New nonet scalar mesons and glueballs: the mass spectra and the production yields in relativistic heavy ion collisions

Abstract

We propose a new nonet scheme for scalar mesons consisting of $f_{0}(980)$, $a_{0}(980)$, $K_{0}^{\ast}(1430)$, and $f_{0}(1770)$, regarding them as quark-antiquark $P$-wave states classified by $\mathrm{SU}(3)$ light flavor symmetry. We investigate their production in relativistic heavy ion collisions, and estimate their yields by applying the statistical model and the quark coalescence model. In contrast to these scalar mesons, we regard $f_{0}(1500)$ as a glueball that is not included in the proposed nonet. We quantify the production yields of $f_{0}(1500)$ by accounting for various internal structures of this state, and compare their yields with those of the new nonet scalar mesons. Given the production yields of these hadrons, our results strongly suggests that $f_{0}(1500)$ is a glueball.

Figures (6)

• Figure 1: Mass spectra of scalar mesons with nonstrangeness and strangeness are shown in the mass region below 2 GeV. The new nonet scalar mesons, $f_{0}(980)$, $a_{0}(980)$, $K_{0}^{\ast}(1430)$, and $f_{0}(1770)$, proposed in this study are indicated by arrows. The glueball candidate, $f_{0}(1500)$, is shown by dashed line. Cf. Fig. \ref{['fig:231109_nonet']}.
• Figure 2: The $\mathrm{SU}(3)$ flavor diagrams are shown for (a) new nonet scalar mesons proposed in this study (cf. Fig. \ref{['fig:250206_spectrum_scalar']}) and (b) ordinary vector mesons.
• Figure 3: The harmonic oscillator frequencies are plotted for the quark masses for up and down quarks ($u$ and $d$), strange quark ($s$), charm quark ($c$), and bottom quark ($b$). They are denoted by $\omega_{n}$, $\omega_{s}$, $\omega_{c}$, and $\omega_{b}$ in the text. The results shown for in the RHIC and LHC parameters, where the LHC results are the same for 2.76 TeV and 5.02 TeV. Interpolating the points, the frequency $\omega_{g}$ for the constituent gluons ($g$) is obtained for the gluon mass $m_{g}=750$ MeV. See Table \ref{['tbl:omega_g']}.
• Figure 4: The phase shifts ccmkappa are shown to indicate (a) $f_{0}(500)$, $f_{0}(980)$, and $f_{0}(1500)$ in $\pi \pi - K\bar{K}$ scatterings and (b) $K_{0}^{\ast}(700)$ and $K_{0}^{\ast}(1430)$ in $\pi K$ scatterings in the calculations in the S-matrix formulation.
• Figure 5: The ratios of the hadron yields from the statistical model and the coalescence model (denoted by coal./stat.) are shown for the parameter set RHIC (Sc.1). The normal hadrons are indicated by the black dots ($\bullet$). The new nonet mesons, i.e., $f_{0}(980)$, $a_{0}(980)$, $K_{0}^{\ast}(1430)$, and $f_{0}(1770)$, are indicated by the red squares ($\blacksquare$). As for $f_{0}(1500)$, the $\bar{n}n$ ($P$-wave), $\bar{n}^{2}n^{2}$ ($S$-wave), and $gg$ ($S$-wave) configurations are indicated by the red triangle ($\blacktriangle$), dot ($\bullet$), and diamond ($\blacklozenge$), respectively ($n=u,d$). The ratios from the S-matrix formulation are shown by black-triangles ($\blacktriangle$). See Table \ref{['tbl:numerical_results']} also.