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Low Scale Type I Seesaw Model for Lepton Masses and Mixings

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Low Scale Type I Seesaw Model for Lepton Masses and Mixings PHYSICAL REVIEW D 101, 035005 (2020) Low scale type I seesaw model for lepton masses and mixings † ‡ A. E. Cárcamo Hernández,* Marcela González , and Nicolás A. Neill Universidad T´ecnica Federico Santa María and Centro Científico-Tecnológico de Valparaíso, Casilla 110-V, Valparaíso, Chile (Received 5 June 2019; accepted 15 January 2020; published 6 February 2020) In contrast to the original type I seesaw mechanism that requires right-handed Majorana neutrinos at energies much higher than the electroweak scale, the so-called low scale seesaw models allow lighter masses for the additional neutrinos. Here we propose an alternative low scale type I seesaw model, where neither linear nor inverse seesaw mechanisms take place, but the spontaneous breaking of a discrete symmetry at an energy scale much lower than the model cutoff is responsible for the smallness of the light active neutrino masses. In this scenario, the model is defined with minimal particle content, where the right- handed Majorana neutrinos can have masses at the ∼50 GeV scale. The model is predictive in the neutrino sector having only four effective parameters that allow to successfully reproduce the experimental values of the six low energy neutrino observables. DOI: 10.1103/PhysRevD.101.035005 I. INTRODUCTION three distinct one-dimensional irreducible representations where the three families of fermions can be accommodated After minimally extending the Standard Model (SM) to rather naturally. This group has been particularly promising include massive neutrinos, the observed fermion mass in providing a predictive description of the current pattern of hierarchy is extended over a range of 13 orders of magni- SM fermion masses and mixing angles [8–47]. Despite tude, from the lightest active neutrino mass scale up to the several models based on the A4 discrete symmetry have been top quark mass. In addition, the small quark mixing angles proposed, most of them have a nonminimal scalar sector, decrease from one generation to the next while in the lepton composed of several SUð2Þ Higgs doublets, even in their sector this hierarchy is not present since two of the mixing low energy limit, and have A4 scalar triplets in the scalar angles are large and the other one is small. Neither of these spectrum whose vacuum expectation value (VEV) configu- features in the flavor sector is explained in the SM. This is rations in the A4 direction are not the most natural solutions the so-called SM flavor puzzle, which has motivated the of the scalar potential minimization equations. Thus, it construction of theories with extended scalar and/or fermion would be desirable to build an A4 flavor model which at low sectors with additional continuous or discrete groups. energies reduces to the SM model and where the different In particular, extensions of the SM with non-Abelian gauge singlet scalars are accommodated into A4 singlets and discrete flavor symmetries are very attractive since they one A4 triplet [with VEV pattern in the (1,1,1) A4 direction] successfully describe the observed pattern of fermion which satisfies the minimization condition of the scalar masses and mixings (for recent reviews on discrete flavor potential for the whole range of values of the parameter groups see Refs. [1–6]), while they can naturally appear space. To this end, in this work we propose an extension of from the breaking of continuous non-Abelian gauge sym- the SM based on the A4 family symmetry, which is metries or from compactified extra dimensions (see Ref. [7] supplemented by a Z4 auxiliary symmetry, whose sponta- and references therein). Several discrete groups have been neous breaking at an energy scale (vS) much lower than the employed in extensions of the SM. In particular, A4 is the model cutoff (Λ) produces the small light active neutrino smallest discrete group with one three-dimensional and mass scale mν. As we will show in the next sections, in this scenario the masses for the active neutrinos are produced by a type I seesaw mechanism [48–51] mediated by *[email protected] † ∼50 [email protected] three GeV right-handed Majorana neutrinos, where ‡ 2 [email protected] mν ∝ ðvS=ΛÞ . Given the low mass scale of the right-handed neutrinos, this model can be classified as a low scale type I Published by the American Physical Society under the terms of seesaw, as it has been coined in the literature [52–62]. There the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to are different realizations of low scale seesaw models, as for the author(s) and the published article’s title, journal citation, example inverse or linear [35,46,63–78], where an addi- and DOI. Funded by SCOAP3. tional lepton number violating mass parameter is added. 2470-0010=2020=101(3)=035005(8) 035005-1 Published by the American Physical Society HERNÁNDEZ, GONZÁLEZ, and NEILL PHYS. REV. D 101, 035005 (2020) In these models, the smallness of mν is related to the SM group. The lepton assignments under the group smallness of the additional parameter. In our case, however, A4 × Z4 are no extra small mass parameter has been included, and the smallness of the light neutrino masses is explained through LL ∼ ð3; 0Þ;NR ∼ ð3; 1Þ; the spontaneous breaking of the auxiliary discrete groups, 0 00 l1R ∼ ð1 ; 1Þ;l2R ∼ ð1; 1Þ;l3R ∼ ð1 ; 1Þ: ð2Þ which leads to a suppression in the Dirac neutrino mass matrix. A From the point of view of the low energy neutrino Here we specify the dimensions of the 4 irreducible observables, the model makes very particular predictions representations by the numbers in boldface and we write the different Z4 charges in additive notation. Regarding the for δCP and θ23, which are not aligned with the central lepton sector, note that the left- and right-handed leptonic values of current fits. Therefore, future improvements in the A A precision of neutrino measurements will provide an exper- fields are accommodated into 4 triplet and 4 singlet imental test of the model. Processes like (i) charged lepton irreducible representations, respectively, whereas the right- A flavor violating decays (l → l0γ) [11,12], (ii) flavor chang- handed Majorana neutrinos are unified into an 4 triplet. ing neutral currents, and (iii) rare top quark decays such as The scalar spectrum of the model includes the SM Higgs ϕ ρ ξ j ¼ 1 t → hc, t → cZ [15], are strongly suppressed, in contrast to doublet and the gauge singlet scalars , j ( , 2, 3). other A4 flavor models (that usually have several Higgs The scalar fields have the following transformation proper- A Z doublets), where these processes can have rates that are at ties under the flavor symmetry 4 × 4: the reach of forthcoming experiments. 00 0 The paper is organized as follows. In Sec. II we describe ϕ ∼ ð1; 0Þ; ρ1 ∼ ð1 ; −1Þ; ρ2 ∼ ð1 ; −1Þ; the model. In Sec. III we present a discussion on lepton ρ3 ∼ ð1; −2Þ; ξ ∼ ð3; −1Þ: ð3Þ masses and mixings and give the corresponding results. We draw our conclusions in Sec. IV. The Appendix provides a We assume the following vacuum configuration for the concise description of the A4 discrete group. A4-triplet gauge singlet scalar ξ: II. MODEL DESCRIPTION vξ hξi¼pffiffiffi ð1; 1; 1Þ; ð4Þ 3 We propose an extension of the SM where the scalar sector is augmented by the inclusion of four gauge-singlet which satisfies the minimization condition of the scalar scalar fields and the SM gauge symmetry is supplemented potential for the whole range of values of the parameter by the A4 × Z4 discrete group. The symmetry G features the space, as shown in Ref. [31]. With the particle content following spontaneous symmetry breaking pattern: previously specified, we have the following relevant vS Yukawa terms for the lepton sector, invariant under the G ¼ SUð2Þ Uð1Þ A Z →; L × Y × 4 × 4 symmetries of the model: v SUð2ÞL × Uð1ÞY → Uð1ÞQ; ð1Þ ðLÞ ðLÞ ¯ 1 ðLÞ ¯ 1 LY ¼ y1 ðLLϕξÞ100 l1R þ y2 ðLLϕξÞ1l2R where the symmetry-breaking scales satisfy the hierarchy Λ Λ 1 vS ∼ Oð1Þ TeV >v, vS is the scale of spontaneous break- ðLÞ ¯ ¯ C Ã þ y3 ðLLϕξÞ10 l3R þ yNðNRNRÞ1ðρ3 þ cρ3Þ ing of the A4 × Z4 discrete group, and v ¼ 246 GeV is the Λ electroweak symmetry breaking scale. As mentioned ¯ ˜ ρ1 ¯ ˜ ρ2 þ y1νðLLϕNRÞ10 þ y2νðLLϕNRÞ100 before, the scalar sector of the SM is augmented by the Λ Λ ξ ξ inclusion of four SM gauge singlet scalars. We add these þ y ðL¯ ϕ˜ N Þ þ y ðL¯ ϕ˜ N Þ þ : :; ð Þ extra scalar fields for the following reasons: (i) to build 3ν L R 3s Λ 4ν L R 3a Λ H c 5 nonrenormalizable charged leptons and Dirac neutrino Yukawa terms invariant under the local and discrete groups, where the dimensionless couplings in Eq. (5) are Oð1Þ crucial to generate predictive textures for the lepton sector; parameters. (ii) to generate a renormalizable Yukawa term for the right- In what follows, we describe the role of each discrete handed Majorana neutrinos, that can give rise to ∼50 GeV group factor of our A4 flavor model. The A4 discrete group masses for these singlet fermions. As we will see below, the yields a reduction of the number of model parameters, observed pattern of SM charged lepton masses and leptonic giving rise to predictive textures for the lepton sector, which mixing angles will arise from the spontaneous breaking of are consistent with the lepton mass and mixing pattern, as the A4 × Z4 discrete group. In order to generate the masses will be shown in Sec.
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