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In Type III seesaw model the heavy neutrinos are contained in leptonictriplet representations. The Yukawa couplings of the triplet fermion and theleft-handed neutrinos with the doublet Higgs field produce the Dirac massterms. Together with the Majorana masses for the leptonic triplets, the lightneutrinos obtain non-zero seesaw masses. We point out that it is also possibleto have a quadruplet Higgs field to produce the Dirac mass terms to facilitatethe seesaw mechanism. The vacuum expectation value of the quadruplet Higgs isconstrained to be small by electroweak precision data. Therefore the Yukawacouplings of a quadruplet can be much larger than those for a doublet. We alsofind that unlike the usual Type III seesaw model where at least two copies ofleptonic triplets are needed, with both doublet and quadruplet Higgsrepresentations, just one leptonic triplet is possible to have aphenomenologically acceptable model because light neutrino masses can receivesizable contributions at both tree and one loop levels. Large Yukawa couplingsof the quadruplet can induce observable effects for lepton flavor violatingprocesses $\mu \to e \gamma$ and $\mu - e$ conversion. Implications of therecent $\mu \to e\gamma$ limit from MEG and also limit on $\mu - e $ conversionon Au are also given. Some interesting collider signatures for the doublycharged Higgs boson in the quadruplet are discussed.

A Higgs Quadruplet for Type III Seesaw and Implications for $\mu \to e\gamma$ and $\mu - e$ Conversion