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 ${}^3$He-B, ${}^3$He-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 \cite{Miransky}. In all considered cases the sum rule appears that 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 $\sum M_{boson}^2=4M_f^2$. Previously this relation was established by Nambu in \cite{Nambu} 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. 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.

Latex, 15 pages

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• On Nambu's Fermion-Boson Relations for Superfluid ${}^3$He-B
• The Higgs mode in a superfluid of Dirac fermions
• ${}^3$He Universe 2020
• Spontaneous helical order of a chiral p-wave superfluid confined in nano-scale channels
• Scalar excitation with Leggett frequency in ${}^3$ He-B and the $125$ GeV Higgs particle in top quark condensation models as Pseudo - Goldstone bosons
• Gauge theory of Lorentz group as a source of the dynamical electroweak symmetry breaking
• Strong dynamics behind the formation of the $125$ GeV Higgs boson
• Grand Challenges in Quantum Fluids and Solids
• Dynamical torsion as the microscopic origin of the neutrino seesaw
• Polarons as stable solitary wave solutions to the Dirac-Coulomb system
• Schwinger - Dyson equation and NJL approximation in massive gauge theory with fermions
• Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
• Bosonic Surface States and Acoustic Spectroscopy of Confined Superfluid ${}^3$He-B
• Modified model of top quark condensation
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• Top condensation model: a step towards the correct prediction of the Higgs mass
• Nambu identity and collective modes in superconductors and superfluid ${}^3$He
• Fermi points and the Nambu sum rule in the polar phase of ${}^3$He