Sterile Neutrinos
Sterile neutrinos are hypothetical, weakly interacting neutrinos that could explain neutrino masses and mixing, adding additional neutrino flavors.
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The statement of the theorem
Define the neutrino field as a hypothetical singlet under the Standard Model gauge group . Its Lagrangian interaction term with Standard Model fermions is suppressed or zero, implying no coupling to or bosons:\n\n$$ \mathcal{L}_{int} = \bar{\nu}_{s} (i \gamma^{\mu} \partial_{\mu}) \nu_{s} + \text{mixing terms} \tag{4} \text{where the mixing term } \mathcal{L}_{mix} \text{ is typically proportional to } \epsilon \bar{\nu}_{s} \nu_{L} + \text{h.c.} \text{ and } \epsilon \ll 1. \tag{5} \text{The absence of } SU(2)_L \text{ coupling is the defining characteristic.} \tag{6}