Momentum Spectrum of Positrons from the Decay ofμ+Mesons

Abstract

The momentum spectrum of positrons from ${\mu }^{+}$ decay has been examined. The detecting instrument was a 20-atmos hydrogen-filled diffusion cloud chamber, operated in a magnetic field of 7000 gauss. The data have been compared with the spin-½ $\mu$-meson theory of Michel, as modified by Behrends, Finkelstein, and Sirlin, to include first radiative corrections, and with the spin $\frac{3}{2}$ theory of Behrends and Fronsdal. Statistical analysis of the 1300 acceptable events yields the shape parameters ${\rho }_R=0.65\mathrm{}\pm 0.05$ (standard deviation) and ${\rho }_{\frac{3}{2}}=0.26\mathrm{}\pm 0.04$ (standard deviation). The theoretical spectra described by shape parameters in the vicinity of the best fits are very similar and this experiment cannot discriminate between the two spin assignments for the $\mu$ meson. The value of ${\rho }_R$ can be related to the Michel parameter ${\rho }_M$, and gives ${\rho }_M=0.67\mathrm{}\pm 0.05$ (standard deviation). The result for ${\rho }_{\mathrm{Michel}}$ was related to published $\beta$-decay data, and restrictions on a common interaction for $\beta$ and $\mu$ decay were deduced.