Time-reversal invariance and the phase of the rho--ω mixing

We use the unitarity sum to rederive in a simple way an explicit formula for the ρ-ω mixing phase in terms of |ε|, ${\Gamma }_{\omega }$, ${\Gamma }_{\rho }$, and $m_{\omega }^{{}^2}-m_{\rho }^{{}^2}$. We then present a systematic study of the condition imposed by T (or CPT) invariance and unitarity on the relative phase and strength of the mixing. It is shown that the departure from T invariance in the ρ-ω system is, in principle, directly demonstrable through the measurement of the ρ-ω mixing phase in e⁺e⁻→π⁺π⁻. The connection between the phase discrepancy and the breakdown of microscopic reversibility is also discussed. Finally, two possible graphical representations for the ρ-ω mixing parameters which exhibit directly the condition imposed by unitarity and time-reversal invariance on the relative phases and strengths of the ρ-ω mixing are given.