A study in depth of f 0 ( 1370 )

Claims have been made that f0(1370) does not exist. The five primary sets of data requiring its existence are refitted with suitable Breit–Wigner amplitudes. Major dispersive effects due to the opening of the 4π threshold are included for the first time; the σ→ 4π amplitude plays a strong role. Crystal Barrel data on p̄p→ 3π at rest require f0(1370) signals of at least 32 and 33 standard deviations (σ) in S0 and P1 annihilation respectively. Furthermore, they agree within 5MeV for mass and width. Data on p̄p→ ηηπ agree and require at least a 19σ contribution. This alone is sufficient to demonstrate the existence of f0(1370). BES II data for J/Ψ → φππ contain a visible f0(1370) signal> 8σ. In all cases, a resonant phase variation is required. Cern–Munich data for ππ elastic scattering are fitted well with the inclusion of some mixing between σ, f0(1370) and f0(1500). Values of Γ2π for f2(1565), ρ3(1690), ρ3(1990) and f4(2040) are determined. PACS. 13.25.Gv; 14.40.Gx; 13.40.Hq