The addition of $SU(2)_L$ triplet fermions of zero hypercharge with the Standard Model (SM) helps to explain the origin of the neutrino mass by the so-called seesaw mechanism. Such a scenario is commonly know as the type-III seesaw model. After the electroweak symmetry breaking the mixings between the light and heavy mass eigenstates of the neutral leptons are developed which play important roles in the study of the charged and neutral multiplets of the triplet fermions at the colliders. In this article we study such interactions to produce these multiplets of the triplet fermion at the electron-positron and electron-proton colliders at different center of mass energies. We focus on the heavy triplets, for example, having mass in the TeV scale so that their decay products including the SM the gauge bosons or Higgs boson can be sufficiently boosted, leading to a fat jet. Hence we probe the mixing between light-heavy mass eigenstates of the neutrinos and compare the results with the bounds obtained by the electroweak precision study.
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