Neutrino masses and the CERN LHC: Testing the type II seesaw mechanism

We demonstrate how to systematically test a well-motivated mechanism for neutrino mass generation (type II seesaw) at the LHC, in which a Higgs triplet is introduced. In the optimistic scenarios with a small Higgs triplet vacuum expectation value v_Δ<10^-4 GeV, one can look for clean signals of lepton-number violation in the decays of doubly charged (H^±±) and singly charged (H^±) Higgs bosons to distinguish the normal hierarchy (NH), the inverted hierarchy (IH), and the quasidegenerate (QD) spectrum for the light neutrino masses. The observation of either H⁺→τ⁺ν or H⁺→e⁺ν will be particularly robust for the spectrum test since they are independent of the unknown Majorana phases. The H⁺⁺ decays moderately depend on a Majorana phase Φ₂ in the NH, but sensitively depend on Φ₁ in the IH. In a less favorable scenario v_Δ>2×10^-4 GeV, when the leptonic channels are suppressed, one needs to observe the decays H⁺→W⁺H₁ and H⁺→tb̄ to confirm the triplet-doublet mixing which in turn implies the existence of the same gauge-invariant interaction between the lepton doublet and the Higgs triplet responsible for the neutrino mass generation. In the most optimistic situation, v_Δ~10^-4 GeV, both channels of the lepton pairs and gauge boson pairs may be available simultaneously. The determination of their relative branching fractions would give a measurement for the value of v_Δ.