Three-pion states and a new approach to the permutation groupS3. II. Pseudoscalar-meson decays

Abstract

Three-pion wave functions with zero spin, and specific isospin and $S_3$ properties, are constructed from powers of the Dalitz-plot variables. They are then used to study the decays of $F$, $D$, and $K$ mesons into three pions. Tests of the selection rules imposed by the standard charm model on $F$ and $D$ decays are discussed, especially in the ratio of rates for the ${\pi }^{+}{\pi }^{+}{\pi }^{-}$ and ${\pi }^0{\pi }^0{\pi }^{+}$ modes; $S_3$ properties play an important role in these tests. In $K$ decay quadratic terms are shown to have a likely origin in a state of mixed $S_3$ symmetry.