Tests of isospin symmetry breaking at $ϕ(1020)$ meson factories

Abstract

In a model of isospin symmetry breaking we obtain the ($e^{-} e^{+} \rightarrow π^{-} π^{+}$) amplitude $Q$ and the isospin $I=0$ and $I=1$ relative phase $ψ$ at the $ϕ(1020)$ resonance in aproximate agreement with experiment. The model predicts $Γ(ϕ\rightarrow ωπ^{0}) \approx 4 \cdot 10^{-4} \;\mbox{MeV}$. We have also obtained $Γ(ϕ\rightarrow η' γ)=5.2 \cdot 10^{-4} \;\mbox{MeV}$. Measuring this partial width would strongly constrain $η$-$η'$ mixing. The branching ratios $BR$ of the isospin violating decays $ρ^{+} \rightarrow π^{+} η$ and $η' \rightarrow ρ^{\pm} π^{\mp}$ are predicted to be $BR(ρ^{+} \rightarrow π^{+} η)=3 \cdot 10^{-5}$ and $BR(η' \rightarrow ρ^{\pm} π^{\mp})=4 \cdot 10^{-3}$, respectively, leading to $BR[ϕ\rightarrow ρ^{\pm} π^{\mp} \rightarrow (π^{\pm} η)π^{\mp} \rightarrow (π^{\pm} γγ)π^{\mp}]=10^{-6}$ and $BR[ϕ\rightarrow η' γ\rightarrow (ρ^{\pm} π^{\mp})γ]=2\cdot 10^{-6}$.