The Radiative Decay of Vector Mesons

In this paper, radiative decays $\rho^0 \to \pi^+\pi^-\gamma, \pi^0\pi^0\gamma$ ,$\phi \to K^+K^-\gamma, K^0 \bar{K^0}\gamma$ are studied systematically in the U(3)$_L\timesU(3)_R$ chiral theory of mesons. The theoretical differential spectrum with respect to photon energy and branch ratio for $\rho^0 \to \pi^+\pi^-\gamma$ agree well with the experimental data. Differential spectrums and branch ratios for $\rho^0 \to \pi^0\pi^0\gamma, \phi \to K^+ K^-\gamma,\phi \to K^0\bar{K^0}\gamma$ are predicted. The process $\phi \to K^0 \bar{K^0} \gamma$ is relevant to precision measurment of CP-violation parameters in the kaon systerm at a $\phi$-factory. We give a complete estimate of the branch ratio for this decay process by including scalar resonance $f_0, a_0$ 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 $\phi\to K^0\bar{K}^0$ CP violation experiments.