Nonet classification of scalar/isoscalar resonances below 1900 MeV: the existence of an extra scalar state in the region 1200–1600 MeV

Abstract

A classification of the IJ P C = 00 ++ mesons is performed on the basis of the Kmatrix analysis of meson spectra in the reactions: (i) GAMS data on πp → π 0 π 0 n, ηηn, ηη ′ n [1, 2, 3]; (ii) Crystal Barrel data on pp (at rest) → π 0 π 0 π 0 , π 0 π 0 η, π 0 ηη [4,5]; (iii) CERN-Münich data on πp → π + π − n [6]; (iiii) BNL data on πN → KKN [7]. The analysis points to the existence of four comparatively narrow scalar resonances which correspond to the following poles of the scattering amplitude (in MeV): (1015 ± 15) − i(43 ± 8), (1300 ± 20) − i(120 ± 20), (1499 ± 8) − i(65 ± 10) and (1780±30)−i(125±70). The scattering amplitude also has a fifth pole f 0 (1530 +90 −250 ) at the complex mass (1530 +90 −250 ) − i(560 ± 140). The masses of the K-matrix poles (bare states) are at 720 ± 100 MeV, 1230 ± 50 MeV, 1260 ± 30 MeV, 1600 ± 50 MeV and 1810 ± 30 MeV. The quark content of the bare states is analyzed using the values of their couplings to the ππ, KK, ηη and ηη ′ . It is shown that one of the bare states in the mass region 1200-1600 MeV is superfluous for the qq classification and should be considered as the lightest glueball. The search for and classification of scalar/isoscalar IJ P C = 00 ++ states is the direct and possibly the only way for identification of the lightest scalar glueball. In refs. [8,9] the K-matrix analysis of the 00 ++ -wave was performed in the mass region up to 1550 MeV, where four scalar resonances (the T-matrix poles at the complex masses: (1008 ± 10) −i(43 ±5), (1290 ±25) −i(120 ±15), (1497 ±6) −i(61 ±5), (1430 ±150) −i(600 ±100), in MeV) were found. Correspondingly, four bare states were determined: the lightest bare state with mass 750 ± 100 MeV is dominantly ss, while three other states, with masses 1240 ± 30 MeV, 1280 ± 30 MeV and 1615 ± 50 MeV, do not contain a large ss component. One of these states, either the state with mass 1240 MeV or the state with mass 1280 MeV, is a natural qq-partner of the lightest bare state. For the other two states two scenarios arose in ref.[9]:(a) both these states are qq mesons; then, in the region 1550-1900 MeV, two ss-rich states exist as the nonet partners of the low-lying 00 ++ -mesons;(b) in the region 1550-1900 MeV there is only one ss-rich 00 ++ state; then one of the low-lying states is exotic, probably the lightest glueball.To resolve these alternatives, the spectra in KK, ηη and ηη ′ channels need to be investigated in the region 1550-1900 MeV: the existence of a strange component in these mesons favours a search for the ss-rich states. The ηη and ηη ′ spectra obtained by the GAMS collaboration [2,3] give a good opportunity for this study. The aim here is to extend the analysis of the 00 ++ -wave to a mass of 1900 MeV, including the ηη and ηη ′ GAMS spectra into the simultaneous fitting procedure. The main purpose is to identify the ss-rich states: the analysis of the π 0 π 0 and π + π − spectra from refs. [9,10] definitely indicates that in the region 1550-1900 MeV there are no 00 ++ resonances with a significant ππ branching ratio...

Structure of $f_0(980)$ from a coupled channel analysis of $S$ -wave $\pi\pi$ scattering

“…In our model this resonance is needed to describe the rise of the ππ scattering phase above the KK threshold. It can be considered as an approximation for the higher resonances, in particular, the f 0 (1300), and our results for the remote poles s II D and s III E should be considered as an estimate rather than the parameters of real physical structures (for the discussion of this energy region see [3,4,5,41,17,43] and references therein).…”

“…Table 4: The of the S-matrix in the √ s-plane (GeV) corresponding to the f 0 (980) resonance. 1.015 − i0.015 [21] 0.987 − i0.040 0.967 − i0.069 [38] 0.988 − i0.023 0.797 − i0.185 [40] 0.984 − i0.039 0.986 − i0.102 [41] 1.015 − i0.043…”

“…A qualitative description of this mass range would require accounting for additional higher resonances, see [5,40,41]. We do not attempt it here, however, we can use our model to demonstrate how the qq state dissolves into the continuum.…”

Towards resolution of the scalar meson nonet enigma

“…This value may be considered as the pole position which gets shifted further down due to strong coupling to, e.g., the KK threshold. For example, recent analysis of various experimental data by Anisovich et al [35] reveals a lowest mass scalar resonance with the pole position at 1015 ± 15 MeV and width of 43 ± 8 MeV. We do not address the question of choosing between the f 0 (980) and f 0 (1000) in this paper.…”

Systematics of quark–antiquark states and scalar exotic mesons

“…allowed us not only to determine reliably the ratios of different two-meson yields (that is rather important for the resonance classification), but also to conclude that the peak in the ηη-spectrum in the reaction π − p → ηηn, which was previously claimed to be the resonance G(1590) [13], appeared in fact as a result of the interference of the broad state f 0 (1200 − 1600) and f 0 (1500) resonance [36]. The data by the Crystal Barrel Collaboration discussed above were obtained from the pp-annihilation at rest.…”