ηAsymmetry WithoutCNonconservation

Abstract

We calculate the charge asymmetry for the reaction ${\pi }^{-}p\to n{\pi }^{+}{\pi }^{-}{\pi }^0$ assuming $C$ invariance for the $\eta$ decay. We find that interference terms with a $3\pi$ background amplitude give a nonzero charge asymmetry. Assuming that the background in the $\eta$ mass region (10 MeV) is about 10% of the $\eta$ signal, we obtain a maximum asymmetry of about 2%, implying that the experimental asymmetry does not necessarily imply $C$ nonconservation.