Testing Radiative Neutrino Mass Models at the LHC

The Large Hadron Collider provides us new opportunities to search for the origin of neutrino mass. Beyond the minimal see-saw models a plethora of models exist which realise neutrino mass at tree- or loop-level, and it is important to be sure that these possibilities are satisfactorily covered by searches. The purpose of this paper is to advance a systematic approach to this problem. Majorana neutrino mass models can be organised by SM-gauge-invariant operators which violate lepton number by two units. In this paper we write down the minimal ultraviolet completions for all of the mass-dimension 7 operators. We predict vector-like quarks, vector-like leptons, scalar leptoquarks, a charged scalar, and a scalar doublet, whose properties are constrained by neutrino oscillation data. A detailed collider study is presented for $O_3=LLQ\bar dH$ and $O_8 = L\bar d\bar e^\dagger \bar u^\dagger H$ completions with a vector-like quark $\chi\sim(3, 2, -\frac{5}{6})$ and a leptoquark $\phi\sim(\bar 3,1,\frac{1}{3})$. The existing LHC limits extracted from searches for vector-like fermions and sbottoms/stops are $m_\chi \gtrsim 620$ GeV and $m_\phi\gtrsim 600$ GeV.