CP Violation in the Decay $\eta\to\pi^+\pi^-\gamma$

We study the CP violating effects in the decay of $\eta\to\pi^+\pi^-\gamma$. We show that to have CP violation in the decay, one has to consider both linear and circular photon polarizations. In the standard model, the polarizations are vanishingly small. However, model-independently, i.e. using only experimental constraint imposed by the limit on $Br(\eta\to\pi^+\pi^-)$ it can be up to $O(10$. We also explore various possible operators and we find that the tensor type operator, possibly arising from a nonzero CP violating electric dipole moment of the strange quark, can induce a sizable linear photon polarization.