High Mass Scalar Mesons Research Articles

Glueballs in Radiative J/ψ Decays

The scalar glueball is observed in a coupled-channel analysis of the S-wave amplitude from BESIII data on radiative J/ψ decays and further data. Ten scalar isoscalar resonances were required to fit the data. Five of them were interpreted as mainly-singlet, five as mainlyoctet resonances in SU(3). The yield of resonances showed a striking peak with properties expected from a scalar glueball: • G0(1865) is produced abundantly in radiative J/ψ decays above a very low background. Its mass is 1σ compatible with the mass calculated in unquenched lattice QCD, and the yield is 1.6σ compatible with the yield calculated in lattice QCD. • The decay analysis of the scalar isoscalar mesons shows that the assignment of mesons to mainly-octet and mainly-singlet states is correct. Even the production of mainly-octet scalar mesons - which should be forbidden in radiative J/ψ decays - peaks at 1865 MeV. The decay analysis requires a small glueball content in the flavor wave function of several scalar resonances. The glueball content as a function of the mass shows a peak compatible with the peak in the yield of scalar isoscalar mesons. The sum of the fractional glueball contributions is compatible with one. • In the reaction Bs → J/ψ + K+K− reported by the LHCb collaboration, a primary ss̄ couples to mesons having a strong coupling to K+K−. Two peaks in the K+K− mass spectrum are seen due to ϕ(1020) and f′2(1525), but there is little evidence for the f0(1710) or other high-mass scalar mesons coupling strongly to KK̄. High-mass scalar mesons are strongly produced by two initial-state gluons but not by an ss̄ pair in the initial state. They must have sizable glueball fractions! • The D wave amplitude in the BESIII data on radiative J/ψ decays reveales a high-mass structure which can be described by a single Breit-Wigner or by the sum of three ϕϕ resonances interpreted as tensor glueballs a long time ago. The structure - and further tensor resonances observed in radiative J/ψ decays - are tentatively interpreted as tensor glueball. • In J/ψ decays into γπ0π0η′ several resonances are reported. The possibility is discussed that the pseudoscalar glueball might be hidden in these data.

ϕ→π0ηγandϕ→π0π0γdecays and mixing between low and high mass scalar mesons

Radiative decays $\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$ and $\ensuremath{\phi}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$ are studied assuming that these decays are caused through the intermediate ${a}_{0}(980)\ensuremath{\gamma}$ and ${f}_{0}(980)\ensuremath{\gamma}$ states, respectively. Fitting the experimental data of the $\ensuremath{\eta}{\ensuremath{\pi}}^{0}$ and ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ invariant mass spectrum in the decays $\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$ and ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$, it is shown that the processes $\ensuremath{\phi}\ensuremath{\rightarrow}{a}_{0}\ensuremath{\gamma}$ and $\ensuremath{\phi}\ensuremath{\rightarrow}{f}_{0}\ensuremath{\gamma}$ are dominated by the ${K}^{+}{K}^{\ensuremath{-}}$ loop interaction rather than the pointlike $\ensuremath{\phi}{a}_{0}({f}_{0})\ensuremath{\gamma}$ one both for the nonderivative and derivative $SPP$ coupling. The experimental data of $\ensuremath{\Gamma}[\ensuremath{\phi}\ensuremath{\rightarrow}{f}_{0}\ensuremath{\gamma}]/\ensuremath{\Gamma}[\ensuremath{\phi}\ensuremath{\rightarrow}{a}_{0}\ensuremath{\gamma}]$ predicts that ${g}_{{f}_{0}K\overline{K}}/{g}_{{a}_{0}K\overline{K}}\ensuremath{\sim}2$. Considering the effects of the mixing between low mass scalar $qq\overline{q}\overline{q}$ states and high mass scalar $q\overline{q}$ states to these coupling constants ${g}_{{f}_{0}K\overline{K}}$ and ${g}_{{a}_{0}K\overline{K}}$, one suggests that this mixing is rather large.

Radiative decays involving [formula omitted] and [formula omitted] and mixing between low and high mass scalar mesons

We analyze the experimental data for ϕ → f 0 ( 980 ) γ , ϕ → a 0 ( 980 ) γ , f 0 ( 980 ) → γ γ and a 0 ( 980 ) → γ γ decay widths in a framework where f 0 ( 980 ) and a 0 ( 980 ) are assumed to be mainly q q q ¯ q ¯ low mass scalar mesons and mixed with q q ¯ high mass scalar mesons. Applied the vector meson dominance model (VDM), these decays amplitudes are expressed by coupling parameters B describing the S ( q q q ¯ q ¯ scalar meson)– V (vector meson)– V (vector meson) coupling and B ′ describing the S ′ ( q q ¯ scalar meson)– V– V coupling. Adopting the magnitudes for B and B ′ as ∼ 2.8 GeV −1 and ∼ 12 GeV −1 , respectively, the mixing angle between a 0 ( 980 ) and a 0 ( 1450 ) as ∼ 9 ° , and the mixing parameter λ 01 causing the mixing between I = 0 q q q ¯ q ¯ state and q q ¯ state as ∼ 0.24 GeV 2 , we can interpret these experimental data, consistently.

Effects on scalar meson decays of strong mixing between low and high mass scalar mesons

We analyse the mass spectroscopy of low mass scalar nonet and high mass scalar nonet+glueball and get the result that the strengths of the inter-mixing between low and high mass scalar mesons are very strong and the strengths of mixing for I = 1, 1/2 scalar mesons and those of I = 0 scalar mesons are almost the same. We perform a χ2 fit based on the decay widths and ratios of these mesons to estimate the effects of inter-mixing and get the result that the inter-mixing has large effects for these decay processes and f0(1710) is preferred as glueball rather than f0(1500). Best-fit values for the coupling constants A, A′ and A″ which represent the couplings of low mass scalar meson N to two pseudoscalar mesons PP, high mass scalar meson N′ to PP and glueball G to PP, respectively are obtained as (A, A′, A″) = (4.0 ± 1.1 GeV−1, 1.8 ± 0.3 GeV−1, − 0.64 ± 0.04 GeV−1).

Mixing among light scalar mesons and L = 1 qq̄ scalar mesons

Following the re-establishment of the σ(500) and the κ(900), the light scalar mesons a0(980) and f0(980) together with the σ(500) and the κ(900) are considered as the chiral scalar partner of pseudoscalar nonet in SU(3) chiral symmetry, and the high mass scalar mesons a0(1450), K*0(1430), f0(1370) and f0(1710) turned out to be considered as the L = 1 qq̄ scalar mesons. We assume that the high mass of the L = 1 qq̄ scalar mesons is caused by the mixing with the light scalar mesons. For the structure of the light scalar mesons, we adopted the qqq̄q̄ model in order to explain the ‘scalar meson puzzle’. The inter-mixing between the light scalar nonet and the high mass L = 1 qq̄ nonet and the intra-mixing among each nonet are analysed by including the glueball into the high mass scalar nonet.