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

Abstract

We analyze the ππ production amplitudes in the excited ϒ decay processes, ϒ(2 S)→ ϒ(1 S) π + π −, ϒ(3 S)→ ϒ(1 S) π + π − and ϒ(3 S)→ ϒ(2 S) π + π −, and the ππ and K K ̄ production amplitudes in the charmonium decay processes, ψ(2 S)→ 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 2 π-production amplitude, following the VMW method. All the ππ (and K K ̄ ) invariant mass spectra are reproduced well with the σ Breit–Wigner amplitudes by using the common parameters, m σ =526 +48 −37 MeV and Γ σ =301 +145 −100 MeV, which is almost consistent with the values obtained in our previous phase shift analyses.