K-matrix analysis of the (IJPC = 00+ +)-wave in the mass region below 1900 MeV

Abstract

We present the results of the current analysis of the partial wave IJ P C = 00 ++ based on the available data for meson spectra (ππ, K K, ηη, ηη ′ , ππππ). In the framework of the K-matrix approach, the analytical amplitude has been restored in the mass region 280 MeV< √ s < 1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f 0 (980), f 0 (1300), f 0 (1500), f 0 (1750) and the broad state f 0 (1200 − 1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels ππ, K K, ηη, ηη ′ , ππππ). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels ππ, K K, ηη, ηη ′ , we estimate the quark/gluonium content of f 0 (980), f 0 (1300), f 0 (1500), f 0 (1750), f 0 (1200 − 1600). For f 0 (980), f 0 (1300), f 0 (1500) and f 0 (1750), their partial widths testify the q q origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f 0 (1200 − 1600) support the idea about gluonium nature of this broad state.→ ππ, K K, ηη, ηη ′ , makes us to apply the other methods to single out the states which are extra ones for the q q-systematics, namely, exotic states. The method based on the consideration of trajectories in the (n, M 2 )-plane (n is radial quantum number of the q q state and M its mass) is discussed in Section 5.On the basis of the extracted partial widths for the channels ππ, K K, ηη, ηη ′ , the following properties of resonances f 0 (980), f 0 (1300), f 0 (1500), f 0 (1750) and broad state f 0 (1200 − 1600) are to claim:1. f 0 (980): This resonance is dominantly the q q state, q q = nn sin ϕ + ss cos ϕ, with a large ss component. Under the assumption that the admixture of the glueball component is

Open-charm meson spectroscopy

“…Experimentally, let us only mention that the recent analysis by BES of the J/Ψ → φπ + π − and J/Ψ → φK + K − data [53] requires a state f 0 (1790) distinct from the f 0 (1710). Recent reanalysis of the Crystal Barrel data [54] suggest the existence of a new state called f 0 (1200 − 1600). Theoretically, one would expect non−qq scalar objects in the mass range below 2 GeV.…”

Systematics of Quark-Antiquark States: Where are the Lightest Glueballs?

“…The extra state, which was found and investigated in [5,6,8], namely, f bare 0 (1580), should be identified as a scalar glueball, for its decay couplings satisfy the requirements inherent in the gluonium, see discussion in [3]. So, …”

“…The combined K-matrix analyses of the spectra have been performed for the mass interval 280 ≤ M ≤ 1950 MeV by including the following final states: I = 0 : ππ, ηη, KK, ηη , ππππ (ρρ, σσ) [5], I = 1 : πη, KK [6], I = 1 2 : Kπ; [7].…”

“…Previous analysis [6] carried out in 1997-1998 was based on the experimental data as follows: (1) GAMS data on the S-wave two-meson production in the reactions πp → π 0 π 0 n, ηηn and ηη n at small nucleon momenta transferred, |t| < 0.2 (GeV/c) 2 [9,10]; (2) GAMS data on the ππ S-wave production in the reaction πp → π 0 π 0 n at large momentum transfers squared, 0.30 < |t| < 1.0 (GeV/c) 2 [9]; (3) BNL data on the reaction π − p → KKn [11]; (4) CERN-Münich data on π + π − → π + π − [12]; (5) Crystal Barrel data on pp (at rest, from liquid H 2 )→ π 0 π 0 π 0 , π 0 π 0 η, π 0 ηη [13,14]. Now the experimental basis has much broadened, and additional samples of data are included into the analysis [5] of the 00 ++ wave as follows: (6) Crystal Barrel data on proton-antiproton annihilation in gas: pp (at rest, from gaseous H 2 ) → π 0 π 0 π 0 , π 0 π 0 η [15].…”

“…The most important ingredients of the new analysis [5] are: (i) the study of KK-spectra that led to the determination of the flavour-octet and flavour-singlet components; (ii) the study of f 0 (1300) produced without background: πN → ππN at large |t|. Figure 9 taken from [5] demonstrates the complex-M plane for the 00 ++ sector.…”