Calculation of the partial width for the decayη→π+π−π0

Abstract

We calculate the partial width for the decay $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ in a linear U(3) ⊗ U${\mathrm{}\left(3\right)\mathrm{}}_{\mathrm{chiral}}$ Lagrangian, using a model discussed previously in the literature by Haymaker and Carruthers. We find $\Gamma (\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0)=58\mathrm{}$ eV which is consistent with a recent calculation of Weinberg using a nonlinear U(3) ⊗ U${\mathrm{}\left(3\right)\mathrm{}}_{\mathrm{chiral}}$ Lagrangian modified so as to incorporate the new mechanism proposed by Kogut and Susskind. However, the result is quite below the latest experimental result of 204 ± 22 eV. In addition, we briefly discuss the history behind the decay $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$, emphasizing those points leading to the present understanding of the problem.