Determination of the strangeness contents of light-flavour isoscalars from its production rates in hadronic Z decays measured at LEP

A new phenomenological approach is suggested to determine the strangeness contents of light-flavour isoscalars. This approach is based on phenomenological laws of hadron production related to the spin, isospin, strangeness content and mass of the particles. The ``effective'' numbers of s and \bar{s} quarks in the isoscalar partners i_1 and i_2 are given by the nonstrange-strange mixing angle \phi: k(i_1)=2\sin^2\phi and k(i_2)=2\cos^2\phi. From the total production rates per hadronic Z decay of all light-flavour hadrons measured so far at LEP the values for k are found to be: k(\eta) \equiv 2-k(\eta^{\prime}) = 0.91 \pm 0.12, k(\phi) \equiv 2-k(\omega) = 1.94 \pm 0.09, k(f_2^{\prime}) \equiv 2-k(f_2) = 1.84 \pm 0.21 and k(f_0) = 0.09 \pm 0.13. Our results on the \eta--\eta^{\prime}, \omega--\phi and f_2--f_2^{\prime} isoscalar mixing are consistent with the present experimental evidence. Quite remarkably, our value for k(\eta) corresponds to the singlet-octet mixing angle \theta_P = -12.4^{\circ} \pm 3.5^{\circ}. The obtained strangeness content of the f_0(980) scalar/isoscalar is not consistent with the values supported by different model studies. However, taking the f_0(980) in our analysis with the mass of the bare state (K-matrix pole) f_0^{bare}(720 \pm 100), the mixing angle is found to be: |\phi_S^{bare}| = 73^{\circ} \pm 7^{\circ} \pm 24^{\circ}, in good agreement with the prediction of the K-matrix analysis.