Fermi Decay of Higher Spin Particles

Abstract

The explicit form for the spin projection operators introduced by Fronsdal is calculated for arbitrary spin and applied to first-order processes involving four fermions. The matrix element for the most general nonderivative interaction is found for the special case in which two of the particles have spin \textonehalf{}. The method of relating matrix elements written in different orders is extended to this case.The theory is applied to the decay of the mu meson, extending the work of Caianiello. It is found that the experimental decay spectrum can be equally well fitted by an assignment of spin \textonehalf{} or $\frac{3}{2}$. The method is then applied to the Fermi decay of hyperons. Lifetimes are calculated for decays in which the initial particle has a spin of \textonehalf{} or $\frac{3}{2}$, and the final particles all have spin \textonehalf{}. All the lifetimes are less than 2 orders of magnitude longer than the corresponding observed lifetimes for the normal mode of decay.The hypothesis of a universal Fermi interaction is extended to include fermions of arbitary spin. Under this hypothesis, the experimental muon spectrum is most closely reproduced with spin $\frac{3}{2}$. The results also indicate that the muon has the same particle-antiparticle character as an electron of the same charge.