G. E. Volovik, M. A. Zubkov
In [1] the relation between the masses (energy gaps) of bosonic excitations and the constituent fermion mass (the fermion energy gap) was considered for $^3$He-B and for the s - wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. In particular, we consider $^3$He-A, the thin films of superfluid He-3, and a toy relativistic model of top quark condensation that generalizes the original model of [2]. In all considered cases the Nambu sum rule relates the masses (energy gaps) $M_{boson}$ of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion $M_f$ as $\sum M_{boson}^2 = 4 m_f^2$. There is the possibility that the dynamical electroweak symmetry breaking is provided by the model of this kind. Then there may exist several composite Higgs bosons with masses related to each other and to the mass of the heaviest fermion (presumably, of the top quark) by the Nambu sum rule.
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http://arxiv.org/abs/1209.0204
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