Study of the Conditions Set by Unitarity and Time-Reversal Invariance in the ρ–ω Mixing with the Three-Body Mixing Formalism

Abstract

Using the three-body interference formalisms recently developed by us, we study the conditions imposed by time-reversal invariance and unitarity on the relative phase and strength of the ρ–ω mixing in the presence of vector meson [Formula: see text]. It is found that the effect of vector meson [Formula: see text] on these conditions when they are compared to those obtained with the usual two-body interference formalisms is very small. Even if the width of [Formula: see text] was ten times larger than the actual one, still this effect would be negligible. Thus, this detailed analysis confirms again the possibility of neglecting the effect of [Formula: see text] in the ρ–ω mixing problem. All the conclusions reached by us in this study are based purely on the experimental data alone and thereby, independent of the detailed dynamical assumptions on the decays of ρ, ω, and [Formula: see text]. We also wish to point out that an upper bound for the ρ–ω mixing strength in the 2π decay mode can be obtained from the knowledge of the masses and partial decay rates of channels other than 2π of ρ and ω.