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Split Higgs triplet

We find if a Higgs triplet with hypercharge has a special dimension-6 operator with the standard model Higgs doublet, i.e. a square of the trilinear triplet-doublet coupling, its scalar(pseudo-scalar) component can obtain a small quadratic term while its pseudo-scalar(scalar) and charged-scalar components can hold their masses heavy enough. Such split Higgs triplet can spontaneously develop a small vacuum expectation value to realize a Majorana neutrino mass generation without causing any high-dimensional lepton number violations including the well-known Weinberg dimension-5 operator. Alternatively it can mediate a non-standard neutrino self-interaction motivated by resolving the tension in Hubble constant measurements. This effective theory with rich observable phenomena can be induced by the Georgi-Machacek Higgs triplets at tree level or some dark matter fields at one-loop order.