Harmonic Analysis on the Dalitz Plot andη→3πDecays

Three different types of two-variable expansions of three-body decay amplitudes and their square moduli are reviewed and compared - a recently suggested expansion based on the group O(4), the standard Dalitz-Fabri power series, and an SU(3) expansion suggested by B. W. Lee. Each of these expansions is then applied to analyze the recently obtained experimental Dalitz plot for the $\eta \to {\pi }^0{\pi }^{+}{\pi }^{-}$ decay.