On the Spin of theμ-Meson

The behavior of a $\mu$-meson of spin $\frac{3}{2}$ is investigated for the processes $\mu \to e+2\mathrm{}\nu$, $\pi \to \mu +\nu$, ${\mu }^{-}+p\text{'}\text{'}\to n\text{'}\text{'}+\nu$. These processes have been chosen because they give direct information on the nature of the $\mu$-meson and do not require second quantization of the $\mu$-meson field, which is not feasible for spin values greater than 1 when electromagnetic interactions are present. The theory used to describe the $\mu$-meson is due to Rarita and Schwinger. The spectra for the $\mu \to e+2\mathrm{}\nu$ decay are obtained for the same modes of decay considered by Tiomno and Wheeler for $\mu$-mesons of spin ½. Their most relevant feature is that none of them goes to zero at maximum electron energy. It is to be hoped that more careful measurements of this spectrum will permit a decision on the spin value of the $\mu$-meson. The $\mu$-capture is studied by assuming the process to happen via an intermediate scalar or pseudoscalar $\pi$-meson. Comparison with the lifetime for $\pi \to \mu$-decay and use of experimental data allow an evaluation of the constant coupling the $\pi$-meson to nucleons. The plausibility of this value is taken as a test for the plausibility of the assumed spin value of the $\mu$-meson. The results do not appear to contradict present-day evidence, due to the uncertainty of the nuclear matrix elements. The formulas obtained apply of course to any spin $\frac{3}{2}$ particle undergoing similar processes.