The Nambu sum rule and the relation between the masses of composite Higgs bosons
Abstract
We review the known results on the bosonic spectrum in various NJL models both in the condensed matter physics and in relativistic quantum field theory including 3He-B, 3He-A, the thin films of superfluid He-3, and QCD (Hadronic phase and the Color Flavor Locking phase). Next, we calculate bosonic spectrum in the relativistic model of top quark condensation suggested in Miransky. In all considered cases the sum rule appears that relates the masses (energy gaps) Mboson of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion Mf as Σ Mboson2 = 4 Mf2. Previously this relation was established by Nambu in Nambu for 3He-B and for the s - wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. We discuss the possibility to apply this sum rule to various models of top quark condensation. In some cases this rule allows to calculate the masses of extra Higgs bosons that are the Nambu partners of the 125 GeV Higgs.
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