Scalar mesons and multichannel amplitudes

Abstract

Properties of scalar-isoscalar mesons are analysed in an unitary model using separable interactions in three decay channels: ππ , KK and an effective 2π2π. We obtain different solutions by fitting various data on the ππ and KK phase shifts and inelasticities including the CERN-Cracow-Munich measurements of the π − p ↑ → π + π − n reaction on a polarized target. Analytical structure of the meson-meson multichannel amplitudes is studied with a special emphasis on the role played by the S-matrix zeroes. S-matrix poles, located in the complex energy plane not too far from the physical region, are interpreted as scalar resonances. We see a wide f 0 (500) , a narrow f 0 (980) and a relatively narrow f 0 (1400) . In one of our solutions a resonance at about 1700 MeV is also found. Total, elastic and inelastic channel cross sections, branching ratios and coupling constants are evaluated and compared with available data. We construct an approximation to our model and show that the Breit-Wigner approach has a limited phenomenological applicability.

CP Violation and Strong Pion-Pion Interactions in the Weak $${B^\pm \to \pi^\pm \pi^\mp \pi^\pm}$$ Decays

“…The needed ππ scattering T matrix corresponds to the solution A of Ref. [10]. The result of our fit (see next section) for the modulus of Γ n * 1 (q 2 ) is plotted in Fig.…”

ππ scattering amplitudes constrained by Roy's equations

“…We have used, as in- * Talk presented at QCD05 conference, Montpellier, July 2005 † This work has been performed in the framework of the IN2P3-Polish Laboratories Convention (project number 99-97) ‡ Unité de Recherche des Universités Paris 6 et Paris 7, associée au CNRS put amplitudes in Roy's equations, the scalarisoscalar (S0), scalar-isotensor (S2) and vectorisovector (P1) waves defined in [4,5]. We have performed simultaneous fits to experimental data and to Roy's equations in the m ππ range from the ππ threshold to 970 MeV using the χ 2 test for χ…”

“…The S0-wave amplitudes have been constructed by fitting the three coupled-channel model predictions for phase shifts and inelasticities (see [5]) to Figure 1. Scalar-isoscalar phase shifts [1] for the solutions "up-flat" (open circles) and "down-flat" (full circles); the round curve indicates the region where the "up-down" ambiguity leads to the largest differences between the two solutions.…”

“…, 7, 9) are constant parameters. Above 970 MeV and up to 2 GeV our coupled channel model [5] amplitude A, fitted to the "down-flat" data, and the amplitude C, constrained by the "up-flat" data, were used. These two representations, one below 970 MeV and the second above were joined smoothly at 970 MeV up to their first derivative.…”

“…We have used our three coupled channel model [5] for the S0-and S2-waves and constructed an analogous one for the P1-wave. The uniform fit has been done in wider m ππ range, than that described in section 2 (hereafter called nonuniform fit).…”