Quark-gluonium content of the scalar-isoscalar states f_0(980), f_0(1300), f_0(1500), f_0(1750), f_0(1420 ^{+150}_{- 70}) from hadronic decays

Abstract

On the basis of the decay couplings f_0 -> \pi\pi, K\bar K, \eta\eta, \eta\eta', which had been found before, in the study of analytical (IJ^{PC}=00^{++})-amplitude in the mass range 450-1900 MeV, we analyse the quark-gluonium content of resonances f_0(980), f_0(1300), f_0(1500), f_0(1750) and the broad state f_0(1420 ^{+ 150}_{-70}). The K-matrix technique used in the analysis makes it possible to evaluate the quark-gluonium content both for the states with switched-off decay channels (bare states, f^{bare}_0) and the real resonances. We observe significant change of the quark-gluonium composition in the evolution from bare states to real resonances, that is due to the mixing of states in the transitions f_0(m_1)-> real mesons-> f_0(m_2) responsible for the decay processes as well. For the f_0(980), the analysis confirmed the dominance of q\bar q component thus proving the n\bar n/s\bar s composition found in the study of the radiative decays. For the mesons f_0(1300), f_0(1500) and f_0(1750), the hadronic decays do not allow one to determine uniquely the n\bar n, s\bar s and gluonium components providing relative pecentage only. The analysis shows that the broad state f_0(1420 ^{+ 150}_{-70}) can mix with the flavour singlet q\bar q component only, that is consistent with gluonium origin of the broad resonance.