The σ-meson production in excited ϒ decay processes: phenomenological analyses

We analyze the ππ production amplitudes in the excited ϒ decay processes, ϒ(2S)→ϒ(1S)π+π−, ϒ(3S)→ϒ(1S)π+π− and ϒ(3S)→ϒ(2S)π+π−, and the ππ and KK̄ production amplitudes in the charmonium decay processes, ψ(2S)→J/ψπ+π− and J/ψ→φπ+π−, φK+K−, including the possible effect of light σ production. The amplitudes are parametrized by the sum of Breit–Wigner amplitudes for the σ and the other relevant particles and of the direct 2π-production amplitude, following the VMW method. All the ππ (and KK̄) invariant mass spectra are reproduced well with the σ Breit–Wigner amplitudes by using the common parameters, mσ=526+48−37 MeV and Γσ=301+145−100 MeV, which is almost consistent with the values obtained in our previous phase shift analyses.