In this paper we investigate the phenomenology of a very light scalar, h, with mass 100 MeV < m h < 10 GeV, mixing with the SM Higgs. As a benchmark model we take the real singlet scalar extension of the SM. We point out apparently unresolved uncertainties in the branching ratios and lifetime of h in a crucial region of parameter space for LHC phenomenology. Bounds from LEP, meson decays and fixed target experiments are reviewed. We also examine prospects at the LHC. For m h m B the dominant production mechanism is via meson decay; our main result is the calculation of the differential p T spectrum of h scalars originating from B mesons and the subsequent prediction of up to thousands of moderate (triggerable) p T displaced dimuons possibly hiding in the existing dataset at ATLAS/CMS or at LHCb. We also demonstrate that the subdominant V h production channel has the best sensitivity for m h m B and that future bounds in this region could conceivably compete with those of LEP.

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, a scalar doublet, and a scalar quadruplet, whose properties are constrained by neutrino oscillation data. A detailed collider study is presented for O 3 = LLQdH and O 8 = Ldē †ū † H completions with a vector-like quark χ ∼ (3, 2, − 5 6 ) and a leptoquark φ ∼ (3, 1, 1 3 ). The existing LHC limits extracted from searches for vector-like fermions and sbottoms/stops are m χ 620 GeV and m φ 600 GeV.

The minimal Type I see-saw model cannot explain the observed neutrino masses and the baryon asymmetry of the Universe via hierarchical thermal leptogenesis without ceding naturalness. We show that this conclusion can be avoided by adding a second Higgs doublet with tan β 4. The models considered naturally accommodate a SM-like Higgs boson, and predict TeV-scale scalar states and low-to intermediate-scale hierarchical leptogenesis with 10 3 GeV MN 1 10 8 GeV.