Determination of the quarkonium--gluonium content of the isoscalar tensor resonances f₂(1920), f₂(2020), f₂(2240), f₂(2300) and of the broad state f₂(2000) based on decay couplings to π⁰π⁰,ηη,ηη'

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In the reactions p p→π⁰π⁰,ηη,ηη' there are four relatively narrow resonances f₂(1920), f₂(2020), f₂(2240), f₂(2300), and a broad one f₂(2000) in the mass region 1990--2400 MeV. In the framework of quark combinatorics we carry out an analysis of the decay constants for all five resonances. It is shown that the relations for the decay constants corresponding to the broad resonance f₂(2000)→π⁰π⁰,ηη, ηη' are the same as those corresponding to a glueball. An additional argument in favour of the glueball--nature of f₂(2000) is the fact that f₂(1920), f₂(2020), f₂(2240), f₂(2300) fit well the q q trajectories in the (n,M²)-plane (where n is the radial quantum number), while the broad f₂(2000) resonance turns out to be an unnecessary extra state for these trajectories.