Phenomenology of Scalar Mesons

A separable potential model of three coupled channels ππ, KK and an effective 2π2π has been constructed and applied in the analysis of the isoscalar S-wave ππ and KK phase shifts and inelasticities. A relatively narrow scalar resonance of mass 1400-1460 MeV has been found. This resonance is consistent with the recent CERN observation of an eventual scalar glueball at 1500 MeV. Other resonances at lower energies like a wide σ meson and a narrow f0(980) have been confirmed. Scalar meson spectroscopy is full of open questions. The internal structure of scalars is also very controversial, for example the f0(980) state is interpreted as qq̄, qq̄qq̄ or KK quasibound state. Mixing of scalar mesons with scalar glueballs is possible; for example the f0(1500) resonance, observed by the Crystal Barrel Collaboration in p̄p annihilation at CERN, was interpreted as a candidate for the lowest scalar glueball. The phenomenology of scalar mesons must include studies of interactions between different mesons produced in the decay channels of scalar mesons. In Ref. the scalar meson spectrum was studied in terms of a relativistic ππ and KK coupled channel model from the ππ threshold up to 1400 MeV. The phenomenological parameters were constrained by fitting the S-wave data extracted from the experimental cross sections on the ππ production by π scattering on unpolarized hydrogen target and further constraints were imposed by the KK phase shift analysis of Ref. . Recently, authors of Ref. have analysed data obtained on a polarized target by the CERN-Cracow-Munich group for the πp↑ → π πn reaction. Separation of the π and a1 exchange amplitudes in this reaction was then possible for the first time. From a set of four solutions for the isoscalar S-wave phase shifts up to 1600 MeV, two of them (”down-flat” and ”up-flat”) satisfy the unitarity constraint. The ”down-flat” solution is in good agreement with the former solution of Ref. up to 1400 MeV. Above 1400 MeV one observes an increase of the phase shifts and larger inelasticities than those seen in 3 . This could be a manifestation of the presence of scalar mesons f0(1370) or f0(1500) in that energy range. There a strong four–pion production has been observed in different experiments together with an evidence of clustering into σσ or ρρ pairs. In Ref. we have extended the isospin 0 S–wave relativistic 2–channel model of Ref. by adding to its ππ and KK channels an effective third coupled channel, here called σσ. The reaction amplitudes T satisfy a system of the coupled channel Lippmann-Schwinger equations: