  We analyze the pipi production amplitudes in the excited Upsilon decay
processes, Upsilon (2S) to Upsilon (1S)pi^+pi^-, Upsilon (3S) to Upsilon
(1S)pi^+pi^- and Upsilon (3S) to Upsilon (2S)pi^+pi^-, and the pipi and KKbar
production amplitudes in the charmonium decay processes, psi (2S) to Jpsi
pi^+pi^- and Jpsi to phi pi^+pi^-, phi K^+K^-, including the possible effect of
light sigma production. The amplitudes are parametrized by the sum of
Breit-Wigner amplitudes for the sigma and the other relevant particles and of
the direct 2pi-production amplitude, following the VMW method. All the pipi
(and KKbar mass spectra are reproduced well with the obtained values of
sigma-parameters, m_sigma =526(+48,-37)MeV and Gamma_sigma =301(+145,-100)MeV,
which is almost consistent with the values in our previous phase shift
analyses.
