The Nambu sum rule and the relation between the masses of composite Higgs bosons

TL;DR

This paper reviews the Nambu sum rule relating bosonic excitation masses to fermion masses across various models, and explores its application to predicting Higgs boson masses in top quark condensation scenarios.

Contribution

It generalizes the Nambu sum rule to a broader class of models and discusses its potential for predicting Higgs boson masses in top quark condensation models.

Findings

The sum rule relates bosonic masses to fermion masses as  M_{boson}^2 = 4 M_f^2.

The relation holds across condensed matter and relativistic quantum field models.

It can be used to estimate masses of additional Higgs bosons in top quark condensation models.

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 $\sum M_{boson}^2 = 4 M_f^2$. 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.