= Majorana neutrino mass from the Weinberg operator
{c}
{title2=$m_\nu=|G|v^2$}
For the gauge-singlet composite $\chi=\widetilde\phi^\dagger L$, the interaction $G\chi^TC^{-1}\chi-G^*\bar\chi C\bar\chi^T$ is electroweak <gauge-invariant>. At the <Higgs field> vacuum, $\chi=v\nu_L/\sqrt2$, giving $\tfrac12(Gv^2\nu_L^TC^{-1}\nu_L-G^*v^2\bar\nu_L C\bar\nu_L^T)$. The <Grassmann variation of a chiral Majorana mass term> therefore identifies the mass parameter as $Gv^2$, with physical mass $|G|v^2$. The dimension-five interaction has a coupling of mass dimension minus one. Under <lepton number> phase rotation, its two terms acquire factors $e^{\pm2i\alpha}$, so it violates continuous lepton number by two units. It is an effective extension of the minimal renormalizable <Standard Model>.
Back to article page
