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 $\Gamma (\varphi \to \omega {\pi }^0)\approx 4\cdot 10^{-4}\text{mbox}MeV$. We have also obtained $\Gamma (\varphi \to {\eta }^{\prime }\gamma )=5.2\cdot 10^{-4}\text{mbox}MeV$. 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 $BR[\varphi \to {\eta }^{\prime }\gamma \to ({\rho }^{\pm }{\pi }^{\mp })\gamma ]=2\cdot 10^{-6}$.

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