Tests for the Spin in the Decay of Particles of Arbitrary Spin

The polarization and angular distribution of a spin-½ particle produced in the decay of a fermion of arbitrary spin into two particles of spins 0 and ½, and in the decay of a boson of arbitrary spin into two different spin-½ particles, one of which is a two-component neutrino, are calculated in terms of the general decay amplitudes. The results are applied to the discussion of tests for the spin of the decaying particle. Restrictions on the possible spins are found in terms of inequalities limiting the values of certain test functions applied to the experimental angular distributions and polarizations. The results for the boson decay are used in a discussion of the spin of the $K_{\mu 2}$ and of the possibility of lepton conservation in the $K_{\mu 2}$ and $\pi -\mu$ decays. A limit of 10% nonconservation of leptons is found if the $K$ spin is 0. Application of the spin tests to the decay of the ${\Lambda }^0$ hyperon provides substantial evidence that the ${\Lambda }^0$ spin is ½.