A 3-3-1 model with low scale seesaw mechanisms

We construct a viable 3-3-1 model with two $SU(3)_L$ scalar triplets, extended fermion and scalar spectrum, based on the $T^{\prime}$ family symmetry and other auxiliary cyclic symmetries, whose spontaneous breaking yields the observed pattern of SM fermion mass spectrum and fermionic mixing parameters. In our model the SM quarks lighter than the top quark, get their masses from a low scale Universal seesaw mechanism, the SM charged lepton masses are produced by a Froggatt-Nielsen mechanism and the small light active neutrino masses are generated from an inverse seesaw mechanism. The model is consistent with the low energy SM fermion flavor data and successfully accommodates the current Higgs diphoton decay rate and predicts charged lepton flavor violating decays within the reach of the forthcoming experiments.


INTRODUCTION
The existence of three fermion families and the observed pattern of Standard Model (SM) fermion masses and mixing angles are not explained within the context of the SM. Whereas in the quark sector, the mixing angles are small, in the lepton sector two of the mixing angles are large and one is small, of the order of the Cabbibo angle. The pattern of SM charged fermion masses is extended over a range of 5 orders of magnitude in the quark sector and a dramatically broader range of about 13 orders of magnitude, when the light active neutrino sector is included. That flavour puzzle of the SM motivates the study of theories with an extended particle spectrum and enlarged symmetries, whose spontaneous breaking produces the observed SM fermion mass and mixing hierarchy. In addition, the SM predicts very tiny branching ratios for the charged lepton flavor violating processes (cLFV) µ → eγ, τ → µγ and τ → eγ, several orders of magnitude below their corresponding projective experimental sensitivity. On the other low scale seesaw models [1][2][3][4][5][6] predict branching ratios for the cLFV processes within the reach of the projective experimental sensitivity. Thus, a future observation of charged lepton flavor violating processes will provide an undubitable evidence of Physics Beyond the Standard Model and will shed light on the dynamics that produces tiny light active neutrino masses and the measured leptonic mixing angles. Furthermore, the origin of the family structure of fermions, which is not addressed by the SM, can be explained in theories having an extended SU (3) C × SU (3) L × U (1) X gauge symmetry, called 3-3-1 models . In these models, the cancellation of chiral anomalies takes place when the number of SU (3) L fermionic triplets is equal to the number of SU (3) L fermionic antitriplets, which happens when the number of fermion generations is a multiple of three. Furthermore, when combined with the QCD asymptotic freedom, the 3-3-1 models predict that the number of fermion generations is exactly three. In addition, the nonuniversal U (1) X charge assignments for the left handed quarks fields in the 3-3-1 models, are crucial for explaining the large mass splitting between the heaviest quark and the two lighter ones. Other phenomenological advantages of the 3-3-1 models are: 1) they address the electric charge quantization [52,53], 2) they contain several sources of CP violation [54,55], 3) they have a natural Peccei-Quinn symmetry, thus allowing to address the strong-CP problem [56][57][58][59], 4) the 3-3-1 models with heavy sterile neutrinos in the fermionic spectrum have cold dark matter candidates as weakly interacting massive particles (WIMPs) [60][61][62][63], 5) they predict the bound sin θ 2 W < 1 4 , for the weak mixing parameter, 6) the 3-3-1 models with three right handed Majorana neutrinos and non SM fermions without non SM electric charges, allow the implementation of a low scale seesaw mechanism, which could be inverse or linear, thus allowing to explain the smallness of the light active neutrinos masses and to predict charged lepton flavor violating process within the reach of the forthcoming experiments. In this work, motivated by the aforementioned considerations, we propose a 3-3-1 model with two SU (3) L scalar triplets, extended fermion and scalar spectrum, consistent with SM fermion masses and mixings. Our model incorpo-rates a Universal low scale seesaw mechanism to generate the masses for the SM quarks lighter than the top quark, a Froggatt-Nielsen mechanism that produces the SM charged lepton masses and an inverse seesaw mechanism that gives rise to small light active neutrino masses. In our model we use the T symmetry, which in combination with other auxiliary symmetries, allows a viable description of the current SM fermion mass spectrum and mixing parameters. We use the double tetrahedral group T since it is the smallest discrete subgroup of SU (2) as well as the smallest group of any kind with 1-, 2-and 3-dimensional representations and the multiplication rule 2 ⊗ 2 = 3 ⊕ 1, thus allowing to reproduce the successful U (2) textures [64]. Note that the discrete group T [49,[64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81], together with the groups A 4 [37,45,, S 4 [16,[117][118][119][120][121][122][123][124][125][126][127][128][129][130] and ∆ (27) [48,, is the smallest group containing an irreducible triplet representation that can accommodate the three fermion families of the Standard model (SM). These groups have attracted a lot of attention of the model building community since they successfully describe the observed SM fermion mass spectrum and mixing parameters. The content of this paper goes as follows. In section 2 A we outline the proposed model, describing its fermionic and scalar spectrum as well as their assignments under the different continuous and discrete groups. The gauge sector of the model is discussed in section 2 B, whereas the scalar potential for two SU (3) L triplets is discussed in section 2 C. The implications of our model in SM quark masses and mixings are discussed in Sec. 3. In Section 4, we present our results in terms of lepton masses and mixing, which is followed by a numerical analysis. The implications of our model in the Higgs diphoton decay rate are discussed in section 5. In section 6, lepton flavor violating decays of the charged leptons are discussed, where sterile neutral lepton masses are constrained. Conclusions are given in section 7. Some technical details are shown in the appendices: Appendix A provides a description of the T discrete group. Appendix B includes a discussion of the scalar potential for a T scalar triplet and its minimization condition.

A. Particle content
We consider a model based on the extended gauge symmetry SU (3) C × SU (3) L × U (1) X (3-3-1 model) which is supplemented by the U (1) Lg global lepton number symmetry and the T × Z 6 × Z 8 × Z 12 discrete group. Our model is an extension of the 3-3-1 model with two SU (3) L scalar triplets, where the scalar sector is augmented by the inclusion of several gauge singlet scalars and the fermion spectrum is enlarged by adding several vector like fermions and right handed Majorana neutrinos. The SU (3) L singlet vector like fermions are introduced in our model in order to implement a Universal Seesaw mechanism [157][158][159] for the generation of the masses of SM quarks lighter than the top quark. We additionally introduce three gauge singlet right handed Majorana neutrinos which are crucial to incorporate the inverse seesaw mechanism in our model. In our model the non SM fermions do not have non SM electric charges, thus implying that the third component of the SU (3) L leptonic triplet is electrically neutral, thus allowing the implementation of an inverse seesaw mechanism [4,[160][161][162][163][164] to generate the small light active neutrino masses. The SM charged lepton masses are produced from a Froggatt-Nielsen mechanism [165], which is triggered by non renormalizable Yukawa interactions involving the SU (3) L scalar triplets η and χ as well as several gauge singlet scalars charged under the different discrete group factors of the model. In our model the hierarchy of SM charged fermion masses and fermionic mixing parameters is produced by the spontaneous breaking of the  Tables I and II, respectively. Notice that in these tables the dimensions of the SU (3) C , SU (3) L and T representations are specified by the numbers in boldface and the different Z N charges are written in additive notation. Let us note that a field ψ transforms under the Z N symmetry with a corresponding q n charge as: ψ → e 2πiqn N ψ, n = 0, 1, 2, 3 · · · N − 1. An explanation of the role of the different discrete group factors of the model is provided in the following. The double tetrahedral group T selects the allowed entries of the mass matrices for SM charged fermions and neutrinos, thus allowing a reduction of the model parameters. In addition, as it will be shown below in Sections 3 and 4, the spontaneous breaking of the T discrete group will be crucial to generate the observed CP violation in both quark and lepton sectors, without the need of invoking complex Yukawa couplings. Let us note that T is the smallest discrete subgroup of SU (2) as well as the smallest group of any kind with 1-, 2-and 3-dimensional representations and the multiplication rule 2⊗2 = 3⊕1, thus allowing to reproduce the successful U (2) textures as pointed out in Ref. [64]. The Z 6 discrete group separates the T scalar triplets (ρ, φ and ζ) participating in the charged lepton Yukawa interactions from the one (ξ) appearing in the neutrino Yukawa terms, thus allowing to treat the charged lepton and neutrino sectors independently. The Z 8 discrete group contributes to generating small lepton number violating Majorana mass terms that yields small µ parameter of the inverse seesaw mechanism that produces the tiny light active neutrino masses. Furthermore, Z 8 discrete group helps in shaping the texture for the SM charged leptons, that allows a reduction of the model parameters. The Z 12 discrete group is crucial for: 1) explaining the SM charged lepton mass hierarchy, 2) shaping the hierarchical structure of the quark mass matrices necessary to get a realistic pattern of quark masses and mixing and 3) generating small lepton number violating Majorana mass terms thus allowing to provide a natural explanation for the tiny value of the light active neutrino masses. The full symmetry G of our model features the following two-step spontaneous breaking: where the symmetry breaking scales fulfill the hierarchy Λ int ∼ v χ v η . It is worth mentioning that the first step of symmetry breaking in Eq. (2.1) is triggered by the SU (3) L scalar triplet χ, whose third component acquires a 10 TeV scale vacuum expectation value (VEV) that breaks the SU (3) L × U (1) X gauge symmetry as well as by the SU (3) L scalar singlets whose VEVs break the T × Z 6 × Z 8 × Z 12 discrete group. The non SM particles get masses at the v χ scale after the spontaneous breaking of the SU (3) L × U (1) X gauge symmetry. We consider v χ ∼ O(10) TeV, because the experimental data on K, D and B meson mixings set a lower bound of about 4 TeV [166] for the Z gauge boson mass in 3-3-1 models, which translates in a lower limit of about 10 TeV for the SU (3) L × U (1) X gauge symmetry breaking scale v χ . In addition, v χ ∼ O(10) TeV is also consistent with the collider constraints as well as with the constraints that the decays B s,d → µ + µ − and B d → K * (K)µ + µ − impose on the Z masses. It is worth mentioning that the LHC searches constrain the Z gauge boson mass in 3-3-1 models to be larger than about 2.5 TeV [167], which corresponds to a lower limit of 6.3 TeV for the SU (3) C × SU (3) L × U (1) X symmetry breaking scale v χ . On the other hand, the decays B s,d → µ + µ − and B d → K * (K)µ + µ − set lower limits on the Z gauge boson mass ranging from 1 TeV up to 3 TeV [15,[168][169][170][171]. Consequently, the scale v χ ∼ O(10) TeV is consistent with the aforementioned constraints. Furthermore, we assume that the discrete symmetries of the model are broken at the same scale of breaking of the SU (3) L × U (1) X gauge symmetry. Moreover, let us note that the second step of symmetry breaking in Eq. (2.1) is triggered by the SU (3) L scalar triplet η, whose first component get a VEV that satisfies v η = v = 246 GeV and provides masses for the SM particles. Note that the U (1) Lg global lepton number symmetry is assumed to be spontaneously broken down to a residual discrete Z Furthermore, the lepton number has a gauge component as well as a complementary global one, as indicated by the following relation: being L g a conserved charge associated with the U (1) Lg global lepton number symmetry. The SU (3) L triplet scalar fields η and ξ can be expanded around the minimum as follows: The SU (3) L fermionic triplets and antitriplets can be represented as: (2.5) With the particle content shown in Tables I and II, the following relevant Yukawa terms for the quark and lepton χ η ϕ σ ξ ρ φ ζ S1 S2 S3 S4 S5 S6 SU (3)C 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SU (3)L 3 3 1 1 1 1 1 1 1 1 1 1 1 sector invariant under the group G arise: where the dimensionless couplings in Eqs. (2.6) and (2.7) are O(1) parameters.
As shown in detail in the Appendix B, the following VEV patterns for the T scalar triplets are consistent with the scalar potential minimization equations for a large region of parameter space: In what regards the T scalar doublets, we consider the following VEV configurations, which are natural solutions of the scalar potential minimization conditions: Furthermore, since the observed pattern of the SM charged fermion masses and quark mixing angles is produced by the spontaneous breaking of the T × Z 6 × Z 8 × Z 12 discrete group, we set the VEVs of the SU (3) L singlet scalar fields with respect to the Wolfenstein parameter λ = 0.225 and the model cutoff Λ, as follows: The gauge bosons associated with the group SU (3) L for the case β = −1/ √ 3 are written as follows: where the electric charges of each gauge field corresponds to the entries of the matrix: The gauge field associated with the U (1) X symmetry is electrically neutral, i.e., it has Q B = 0 and is represented as follows: The gauge sector associated with the SU (3) L × U (1) X group of the 3-3-1 models, is composed of five electrically neutral and four electrically charged gauge bosons. In the gauge boson spectrum there is one massless electrically neutral gauge boson which corresponds to the photon and eight massive gauge boson fields, namely, Z W ± , Z , W ± , K 0 , K 0 . Five of the massive gauge bosons, Z , W ± , K 0 , K 0 acquire their masses after the spontaneous breaking whereas the Z and W ± gauge bosons get massive after electroweak symmetry breaking. Replacing Eq. (2.15) in the kinetic term of the lagrangian give rise to The gauge boson mass terms as well as interactions between the scalar and gauge bosons [172] arise from the following kinetic term: where the covariant derivative in 3-3-1 models is defined as follows: Notice that the first two terms of Eq. (2.14), which are denoted as (1), include the couplings between the gauge bosons and the derivatives of the scalar fields, thus allowing to get information about each would-be Goldstone boson interacting with its corresponding massive gauge boson. In addition, the last term of Eq. (2.14), which is denoted as (2), contains information about the masses of the gauge bosons and its couplings with the physical scalar fields. The different entries of the gauge boson squared mass matrices are obtained from the following relation: where for the charged gauge bosons V i = W ± , W ± , whereas for the neutral ones V i = W 3 , W 8 , B, K 0 , K 0 . Then, the squared mass matrices for the charged and neutral gauge bosons are respectively given by: After the diagonalization, the gauge bosons mass spectrum is summarized in Table (III) Gauge Boson Squared Mass The squared masses for the Z and Z gauge bosons can be approximatelly written as [13]: where c W = cos θ W , s W = sin θ W and v eta = 246 GeV. Consequently, for v χ ≈ 10 TeV, we find that the heavy gauge bosons have the masses M W ≈ 3.3 TeV and M Z ≈ 4.5 TeV.

C. Scalar potential for two SU (3)L scalar triplets
For the sake of simplicity we neglect the mixing terms between the SU (3) L scalar triplets and the gauge singlet scalars. Then, the scalar potential for two SU (3) L scalar triplets takes the form: where χ and η are the SU (3) L scalar triplets acquiring vacuum expectation values (VEVs) in their third and first components, respectively. The minimization conditions of the aforementioned scalar potential yields the following relations: Thus, the VEV patterns for the SU (3) L scalar triplets χ and η are compatible with a global minimum of the scalar potential of (2.21). Solving these equations, the mass parameters can be obtained: replacing these mass parameters in the Higgs potential, the neutral and charged scalar mass spectrum resulting from the two SU (3) L scalar triplets can be obtained from the following relations: for the neutral scalar masses Φ i = ξ χ , ξ η , ζ χ , ζ η , χ 0 , η 0 and charged scalar masses Φ i = χ ± , η ± respectively. The scalar mass matrices are shown below: (2.27) Finally, the physical scalar mass spectrum resulting from the SU (3) L scalar triplets η and χ is summarized in Table IV.

Scalars Masses
The physical scalar spectrum resulting from the two SU (3) L scalar triplets is composed of the following fields: 2 CPeven Higgs bosons (h 0 1 , H 0 1 ) and one neutral Higgs boson (H 0 2 ). The scalar h 0 1 is identified with the SM-like 125 GeV Higgs boson found at the LHC. It's noteworthy that the neutral Goldstone bosons G 0 1 , G 0 2 , G 0 3 and G 0 3 are associated to the longitudinal components of the Z, Z , K 0 and K 0 gauge bosons. Furthermore, the charged Goldstone bosons G ± 1 and G ± 2 are associated to the longitudinal components of the W ± and W ± gauge bosons respectively.

QUARK MASSES AND MIXINGS
In this section, we show that our model is able to reproduce the observed pattern of SM quark masses and mixings. From the quark Yukawa terms, it follows that the up-type mass matrix in the basis (u 1L , u 2L , u 3L , T L , T 1L , T 3L ) versus (u 1R , u 2R , u 3R , T R , T 1R , T 2R ) takes the form: λv S1 , while the down type quark mass matrix written in the basis Assuming that the exotic quarks have TeV scale masses, we find that the SM quarks (excepting the top quark) get their masses from a Universal seesaw mechanism mediated by the two exotic up-type and three down-type quarks T n (n = 1, 2 and B i (i = 1, 2, 3), respectively. Due to the symmetries of the model, there are no mixing mass terms between the top quark and the remaining up-type quarks. Thus, the Universal Seesaw mechanism gives rise to the following SM quark mass matrices: where we have set (m B ) j = m B (j = 1, 2, 3) and considered m T ∼ m B ∼ v χ ∼ v S4 . Let us note that in our model, the dominant contribution to the Cabbibo mixing arises from the up-type quark sector, whereas the down-type quark sector contributes to the remaining CKM mixing angles. Given that we are considering real Yukawa couplings, in order to account for CP violation in the quark sector we take v S3 to be complex, which implies that the only complex entry in the SM quark mass matrices is b 13 . Thus, in this scenario, and taking into account that the scalar S 3 is a T doublet charged under the Z 12 symmetry as shown in Table I, the observed CP violation in the quark sector will arise from the spontaneous breaking of the T × Z 12 discrete group by the vacuum expectation value of the S 3 scalar.
The experimental values of the physical quark mass spectrum [173,174], mixing angles and Jarlskog invariant [175] can be obtained from the following benchmark point:   Table V our model successfully reproduces the low energy quark flavor data by having the quark model parameters of order unity. The symmetries of our model give rise to quark mass matrix textures that successfully explain the SM quark mass spectrum and mixing parameters, without requiring the introduction of a hierarchy in the effective free parameters of the quark sector. These effective parameters only need to be mildly tuned in order to perfectly reproduce the observed quark mass spectrum and CKM parameters. Finaly to close this section we briefly comment about the LHC signatures of exotic quarks in our model. As follows from the quark Yukawa terms of Eq. (2.6), the exotic quarks have mixing mass terms with all SM quarks, excepting the top quark. Such mixing terms allow that these exotic quarks can decay into any of the scalars of the model and a SM quark. These exotic quarks can decay into a SM quark and the SM-like Higgs boson. Such exotic quarks can be produced in pairs at the LHC via gluon fusion and Drell-Yan mechanism. Consequently, observing an excess of events in the six jet final state can be a signal of support of this model at the LHC. A detailed study of the exotic quark production at the LHC and the exotic quark decay modes is beyond the scope of this work and is left for future studies.

LEPTON MASSES AND MIXINGS.
From the charged lepton Yukawa interactions given in Eq. (2.7) and using Eqs. (2.8) and (2.10) together with the product rules of the T group shown in the Appendix, we find that the charged lepton matrix is given by: where f i with i = 1, 2, 3 are O(1) dimensionless parameters assumed to be real. Regarding the neutrino sector, from the lepton Yukawa terms given in Eq. (2.7), we find the following neutrino mass terms: where the neutrino mass matrix M ν is where A, B, C and D are given by: As shown in detail in Ref. [176], the full rotation matrix that diagonalizes the neutrino mass matrix M ν is approximately given by where 9) and the physical neutrino mass matrices are: 10) where M Furthermore, from Eqs. (4.4)-(4.7) and (4.10), we find for the light active neutrino mass scale, the estimate m ν ∼ λ 22 v ϕ ∼ 50 meV. Consequently, our model provides a natural explanation for the smallness of the light active neutrino masses.
The sterile neutrinos can be pair produced at the Large Hadron Collider (LHC), via a Drell-Yan annihilation mediated by a heavy Z gauge boson. The sterile neutrinos mix the light active ones thus allowing the sterile neutrinos to decay into SM particles, so that the final decay products will be a SM charged lepton and a W gauge boson. Consequently, the observation of an excess of events in the dilepton final states above the SM background, can be a signal in support of this model at the LHC. Studies of inverse seesaw neutrino signatures at the colliders as well as the production of heavy neutrinos at the LHC are carried out in Refs. [177][178][179][180]. A comprehensive study of the implications of our model at colliders goes beyond the scope of this work and will be done elsewhere.
By varying the lepton sector model paramerers, we obtain values for the charged lepton masses, neutrino mass squared differences and leptonic mixing parameters in very good agreement with the experimental data, as shown in Table VI. This shows that our model can successfully accommodate the experimental values of the physical observables of the lepton sector. It is worth mentioning that the range for the experimental values in Table (VI) were taken from [181] for the case of normal hierarchy. Let us note that we only consider the case of normal hierarchy since it is favored over more than 3σ than the inverted neutrino mass ordering. Furthermore, let us note that given that we are considering real Yukawa couplings in our model, the observed CP violation in the lepton sector is generated by the spontaneous breaking of the T × Z 6 × Z 8 discrete group by the vacuum expectation values of the ρ, φ, ζ and ξ scalars.   [181] are also shown for comparison. Figure 1 shows the correlation between the leptonic mixing parameters and the leptonic Dirac CP violating phase for the case of normal neutrino mass hierarchy. To obtain these Figures the lepton sector parameters were randomly generated in a range of values where the neutrino mass squared splittings and leptonic mixing parameters are inside the 3σ experimentally allowed range. We found a leptonic Dirac CP violating phase in the range 180 • δ CP 205 • , whereas the leptonic mixing parameters are obtained to be in the ranges 0.3196 sin 2 θ 12 0.3202, 0.4900 sin 2 θ 23 0.4925 and 0.0205 sin 2 θ 13 0.0240. 3.196 3.197 3.198 3.199 3 185 190 195 200 cp (c) Correlation between the atmospheric mixing parameter sin 2 θ23 and the leptonic Dirac CP-violating phase δCP . Figure 1: Correlations between the leptonic mixing parameters and the leptonic Dirac CP violating phase.

HIGGS DIPHOTON RATE
The explicit form of the h → γγ decay rate is [182][183][184][185][186][187] Here ρ i are the mass ratios ρ i = The numerical values of these parameters are given in Table VII. Let us note that in our model the Higgs-top quark coupling is very close to the SM expectation, i.e., a htt 1, since the mixing between the CP even neutral scalar fields ξ η and ξ χ is very suppressed, being the 126 GeV SM like Higgs boson mainly composed of the ξ η field. The dimensionless loop factors F 1/2 (ρ) and F 1 (ρ) for spin-1/2 and spin-1 particles in the loop, respectively are [182][183][184][185][186][187][188][189]: for ρ > 1. (5.8) In what follows we determine the constraints that the Higgs diphoton signal strength imposes on our model. To this end, we introduce the ratio R γγ , which normalizes the γγ signal predicted by our model relative to that of the SM: The normalization given by (5.9) for h → γγ was also used in [126,187,[190][191][192][193][194].
The ratio R γγ has been measured by CMS and ATLAS with the best fit signals [195,196]:  Here we set ν χ = 10 TeV.

LEPTON FLAVOR VIOLATING CONSTRAINTS
In this section we will determine the constraints on the model parameter space imposed by the charged lepton flavor violating processes µ → eγ, τ → µγ and τ → eγ. As mentioned in the previous section, the sterile neutrino spectrum of the model is composed of six nearly degerate heavy neutrinos. These sterile neutrinos together with the heavy W gauge boson induce the l i → l j γ decay at one loop level, whose Branching ratio is given by: [2,197,198]: boson masses larger than 4 TeV to fulfill the constraints arising from on K, D and B meson mixings [166]. As seen from Figure 2, the obtained values for the branching ratio of µ → eγ decay are below its experimental upper limit of 4.2 × 10 −13 and are within the reach of future experimental sensitivity, in the allowed model parameter space. In the region of parameter space consistent with µ → eγ decay rate constraints, the maximum obtained branching ratios for the τ → µγ and τ → eγ decays can reach values of the order of 10 −13 , which is four orders of magnitude below their corresponding upper experimental bounds of 4.4 × 10 −8 and 3.3 × 10 −8 , respectively. Consequently, our model is compatible with the charged lepton flavor violating decay constaints provided that the sterile neutrino are lighter than about 1.6 TeV and 4.5 TeV for W gauge boson masses of 4 TeV and 8 TeV, respectively.

CONCLUSIONS
We have constructed a viable 3-3-1 model with two SU (3) L scalar triplets, extended fermion and scalar spectrum, based on the T family symmetry and other auxiliary cyclic symmetries, whose spontaneous breaking produces the observed pattern of SM fermion masses and mixing angles. In our model the SM quarks lighter than the top quark, get their masses from a low scale Universal seesaw mechanism, whereas the SM charged lepton masses are produced by a Froggatt-Nielsen mechanism. In addition, the small light active neutrino masses are generated from an inverse seesaw mechanism. Our model is consistent with the low energy SM fermion flavor data and successfully accommodates the current Higgs diphoton decay rate constraints as well as the constraints arising from charged lepton flavor violating processes. In particular, 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 1.6 TeV and 4.5 TeV for W gauge boson masses of 4 TeV and 8 TeV, respectively. We have found that in the allowed region of parameter space, the obtained maximum values of the µ → eγ branching ratio are close to about 4 × 10 −13 , which is within the reach of future experimental sensitivity. Furthermore, the obtained branching ratios for the τ → µγ and τ → eγ decays can reach values of the order of 10 −13 . Consequently, our model predicts charged lepton flavor violating decays within the reach of future experimental sensitivity.
Appendix A: The product rules for T' The double tetrahedral group T is the smallest discrete subgroup of SU (2) as well as the smallest group of any kind with 1-, 2-and 3-dimensional representations and the multiplication rule 2 ⊗ 2 = 3 ⊕ 1, thus allowing to reproduce the successful U (2) textures [64]. It has the following tensor product rules [199]: (A.1) where p 1 = e iφ 1 and p 2 = e iφ 2 .