C, P, and CP asymmetry observables based on triple product asymmetries

Triple product asymmetries have been used to probe CP violation in $K$, $D$, and B decays. Here we review the interpretation of those asymmetries, and note that it is possible to construct twelve measurable triple product asymmetries for the decay of a particle into a four body final state. Eight of these asymmetries are introduced here and nine have never been measured before. These can be used to systematically test C, P, and CP symmetries in decays to four body final states. In particular we note that these asymmetries can be used to study symmetry invariance in Higgs, $Z^0$, top-quark, and hadron decay (both baryon and meson) as well as for $\tau^\pm$ decay at production threshold.