The $τ$ neutrino as a Majorana particle

Abstract

A Majorana mass term for the $τ$ 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 $τ$ neutrino, by measuring fermion number violating processes in a deep inelastic scattering experiment $νp \rightarrow τX$. We show that, if the neutrino beam is obtained from the decay of high energetic pions, the probability of obtaining "wrong sign" $τ$ leptons is suppressed by a factor ${\cal{O}}(m_{ν_τ}^2 θ^2/m_μ^2)$ instead of the naively expected suppression factor $θ^2 m_{ν_τ}^2/E_ν^2$, where $E_ν$ is the $τ$ neutrino energy, $m_{ν_τ}$ and $m_μ$ are the $τ$-neutrino and muon masses, respectively, and $θ$ is the $ν_μ$ - $ν_τ$ mixing angle. If $m_{ν_τ}$ is of the order of 10 MeV and $θ$ is of the order of $0.01 - 0.04$ (the present bounds are ($m_{ν_τ} < 35 MeV, θ< 0.04$) the next round of experiments may be able to distinguish between Majorana and Dirac $τ$-neutrinos.