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Some Phenomenological Aspects of the 3-3-1 Model with the Cаrcamo-Kovalenko-Schmidt Mechanism

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Some Phenomenological Aspects of the 3-3-1 Model with the Cаrcamo-Kovalenko-Schmidt Mechanism PHYSICAL REVIEW D 100, 015004 (2019) Some phenomenological aspects of the 3-3-1 model with the Cárcamo-Kovalenko-Schmidt mechanism † ‡ ∥ H. N. Long,1,2,* N. V. Hop,3, L. T. Hue,4,5, N. H. Thao,6,§ and A. E. Cárcamo Hernández7, 1Theoretical Particle Physics and Cosmology Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam 2Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam 3Department of Physics, Can Tho University, 3/2 Street, Can Tho 900000, Vietnam 4Institute for Research and Development, Duy Tan University, Da Nang City 550000, Vietnam 5Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 100000, Vietnam 6Department of Physics, Hanoi Pedagogical University 2, Phuc Yen, Vinh Phuc 280000, Vietnam 7Universidad T´ecnica Federico Santa María and Centro Científico-Tecnológico de Valparaíso, Casilla 110-V, Valparaíso, Chile (Received 18 April 2019; published 8 July 2019) We perform a comprehensive analysis of several phenomenological aspects of the renormalizable extension of the inert 3-3-1 model with sequentially loop-generated Standard Model fermion mass hierarchy. Special attention is paid to the study of the constraints arising from the experimental data on the ρ parameter, as well as those ones resulting from the charged lepton flavor violating process μ → eγ and dark matter. We also study the single Z0 production via Drell-Yan mechanism at the LHC. We have found that Z0 gauge bosons heavier than about 4 TeV comply with the experimental constraints on the oblique ρ parameter as well as with the collider constraints. In addition, we have found that the constraint on the charged lepton flavor violating decay μ → eγ sets the sterile neutrino masses to be lighter than about 1.12 TeV. In addition the model allows charged lepton flavor violating processes within reach of the forthcoming experiments. The scalar potential and the gauge sector of the model are analyzed and discussed in detail. Our model successfully accommodates the observed dark matter relic density. DOI: 10.1103/PhysRevD.100.015004 I. INTRODUCTION the Froggatt-Nielsen (FN) mechanism [1]. According to the FM mechanism, the mass differences between generations Despite its great successes, the Standard Model (SM) of fermions arise from suppression factors depending on does not explain the observed mass and mixing hierarchies the FN charges of the particles. It has been noticed that in in the fermion sector, which remain without a compelling order to implement the aforementioned mechanism, the explanation. It is known that in the SM, the masses of the effective Yukawa interactions have to be introduced, thus matter fields are generated from the Yukawa interactions. In – – making this theory nonrenormalizable. From this point of addition, the Cabibbo Kobayashi Maskawa quark mixing view, the recent mechanism proposed by Cárcamo, matrix is also constructed from the same Yukawa cou- Kovalenko, and Schmidt [2] (called by CKS mechanism) plings. To solve these puzzles, some mechanisms have been based on sequential loop suppression mechanism, is more proposed. To the best of our knowledge, the first attempt to natural since its suppression factor arises from the loop explain the huge differences in the SM fermion masses is factor l ≈ ð1=4πÞ2. One of the main purposes of the models based on the gauge group SUð3Þ × SUð3Þ × Uð1Þ (for short, 3-3-1 *[email protected] C L X † model) [3–10] is concerned with the search of an explan- [email protected] ‡ [email protected] ation for the number of generations of fermions. Combined §[email protected] with the QCD asymptotic freedom, the 3-3-1 models ∥ [email protected] provide an explanation for the number of fermion gen- 1 erations. These models have nonuniversal Uð ÞX gauge Published by the American Physical Society under the terms of assignments for the left handed quarks fields, thus implying the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to that the cancellation of chiral anomalies is fulfilled when 3 the author(s) and the published article’s title, journal citation, the number of SUð ÞL fermionic triplets is equal to the 3 3 and DOI. Funded by SCOAP . number of SUð ÞL fermionic antitriplets, which happens 2470-0010=2019=100(1)=015004(21) 015004-1 Published by the American Physical Society LONG, HOP, HUE, THAO, and CÁRCAMO HERNÁNDEZ PHYS. REV. D 100, 015004 (2019) when the number of fermion families is a multiple of three. Section III is devoted to gauge boson mass and mixing. Some other advantages of the 3-3-1 models are: (i) they Taking into account of data on the ρ parameter, and if solve the electric charge quantization [11,12], (ii) they only contributions of the gauge bosons are mentioned, we contain several sources of CP violation [13,14], and will show that the mass of the heavy neutral boson Z0 (iii) they have a natural Peccei-Quinn symmetry, which will be constrained nearly to the excluded regions derived solves the strong-CP problem [15–18]. from other experimental data such as LHC searches, In the framework of the 3-3-1 models, most of the and K, D, and B meson mixing. The Higgs sector is research is focused on radiative seesaw mechanisms, and considered in Sec. IV. The Higgs sector consists of two but some involving nonrenormalizable interactions intro- parts: the first part contains lepton number conserving duced to explain the SM fermion mass and mixing pattern terms and the second one is lepton number violating. We (see references in Ref. [19]). study in details the first part and show that the Higgs The FN mechanism was implemented in the 3-3-1 sector has all necessary ingredients. The ρ parameter will models in Ref. [20]. It is interesting to note that the FN be investigated including Higgs contributions. In Sec. V, mechanism does not produce a new scale since the scale of lepton flavor violating decays of the charged leptons are the flavor breaking is the same as the symmetry breaking discussed, where sterile neutral lepton masses are con- scale of the model. strained. Section VI is devoted to the production of the 0 The CKS mechanism has been implemented for the first heavy Z and the heavy neutral scalar H4. In Sec. VII,we time in thepffiffiffi 3-3-1 model without exotic electric charges deal with the DM relic density. We make conclusions in (β ¼ −1= 3) in Ref. [19]. The implementation of the CKS Sec. VIII. The scalar potential of the model is given in mechanism in the 3-3-1 model leads to viable renormaliz- Appendix. able 3-3-1 model that provides a dynamical explanation for the observed SM fermion mass spectrum and mixing parameters consistent with the SM low energy fermion II. REVIEW OF THE MODEL flavor data [19]. It is worth mentioning that the extension of To implement the CKS mechanism, only the heaviest the inert 331 model of Ref. [19] contains a residual discrete particles such as the exotic fermions and the top quark get ðLgÞ — Z2 lepton number symmetry arising from the sponta- masses at tree level. The next medium ones: bottom, neous breaking of the global U 1 symmetry. Under this charm quarks, tau, and muon get masses at one-loop level. ð ÞLg residual symmetry, the leptons are charged and the other Finally, the lightest particles: up, down, strange quarks and particles are neutral [19]. the electron acquire masses at two-loop level. To forbid the However, in the mentioned work, the authors have just usual Yukawa interactions, the discrete symmetries should focused on the data concerning fermions (both quarks and be implemented. Hence, the full symmetry of the model leptons including neutrino mass and mixing), but some under consideration is questions are open for the future study. SUð3Þ × SUð3Þ × Uð1Þ × Z4 × Z2 × Uð1Þ ; ð1Þ The purpose of this work is to study several phenom- C L X Lg enological aspects of the renormalizable extension of the inert 3-3-1 model with sequentially loop-generated SM where Lg is the generalized lepton number defined in fermion mass hierarchy. In particular, the constraints Refs. [19,21]. It is interesting to note that, in this model, arising from the experimental data on the ρ parameter, as the light active neutrinos get their masses from a combi- well as those ones resulting from the charged lepton flavor nation of linear and inverse seesaw mechanisms at two- violating process μ → eγ and dark matter. Furthermore our loop level. work discusses the Z0 production at proton-proton collider As in the ordinary 3-3-1 model without exotic electric 3 via quark-antiquark annihilation. To determine the oblique charges, the quark sector contains the following SUð ÞC × ρ 3 1 SUð3Þ × Uð1Þ representations [19] parameter constraints on the SUð ÞL × Uð ÞX symmetry L X breaking scale vχ, which will be used to constrain the heavy T à 0 Q ¼ðD ; −U ;J Þ ∼ ð3; 3 ; 0Þ; Z gauge boson mass, we proceed to study in detail the nL n n n L gauge and Higgs sectors of the model. In addition we 1 T ∼ 3 3 1 2 determine the constraints imposed by the charged lepton Q3L ¼ðU3;D3;TÞL ; ; 3 ;n¼ ; ; μ → γ flavor violating process e and dark matter on the 1 2 model parameter space. In what regards the scalar potential ∼ 3 1 − ∼ 3 1 1 2 3 DiR ; ; 3 ;UiR ; ; 3 ;i¼ ; ; ; of the model, due to the implemented symmetries, the Higgs sector is rather simple and can be completely solved.
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