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

We revisit, scrutinize, improve, confirm and complete our previous results [1-4] from the scalar digluonium sum rules within the standard SVZ-expansion at N2LO without instantons and beyond the minimal duality ansatz: one resonance circle plus 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-sigma B , f(sigma B)] = [1.07(13), 0.46(16)], [M-G1, f(G1)] = [1.55(12), 0.37(11)] GeV and the corresponding masses of the radial excitations: M-sigma'B = 1.11(12) and MG('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-G2 similar or equal to 2.99(22) GeV. Combining these results with some Low-Energy Vertex Sum Rules (LEV-SR), we predict some hadronic widths and classify these states into two groups: - The sigma-like (sigma(B), sigma'(B) which decay copiously to pi pi rom OZI-violating process and the sigma'(B) to 2(pi pi)S through sigma sigma - The G-like (G(1), G'(1) and eventually G2) which decay into eta'eta, eta eta through the U(1)A gluonic vertex. Besides some eventual mixings with quarkonia states, we may expect that the observed sigma/f(0)(500) and f(0)(1.37) are sigma-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 psi(G)(0) = 2.09(29) GeV4 and its slope 10(2) x psi'(G); (0) = -22(29) GeV2. Our results are summarized in Table 1. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study revisits the scalar digluonium sum rules and extracts important data regarding the masses and couplings of gluonia. Predictions are made for the hadronic decay modes of different types of gluonia. The results also estimate the conformal charge and its slope, providing valuable insights into the complex spectra of scalar mesons.