  The decay modes and fractions in particle physics are some quantitative and
very complex questions. Various decays of particles and some known decay
formulas are discussed. Many important decays of particles and some known
decays of resonances can be generally described by the square of some types of
the associated Legendre functions. It is combined with the selection rule, then
the agreements are very good. The decay formulas of the similar decay modes are
the same. For the same types of particles, the coupling constants are kept to
be invariant, and only six constants are independent. The simplest dynamical
basis is probably that the decay formulas are the square of the solution of
free field equation of the decay particles in the momentum coordinate system.
Further, we discuss some general decays and their rules. Finally, we apply the
decay formulas to some massive hadrons.
