The σ-meson production in excited ϒ decay processes: constraint from chiral symmetry

In the recent letter [T. Komada, M. Ishida, S. Ishida, Phys. Lett. B 508 (2001) 31], hereafter referred to as I, we have shown that the ππ mass spectra in various excited ϒ decay processes are phenomenologically well reproduced by a coherent sum of σ Breit–Wigner amplitude and of the direct 2π-production amplitude. On the other hand, the ππ-production amplitude was widely believed to be suppressed generally near the threshold, because of the derivative coupling property of Nambu–Goldstone π meson. In this Letter we show that the “threshold-suppression” does not hold in the process with large energy release, in conformity with the steep increase from the ππ threshold observed in the transition ϒ(3S→1S), and that the method of I is consistent with chiral symmetry. Furthermore, applying an effective amplitude explicitly consistent with chiral symmetry, we reanalyze the typical ππ-spectra.