The $\tau$ neutrino as a Majorana particle

A Majorana mass term for the $\tau$ neutrino would induce neutrino - antineutrino mixing and thereby a process which violates fermion number by two units. We study the possibility of distinguishing between a massive Majorana and a Dirac $\tau$ neutrino, by measuring fermion number violating processes in a deep inelastic scattering experiment $\nu p \rightarrow \tau X$. We show that, if the neutrino beam is obtained from the decay of high energetic pions, the probability of obtaining "wrong sign" $\tau$ leptons is suppressed by a factor ${\cal{O}}(m_{\nu_{\tau}}^2 \theta^2/m_{\mu}^2)$ instead of the naively expected suppression factor $\theta^2 m_{\nu_{\tau}}^2/E_{\nu}^2$, where $E_{\nu}$ is the $\tau$ neutrino energy, $m_{\nu_{\tau}}$ and $m_{\mu}$ are the $\tau$-neutrino and muon masses, respectively, and $\theta$ is the $\nu_{\mu}$ - $\nu_{\tau}$ mixing angle. If $m_{\nu_{\tau}}$ is of the order of 10 MeV and $\theta$ is of the order of $0.01 - 0.04$ (the present bounds are ($m_{\nu_{\tau}} < 35 MeV, \theta < 0.04$) the next round of experiments may be able to distinguish between Majorana and Dirac $\tau$-neutrinos.