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A Higgs Quadruplet for Type III Seesaw and Implications for $μ\to eγ$ and $μ- e$ Conversion

In Type III seesaw model the heavy neutrinos are contained in leptonic triplet representations. The Yukawa couplings of the triplet fermion and the left-handed neutrinos with the doublet Higgs field produce the Dirac mass terms. Together with the Majorana masses for the leptonic triplets, the light neutrinos obtain non-zero seesaw masses. We point out that it is also possible to have a quadruplet Higgs field to produce the Dirac mass terms to facilitate the seesaw mechanism. The vacuum expectation value of the quadruplet Higgs is constrained to be small by electroweak precision data. Therefore the Yukawa couplings of a quadruplet can be much larger than those for a doublet. We also find that unlike the usual Type III seesaw model where at least two copies of leptonic triplets are needed, with both doublet and quadruplet Higgs representations, just one leptonic triplet is possible to have a phenomenologically acceptable model because light neutrino masses can receive sizable contributions at both tree and one loop levels. Large Yukawa couplings of the quadruplet can induce observable effects for lepton flavor violating processes $μ\to e γ$ and $μ- e$ conversion. Implications of the recent $μ\to eγ$ limit from MEG and also limit on $μ- e $ conversion on Au are also given. Some interesting collider signatures for the doubly charged Higgs boson in the quadruplet are discussed.