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Register a new userThe Fragmented Glueball: A Personal View
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Authors
Eberhard Klempt
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A coupled-channel analysis has been performed to identify the spectrum of scalar mesons. The data include BESIII data on radiative $J/psi$ decays into $pi^0pi^0$,$K_SK_S$, $etaeta$, and $omegaphi$, 15 Dalitz plots from $bar pN$ annihilation at rest at LEAR, the CERN-Munich multipoles for $pipi$ elastic scattering, the $S$-wave from BNL data on $pipi$ scattering into $K_SK_S$, from GAMS data on $pipito pi^0pi^0, etaeta$, and $etaeta$, and NA48/2 data on low-mass $pipi$ interactions from $K^pmtopipi e^pm u$ decays. The analysis reveals the existence of ten scalar isoscalar resonances. The resonances can be grouped into two classes: resonances with a large SU(3) singlet component and those with a large octet component. The production of isoscalar resonances with a large octet component should be suppressed in radiative $J/psi$ decays. However, in a limited mass range centered at 1900,MeV, these mesons are produced abundantly. Mainly-singlet scalar resonances are produced over the full mass range but with larger intensity at 1900,MeV. The total scalar isoscalar yield in radiative decays into scalar mesons shows a clear peak which is interpreted as the scalar glueball of lowest mass.
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The center-of-gravity rule is tested for heavy and light-quark mesons. In the heavy-meson sector, the rule is excellently satisfied. In the light-quark sector, the rule suggests that the $a_0(980)$ could be the spin-partner of $a_2(1320)$, $a_1(1260)$, and $b_1(1235)$; $f_0(500)$ the spin-partner of $f_2(1270)$, $f_1(1285)$, and $h_1(1170)$; and $f_0(980)$ the spin-partner of $f_2(1525)$, $f_1(1420)$, and $h_1(1415)$. From the decay and the production of light scalar mesons we find a consistent mixing angle $theta^{rm s}=(14pm4)^circ$. We conclude that $f_0(980)$ is likely octet-like in SU(3) with a slightly larger $sbar s$ content and $f_0(500)$ is SU(3) singlet-like with a larger $nbar n$ component. The $a_0(1450)$, $K^*_0(1430)$, $f_0(1500)$ and $f_0(1370)$ are suggested as nonet of radial excitations. The scalar glueball is discussed as part of the wave function of scalar isoscalar mesons and not as additional intruder. It seems not to cause supernumerosity.
The mixing between the $f_2(1270)$, the $f_2(1525)$, and the $2^{++}$ glueball is determined and tested. The mass and the hadronic decay widths of the $G_2$ and the branching ratio $B(J/psirightarrowgamma G_2)$ are predicted.
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We have revisited glueball mixing with the pseudoscalar mesons in the MIT bag model scheme. The calculation has been performed in the spherical cavity approximation to the bag using two different fermion propagators, the cavity and the free propagators. We obtain a very small probability of mixing for the eta at the level of $0.04-0.1% and a bigger for the eta at the level of 4-12%. Our results differ from previous calculations in the same scheme but seem to agree with the experimental analysis. We discuss the origin of our difference which stems from the treatment of our time integrations.
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