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 $v_{\Delta }<{10}^{-4}\mathrm{GeV}$, one can look for clean signals of lepton-number violation in the decays of doubly charged ($H^{\pm \pm }$) and singly charged ($H^{\pm }$) 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 $H^{+}\to {\tau }^{+}\overline{\nu }$ or $H^{+}\to e^{+}\overline{\nu }$ 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 $v_{\Delta }>2\times {10}^{-4}\mathrm{GeV}$, when the leptonic channels are suppressed, one needs to observe the decays $H^{+}\to W^{+}{H}_1$ and $H^{+}\to t\overline{b}$ 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, $v_{\Delta }\sim {10}^{-4}\mathrm{GeV}$, 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 $v_{\Delta }$.

• Received 28 May 2008

DOI:https://doi.org/10.1103/PhysRevD.78.015018