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Top-quark and neutrino composite Higgs bosons

In the context of top-quark condensation models, the top-quark alone is too light to saturate the correct value of the electroweak scale by its condensate. Within the seesaw scenario the neutrinos can have their Dirac masses large enough so that their condensates can provide significant contribution to the value of the electroweak scale. We address the question of a phenomenological feasibility of the top-quark and neutrino condensation conspiracy against the electroweak symmetry. Mandatory is to reproduce the masses of electroweak gauge bosons, the top-quark mass and the recently observed scalar mass of $125\,\mathrm{GeV}$ and to satisfy the upper limits on absolute value of active neutrino masses. To accomplish that we design a reasonably simplified effective model with two composite Higgs doublets. Additionally, we work with a general number $N$ of right-handed neutrino flavor triplets participating on the seesaw mechanism. There are no experimental constraints limiting this number. The upper limit is set by the model itself. Provided that the condensation scale is of order $10^{17-18}\,\mathrm{GeV}$ and the number of right-handed neutrinos is ${\cal O}(100-1000)$, the model predicts masses of additional Higgs bosons below $250\,\mathrm{GeV}$ and a suppression of the top-quark Yukawa coupling to the $125\,\mathrm{GeV}$ particle at the $\sim60\,%$ level of the Standard model value.