Weak-Interaction Effects inη→π+π−γ

Parity-violating effects due to the strangeness-conserving nonleptonic weak interaction are studied in the process $\eta \left(X^0\right)\to {\pi }^{+}{\pi }^{-}\gamma$. The circular polarization and the parity-violating linear polarization are calculated in the framework of the Cabibbo theory by using a pole model for the strong and electromagnetic interactions. The isoscalar ($\sim {cos}^2\theta$) and isovector ($\sim {sin}^2\theta$) components of the weak Hamiltonian are found to give comparable contributions. The magnitude of the circular polarization is obtained to be (1-5) × ${10}^{-9\mathrm{}}$ and the linear polarization, being dependent on final-state interactions, is smaller by nearly two orders of magnitude. In theories with a large isovector component in the weak nonleptonic Hamiltonian (theories involving neutral currents or second-class currents) the circular polarization can be larger, an estimate giving (1-3) × ${10}^{-8\mathrm{}}$.