low-Energy Vertex Sum Rules (LEV-SR), we predict some hadronic widths and classify them into two groups: – The σ-like ( σ B , σ B ′ ) which decay copiously to ππ from OZI-violating process and the σ B ′ to 2 ( π π ) S through σσ. – The G-like ( G 1 , G 1 ′ and eventually G 2 ) which decay into η ′ η , η η through the U ( 1 ) A gluonic vertex. Besides some eventual mixings with quarkonia states, we may expect that the observed σ / f 0 ( 500 ) and f 0 ( 137 ) are σ-like while the f 0 ( 1.5 ) and f 0 ( 1.7 ) are G-like gluonia. The high mass G 2 ( 2.99 ) can also mix with the G 1 , G 1 ′ to bring the gluon component of the gluonia candidates above 2 GeV. We also estimate the conformal charge ψ G ( 0 ) = 2.09 ( 29 ) GeV4 and its slope ψ G ′ ( 0 ) = 0.95 ( 30 ) GeV2. Our results are summarized in Table 1.