We discuss here the possible production of the hypothetical spin-zero $W$ boson ($W_0$) recently proposed by T. D. Lee, either through the decay of a directly produced spin-one $W\left(W_1\right)$ or by direct production in the reactions $\nu +\mathrm{Fe}\to \mathrm{Fe}+W_0+\mu$ and $\mu +\mathrm{Fe}\to \mathrm{Fe}+W_0+\nu$. Theoretical cross sections and differential distributions are presented here for $W_1$ masses between 2 and 40 $\frac{\mathrm{GeV}}{c^2}$ and $W_0$ masses between 2 and 8 $\frac{\mathrm{GeV}}{c^2}$ for beam energies from 80 to 300 GeV. We show that assuming nonzero muon mass in the calculations for a neutrino beam, rather than zero muon mass as suggested by Lee, can increase the total theoretical cross section by up to a factor of 1000 if $M_1$ is greater than $4M_0$ or if the $W_1$'s anomalous magnetic moment is near 1. In general, the production cross sections with incident neutrinos for $W_0$'s are down from those for $W_1$'s by a factor of 20-100, while the cross sections with incident muons are nearly equal. The effects of the $W_1$'s anomalous magnetic moment, $W_0$ and $W_1$ mass, and incident energy upon cross sections and distributions are discussed for the coherent and incoherent cases. Possible signatures for detecting a $W_0$ either in the decay of a $W_1$ or in a $q^2-\nu$ plot in direct production are discussed.

• Received 24 September 1971

DOI:https://doi.org/10.1103/PhysRevD.5.638