Lifetimes and Decay Spectra ofτ′+andKμ3+

Nuclear emulsion stacks were exposed to the Bevatron ∼360-Mev/c unseparated $K^{+}$ beam at two different distances from the target. The $K_L$ to ${\tau }^{\prime }$ and $K_L$ to $K_{\mu 3}$ ratios at the two positions, combined with the known $K_L$ lifetime, yield (${1.0}_{-0.3\mathrm{}}^{+0.5\mathrm{}}$)×${10}^{-8\mathrm{}}$ sec for the ${\tau }^{\prime }$ mean life and (${1.2}_{-0.4\mathrm{}}^{+1.0\mathrm{}}$)×${10}^{-8\mathrm{}}$ sec for the $K_{\mu 3}$ mean life. These lifetimes, when compared with other $K^{+}$ lifetimes, are consistent with a single lifetime for all $K^{+}$ mesons. The ${\pi }^{+}$ energy spectrum from ${\tau }^{\prime +}$ decay is obtained, using 72 events, and by Dalitz-type analysis is found to be consistent with spin zero but would be unlikely for spin one. Hence, the ${\tau }^{\prime }$ spin is consistent with being the same as that of the $\tau$. The ${\mu }^{+}$ energy spectrum from ${K_{\mu 3}}^{+}$ decay is obtained from 0 to 63 Mev, using 47 events, and is found to be consistent with the energy distribution of the density of final states in the region. The relative abundances of ${\tau }^{+}$, ${\tau }^{\prime +}$, and ${K_{\mu 3}}^{+}$ are found to be 0.052±0.003, 0.015±0.002, and 0.028±0.004, respectively, the $K_{\mu 3}$ abundance having been estimated by assuming that the ${\mu }^{+}$ spectrum above 63 Mev is proportional to the density of final states.