The Nambu Sum Rule in the Composite Two Higgs Doublet Model

A realization of the composite Higgs scenario in the context of the effective model with the $$SU(2)_L\times U(1)_R$$ S U ( 2 ) L × U ( 1 ) R symmetric four-Fermi interactions proposed by Miransky, Tanabashi and Yamawaki is studied. The model implements Nambu’s mechanism of dynamical electroweak symmetry breaking leading to the formation of $${{\bar{t}}}t$$ t ¯ t and $${{\bar{b}}}b$$ b ¯ b quark condensates. We explore the vacuum structure and spectrum of the model by using the Schwinger proper-time method. As a direct consequence of this mechanism, the Higgs acquires a mass in accord with its experimental value. The present prediction essentially differs from the known overestimated value, $$m_\chi = 2m_t$$ m χ = 2 m t , making more favourable the top condensation scenario presented here. The mass formulas for the members of the second Higgs doublet are also obtained. The Nambu sum rule is discussed. It is shown that the anomalous $$U(1)_A$$ U ( 1 ) A symmetry breaking modifies this rule at next to leading order in $$1/N_c$$ 1 / N c .

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“…(26) (see also Eq. (D.41) and [35]). As one can see, the mass matrix eigenstates are χ α and φ α with the following squared values…”

Section: Higgs Sector and The Gap Equationmentioning

confidence: 92%

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

Osipov¹,

Hiller

Blin

et al. 2020

Eur. Phys. J. C

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Masses of two Higgs doublets within effective theory with four-quark interactions

Osipov

Khalifa

2020

J. Phys.: Conf. Ser.

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The composite Higgs scenario in the context of the effective model with SU(2) L × U(1) R symmetric four-fermion interaction proposed by Miransky, Tanabashi and Yamawaki (MTY) is considered. The low-energy dynamics of the model is described by the effective Lagrangian obtained by the Schwinger-DeWitt technique. The questions of the Nambu sum rule and the spectrum of Higgs states are addressed in detail.

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Top–Bottom Condensation Model: Symmetries and Spectrum of the Induced 2HDM

Osipov¹,

Hiller²,

Blin³

et al. 2021

Symmetry

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Here, we use the Schwinger–DeWitt approach to address the four-fermion composite Higgs effective model proposed by Miransky, Tanabashi and Yamawaki (MTY). The surprising benefit of such an approach is that it is possible to ascribe to a SM-type Higgs a quark–antiquark structure of predominantly a b¯b nature with a small t¯t admixture, which in turn yields a Higgs mass compatible with the observed value of 125 GeV. We discuss this result in a detailed and pedagogical way, as it goes against the common belief that this model and akin composite descriptions should predict a Higgs mass-of-order of twice the top quark mass, contrary to empirical evidence. A further aspect of this approach is that it highlights the link of the SU(2)L×U(1)R symmetric four-fermion MTY model interactions of the heavy quark family to a specific two-Higgs-doublet model (2HDM), and the necessity to go beyond the one Higgs doublet to obtain the empirical Higgs mass within composite models. By appropriately fixing the symmetry-defining interaction parameters, we show that the resulting CP-preserving spectrum harbors the following collective states at the electroweak scale ΛEW=246 GeV: a light scalar to which the standard Higgs is associated; a heavier neutral state preconized as the Nambu partner of the standard Higgs within the Nambu sum rule; the expected triplet of Goldstone bosons associated with the longitudinal polarizations of the electroweak massive bosons; and a neutral pseudoscalar state that in the limit of a global U(1)A symmetry would be a Goldstone mode. The anomalous breaking of this axial symmetry is a subleading effect in a large Nc counting scheme, and we discuss how it modifies the leading-order Nambu sum rule result and its relevance for the qualitative description of the spectrum.

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The Nambu Sum Rule in the Composite Two Higgs Doublet Model

Cited by 3 publications

References 24 publications

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

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

Masses of two Higgs doublets within effective theory with four-quark interactions

Top–Bottom Condensation Model: Symmetries and Spectrum of the Induced 2HDM

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