Chiral-Symmetry Breaking and the Electromagnetic Interaction in theη→3πDecay

We discuss the $\eta \to 3\pi$ decay within the framework of current algebra and soft-meson theorems using both the conventional electromagnetic interaction and isospin-breaking terms ("$U_3$" terms) from the same representation as the strong interaction. The interrelation between the strong Hamiltonian and the SU(2)-violating interactions is discussed. We find that the electromagnetic interaction gives a value of the decay width which is too small by three orders of magnitude. Using isospin-breaking contributions transforminǵ as a member of the same representation of SU(3) × SU(3) as the strong Hamiltonian, the decay width is not adequately described in either the $(3, \overline{3})+(\overline{3}, 3)$, $(6, \overline{6})+(\overline{6}, 6)$, or (8,8) models. Consistent use of all possible soft-pion theorems demonstrates that it is incorrect to neglect certain $\sigma$ terms that have been discarded in the existing literature.