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

Abstract

In a model of isospin symmetry breaking we obtain the ($e^{-}{e}^{+}\to {\pi }^{-}{\pi }^{+}$) amplitude $Q$ and the isospin $I=0$ and $I=1$ relative phase $\psi$ at the $\varphi (1020)$ 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 $\eta$-${\eta }^{\prime }$ mixing. The branching ratios $BR$ of the isospin violating decays ${\rho }^{+}\to {\pi }^{+}\eta$ and ${\eta }^{\prime }\to {\rho }^{\pm }{\pi }^{\mp }$ are predicted to be $BR({\rho }^{+}\to {\pi }^{+}\eta )=3\cdot 10^{-5}$ and $BR({\eta }^{\prime }\to {\rho }^{\pm }{\pi }^{\mp })=4\cdot 10^{-3}$, respectively, leading to $BR[\varphi \to {\rho }^{\pm }{\pi }^{\mp }\to ({\pi }^{\pm }\eta ){\pi }^{\mp }\to ({\pi }^{\pm }\gamma \gamma ){\pi }^{\mp }]=10^{-6}$ and $BR[\varphi \to {\eta }^{\prime }\gamma \to ({\rho }^{\pm }{\pi }^{\mp })\gamma ]=2\cdot 10^{-6}$.

11 pages 2 Figures ( not included available on request ), Latex, Karlsruhe TTP42-93

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• Study of isospin violating $\varphi$ excitation in $e^{+}{e}^{-}\to \omega {\pi }^0$
• The phi to pi+ pi- decay within a chiral unitary approach
• Extracting Br(omega->pi^+ pi^-) from the Time-like Pion Form-factor
• New Data from SND Detector in Novosibirsk