In this paper, radiative decays ρ 0 → π + π − γ, π 0 π 0 γ ,φ → K + K − γ, K 0K 0 γ are studied systematically in the U(3)L×U(3)R chiral theory of mesons. The theoretical differential spectrum with respect to photon energy and branch ratio for ρ 0 → π + π − γ agree well with the experimental data. Differential spectrums and branch ratios for ρ 0 → π 0 π 0 γ, φ → K + K − γ, φ → K 0K 0 γ are predicted. The process φ → K 0K 0 γ is relevant to precision measurment of CP-violation parameters in the kaon systerm at a φ-factory. We give a complete estimate of the branch ratio for this decay process by including scalar resonance f0, a0 poles, nonresonant smooth amplitude and an abnormal parity process with K * pole which hasn't been considered before. We conclude that processes with intermediate K * do not pose a potential background problem for φ → K 0K 0 CP violation experiments.

We make comments on ref.[1], and provide partial wave analysis to the decays of excited heavy S-wave 1 − quarkonia into the basic 1 − quarkonia state plus ππ. It is revealed that there exist contributions of D-wave transition in ψ −→ J/ψππ, Υ(2S) −→ Υ(1S)ππ and Υ(3S) −→ Υ(1S)ππ by using the data-fitting results in ref. [1]. A possible experimental method to measure the D-wave directly is discussed.

We make comments on ref.[1], and provide partial wave analysis to the decays of excited heavy S-wave 1 − quarkonia into the basic 1 − quarkonia state plus ππ. It is revealed that there exist contributions of D-wave transition in ψ −→ J/ψππ, Υ(2S) −→ Υ(1S)ππ and Υ(3S) −→ Υ(1S)ππ by using the data-fitting results in ref. [1]. A possible experimental method to measure the D-wave directly is discussed.