Use of Weak Partial Conservation of Axial-Vector Current to Resolve theη→3πPuzzle

Abstract

Current algebra and strong partial conservation of axial-vector current (PCAC) predict a good value for the slope of the decay $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ but also the (experimentally contradicted) approximate vanishing of the $\eta \to 3\pi$ rates. We show that weak PCAC provides a framework in which the good result remains valid, but the bad one does not. The only speculative step is the assignment of the most plausible quantum numbers of the $H\left(990\right)\mathrm{}$.