Nambu sum rule in the NJL Models: from superfluidity to top quark condensation

Abstract

It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models [1]. This rule was originally considered by Nambu for superfluid 3 He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is ∼ 325 GeV. They together satisfy the Nambu sum rule M

Schwinger–Dyson equation and NJL approximation in massive gauge theory with fermions

“…(45) is satisfied near to the criticality. The important feature of the NJL model that was not considered here is the Nambu sum rule [44,46,45,47] that relates the values of masses of scalar excitations with the value of dynamical fermion mass. In our case this sum rule gives for the Higgs boson M H = 2m.…”

Top condensation model: a step towards the correct prediction of the Higgs mass

“…Consider the Yukawa part of the Lagrangian density (23) which can be made into a somewhat more explicit formula for the Yukawa couplings (see Appendix E for details)…”

“…The result m χ = 2m t is an analogue of the relation found in the Nambu-Jona-Lasinio (NJL) model [19,20] for the mass of the scalar fermion-antifermion bound state (so called σ -meson) m σ = 2m f , where m f is the mass of the fermion in the Nambu-Goldstone phase. The generalized form of this relation is known as the Nambu sum rule [21][22][23]. According to this hypothesis, collective bosonic modes arising in a system with four-Fermi interactions can be combined into pairs (the so-called Nambu partners) for each of which the equality m 2 1 + m 2 2 = 4m 2 f is fulfilled.…”

“…It follows from the Nambu sum rule that a phenomenologically acceptable result m χ m t / √ 2 can be obtained only in the extended version of the top-condensation model containing at least two doublets of Higgs fields. In the latter case the sum rule suggests the existence of a Nambu partner for the standard Higgs boson with a mass around 325 GeV [23]. It is generally believed (see e.g., [24,25]) that the conventional topcondensation models with two Higgs doublets [7,10,11] can-0123456789().…”

Modified top quark condensation model with the extra heavy fermion, the 125 GeV pseudo-Goldstone boson, and the additional heavy scalar bosons

“…See also[61][62][63], where some other composite models of the Higgs bosons were proposed basing on an analogy to the models of condensed matter physics.…”