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(Delta) < 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+ -> tau(+)(nu) over bar or H+ -> e(+)(nu) over bar 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 Phi(2) in the NH, but sensitively depend on Phi(1) in the IH. In a less favorable scenario v(Delta) > 2 x 10(-4) GeV, when the leptonic channels are suppressed, one needs to observe the decays H+ -> W+H1 and H+ -> t (b) over bar 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(Delta) similar to 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(Delta).