Analysis of the meson-meson data in the framework of the dispersion D -matrix method

We describe the meson-meson data for the (IJPC=00⁺⁺) wave at 280≤√s≤1900 MeV in two approaches: (i) the K-matrix approach and (ii) the dispersion relation D-matrix method. With a good description of low-energy data (at 280≤√s≤900 MeV) as well as the data of two-meson transition amplitudes and antiproton-proton annihilation into three pseudoscalar meson states (at 450≤√s≤1950 MeV) we have found the positions of the resonance poles: (i) for the σ meson pole: M_σ=(390±35)-i(235±50) MeV; (ii) two poles for the f₀(980), on the second sheet (under the ππ cut): MI=(1011±5)-i(35±5) MeV, and on the third sheet (under the ππ and KK̄ cuts), MII=(1035±50)-i(460±50) MeV; for the f₀(1370) meson, M=(1285±30)-i(160±20) MeV; for the f₀(1500) meson, M=(1488±4)-i(53±5) MeV; for the f₀(1790) meson, M=(1775±25)-0ex0exi(140±15) MeV; and for the broad state f₀(1200--1600) M=(1540±120)-i(550±70) MeV. Our estimation of the scalar-isoscalar scattering length obtained under different parameterizations and assumptions about the quality of low-energy ππ scattering data is a₀⁰=(0.215±0.040)m_π^-1. We also discuss the idea according to which the σ meson could be a remnant of the confinement singularity, 1/s², in a white channel.