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

Stephan Narison (1)

1 LUPM - Laboratoire Univers et Particules de Montpellier

We revisit, scrutinize, improve, confirm and complete our previous results [1–4] 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: $[M_{{\sigma }_B},f_{{\sigma }_B}]=[1.07(13),0.46(16)],[M_{G_1},f_{G_1}]=[1.55(12),0.37(11)]$ GeV and the corresponding masses of the radial excitations: $M_{{\sigma }_B^{\prime }}=1.11(12)$ and $M_{G_1^{\prime }}=1.56(14)$ GeV which are (unexpectedly) almost degenerated with the ground states. The 2nd radial excitation is found to have a much heavier mass: $M_{G_2}\simeq$ 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 σ-like (${\sigma }_B,{\sigma }_B^{\prime }$) which decay copiously to ππ from OZI-violating process and the ${\sigma }_B^{\prime }$ to $2(\pi \pi )S$ through σσ. – The G-like $(G_1,G_1^{\prime }$ and eventually $G_2$) which decay into ${\eta }^{\prime }\eta ,\eta \eta$ 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 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 $G_1,G_1^{\prime }$ 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 ${10}^2\times {\psi }_G^{\prime }(0)=-22(29)$ GeV². Our results are summarized in Table 1.

Mots clés: QCD spectral sum rules; Perturbative and non-perturbative QCD; Exotic hadrons; Masses and decay constants; hadron spectroscopy; glueball; mass spectrum; charge: conformal; spectral representation: parametrization; sum rule; scalar meson; quantum chromodynamics; duality; low-energy theorem; excited state; correlation function; eta(958); f0(980); f0(600); mixing; mixing angle; anomaly: U(1)

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]; Physique des Hautes Energies - Expérience [hep-ex]; Physique des Hautes Energies - Réseau [hep-lat]

Stephan Narison. Di-gluonium sum rules, I = 0 scalar mesons and conformal anomaly. Nucl.Phys.A, 2022, 1017, pp.122337. ⟨10.1016/j.nuclphysa.2021.122337⟩. ⟨hal-03341180⟩