Experimental Consequences of the Majorana Theory for the Muon's Neutrino

The Majorana theory applied to the muon's neutrino predicts lepton-nonconserving phenomena with a small probability of second order in $m_{\nu }$, the neutrino mass, and $a$, the deviation from $V-A$ theory. In particular, in the coupled reactions $\pi \to \mu +{\nu }_{\mu }$, ${\nu }_{\mu }+Z\to Z^{\prime }+\mu$, where $Z$ and $Z^{\prime }$ are nuclei, there is a small probability that the muon produced in the second reaction has the same sign as the original $\pi$. This probability is computed to lowest order in $a$ and $m_{\nu }$. It may be as great as 8/100, consistent with present experimental upper limits on $a$ and ${\mu }_{\nu }$. If we assume $a=0\mathrm{}$, the probability goes as $m_{\nu }^{}{}_{}{}^2$ and cannot be more than 1/200. If a small lepton-nonconserving effect were to be observed, the problem might arise of distinguishing between nonvanishing $a$ and nonvanishing $m_{\nu }$. This might be done by an improved measurement of the high-energy part of the electron spectrum in $\mu$ decay. To this end the electron spectrum is calculated exactly as a function of energy, angle, ${\mu }_{\nu }$, and $a$. It is seen that $m_{\nu }$ has an enhanced influence on the high-energy part, whereas the influence of $a$ is of the same order of magnitude at all energies.