The Nambu Sum Rule in the Composite Two Higgs Doublet Model


The spectrum of spinless modes in a model with the \(SU{{(2)}_{L}} \times U{{(1)}_{R}}\) symmetrical four-quark-interaction proposed by Miransky, Tanabashi, and Yamawaki is studied. For the sake of simplicity, only four-fermion interactions of top and bottom quarks are considered. The spinless modes result from spontaneous electroweak interaction symmetry breaking and are coupled quark–antiquark states associated with two \(SU\left( 2 \right)\) Higgs doublets. Their dynamics is described by the effective Lagrangian obtained by the Schwinger–DeWitt method. The spectrum is represented by excitations of five types, the mass of each being expressed by the parameters of the model. It is shown that the model yields phenomenologically acceptable values of both the mass of quarks \({{m}_{t}} = 173\,\,{\text{GeV}}\) and \({{m}_{b}} = 4.18\,\,{\text{GeV}}\) and the mass of the standard Higgs state \({{m}_{{{{\chi }_{1}}}}} = 125\,\,{\text{GeV}}\). The masses of the particles that comprise the second Higgs doublet, \({{m}_{{{{h}^{ \pm }}}}} = 275\,\,{\text{GeV}}\), \({{m}_{{{{\chi }_{2}}}}} = 346\,\,{\text{GeV}}\), and \({{m}_{{{{\phi }_{0}}}}} = 125\,\,{\text{GeV}}\), have been calculated. The Nambu sum rule and the conditions for satisfying it in the theories with the broken \(~U{{(1)}_{A}}\) symmetry are discussed

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A.A. Osipov would like to thank C.T. Hill for his interest in this study and their correspondence, as well as expresses gratitude to the European Cooperation in Science and Technology for support provided within the COST Action CA16201 project.

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Translated by O. Lotova

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Osipov, A.A., Khalifa, M.M. The Nambu Sum Rule in the Composite Two Higgs Doublet Model. Phys. Part. Nuclei Lett. 17, 296–302 (2020).

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