Neutrino Phenomenology and Dark matter in an $A_4$ flavour extended B-L model

We present an $\rm A_4$ flavor extended $\rm B-L$ model for realization of eV scale sterile neutrinos, motivated by the recent experimental hints from both particle physics and cosmology. The framework considered here is a gauged $\rm B-L$ extension of standard model without the introduction of right-handed neutrinos, where the gauge triangle anomalies are canceled with the inclusion of three exotic neutral fermions $N_{i}$ ($i=1,2,3$) with $\rm B-L$ charges $-4,-4$ and $5$. The usual Dirac Yukawa couplings between the SM neutrinos and the exotic fermions are absent and thus, the model allows natural realization of eV scale sterile-like neutrino and its mixing with standard model neutrinos by invoking $\rm A_4$ flavor symmetry. We demonstrate how the exact tri-bimaximal mixing pattern is perturbed due to active-sterile mixing by analyzing $3+1$ case in detail. % and $3+2$ case briefly. We also show the implication of eV scale sterile-like neutrino on various observables in neutrino oscillation experiments and the effective mass in neutrinoless double beta decay. Another interesting feature of the model is that one of three exotic fermions is required to explain eV scale phenomena, while the lightest fermion mass eigenstate of the other two is a stable dark matter candidate. We constrain the gauge parameters associated with $U(1)$ gauge extension, using relic density and collider bounds.


Introduction
Albeit its success, Standard Model (SM) is not the complete theory of nature to explain many observed phenomena. Neutrino oscillation experiments, in contrast to the zero mass prediction of SM, have confirmed the need for massive neutrinos and thus, necessitates for physics beyond the SM (BSM). The massive neutrinos and most of neutrino oscillation data can be explained in a framework of three active neutrinos through the elegant canonical seesaw mechanism [1][2][3][4][5][6], whereas some experimental observations are strongly hinting towards one or two additional light neutrinos with eV scale masses and O(0.1) mixing with active neutrinos [7][8][9][10][11], stemming from particle physics, cosmology and astrophysics (for details, reader may refer to the white paper [12]). While large number of experiments are coming up in next few years in order to investigate the possible presence of eV scale sterile neutrinos, which would be a ground-breaking discovery, there are few model building efforts in this direction. The aim of this work is to provide a simple BSM framework explaining the presence of one eV scale sterile neutrino along with O(0.1) mixing with active neutrinos and their effects on neutrinoless double beta decay (NDBD). This model also provides a detail study of DM phenomenology via a TeV scale fermionic DM and the collider constraints from Z mass.
The smallness of neutrino mass and their hierarchical structure become one of the most challenging problems in particle physics. In the standard scenario of three active neutrino oscillation, two mass-squared differences of order 10 −5 eV 2 and 10 −3 eV 2 , are observed from solar and atmospheric neutrino oscillation experiments respectively [13]. In fact, the absolute scale of neutrino mass still remains as an open question to be solved, however, there exists an upper bound on the sum of active neutrino masses, m ν < 0.12 eV from cosmological observations [14]. Over the last two decades, several dedicated experiments have determined the neutrino oscillation parameters rather precisely, though few of them are still unknown. These include the neutrino mass ordering, the exact domain of the atmospheric mixing angle θ 23 (octant problem) and the CP violating phase δ CP . But there exist few experimental anomalies, which can not be explained within the standard three neutrino framework. Of them, one is the possible presence of sterile neutrinos [15], which is evident from the antineutrino flux measurement in LSND [12] and MiniBooNE [16] experiments. The excess flux ofν e in appearance mode during ν µ → ν e oscillation, hints towards the possible existence of at least one additional state with eV scale mass [17]. This new state should not have any gauge interaction as per the Z-boson precision measurement and hence being sterile in nature. Thus, theoretical explanation of eV scale sterile neutrinos and its order of 0.1 mixing with the active neutrinos is worth to study through possible BSM frameworks. The non-trivial mixing of such a light sterile neutrino with SM neutrinos are well studied in the literature within different seesaw framework [18][19][20][21][22][23][24][25][26]. Along with these issues, the nature of neutrinos, i.e., whether it is Dirac or Majorana also remains unexplained. The only way to test the Majorana nature of neutrinos is through the extremely rare lepton-number violating neutrino-less double beta decay (NDBD) experiments.
One more well-known challenging problem in particle cosmology is that, SM doesn't have any explanation about the existence of DM even though we have enough indirect gravitational evidence about its existence. Attempts have been made through DM getting scattered off the SM particles i.e., in the context of direct searches, and the well known collaborations include LUX, XENON, PICO, PandaX etc [27,28]. Study of excess in positron, electron or Gamma excess i.e., indirect signals, and the experiments include AMS-02, H.E.S.S, MAGIC, Fermi-LAT etc [29][30][31][32][33]. Apart from these, dark sector particle production is also probed in the accelerator experiments as well.
To explain these experimental discrepancies, SM needs to be extended with extra symmetries or particles. Discrete symmetries are mostly preferred by the phenomenologists for model building purpose as they restrict the interaction terms by giving a specific structure to the mass matrix. A 4 flavor symmetry is widely used in neutrino phenomenology as it gives the simple tribimaximal (TBM) mixing, which is more or less compatible with the standard neutrino mixing matrix (U PMNS ). But this mixing pattern predicts a vanishing reactor mixing angle θ 13 [34], which conflicts the current experimental observation. Myriad amount of literature is focused on neutrino phenomenology with A 4 symmetry in the frameworks of different seesaw mechanism [34][35][36][37][38][39]. Apart from neutrino phenomenology, phenomenological study of DM has been made within A 4 framework [40][41][42][43][44], but very few literature have been devoted to study these phenomena with gauge extended A 4 flavor symmetric model. We consider a minimal extension of SM with A 4 and U(1) B−L symmetry in addition to three flavon fields and three singlet scalars, responsible for the breaking of A 4 and U(1) B−L symmetry respectively. This model includes three additional fermions with exotic B − L charges of −4, −4, 5 to protect from triangle gauge anomalies. This extension enhances the predictability of the model by explaining different phenomenological consequences like DM, neutrino mass and NDBD, compatible with the current observations. This manuscript is structured as: section 2 follows the brief description of model and particle content along with the full Lagrangian and symmetry breaking. In section 3, we discuss the neutrino masses and mixing with one sterile-like neutrino scenario and section 4 includes the contribution of active-sterile mixing to the NDBD as per current experimental observation. In section 5, we illustrate a detailed description of DM phenomenology and collider bounds on new gauge parameters within the model framework. In section 6, we summarize and conclude the phenomenological consequences of the model.

Model Description
We propose a new variant of U(1) B−L gauge extension of SM with additional A 4 flavor symmetry, which includes three new neutral fermions N i 's (i = 1, 2, 3) with exotic B − L charges −4, −4 and +5 to nullify the triangle gauge anomalies [45]. This choice of adding three exotic fermions in the context of B − L framework has been explored in several previous works [46][47][48][49][50][51][52][53]. The spontaneous symmetry breaking of B − L gauge symmetry is realized with three singlet scalars (φ 2 , φ 4 and φ 8 ), which also generate mass terms to all exotic fermions and the new gauge boson. Additionally, A 4 flavor symmetry is used to study the neutrino phenomenology in this model. Apart from the usual SM Higgs doublet and the above mentioned three scalar singlets, responsible for electroweak symmetry and U(1) B−L symmetry breaking respectively, there are three SM singlet flavon fields φ T , χ, ζ to break the A 4 flavor symmetry.
In this work, we intend to provide a detailed description of oscillation phenomenology with one sterile-like neutrino scenario. The complete field content with their corresponding charges are provided in Tables 1 and 2. The multiplication rules under A 4 symmetry group is outlined in Appendix. Table 1: SM field content of lepton and Higgs sectors alongwith their corresponding charges.
Field Table 2: Complete field content with their corresponding charges of the proposed model.

Scalar potential and symmetry breaking pattern
Considering all the scalar content of the model, the potential can be written as Moving towards symmetry breaking pattern, first the A 4 flavor symmetry is broken by the flavon fields. Then, the spontaneous breaking of B − L gauge symmetry is implemented by assigning non-zero VEV to the scalar singlets φ 2 , φ 4 and φ 8 . Finally, the Higgs doublet breaks the SM gauge symmetry to a low energy theory. The VEV alignment of the scalar fields are denoted as follows.

CP-odd and CP-even scalar mass matrices
The scalar fields H = (H + , H 0 ) T and φ i , (i = 2, 4, 8) can be parametrized in terms of real scalars (h i ) and pseudo scalars (A i ) as (2. 3) The diagonalization of the above mass matrix results the mass eigenstates, represented by H 1 , H 2 and H 3 . Moving to the CP-odd components, A 2 , A 4 and A 8 (corresponding to φ 2 , φ 4 and φ 8 ), the mass matrix in the basis (A 2 , A 4 , A 8 ) is given by (2.4) The above mass matrix upon diagonalization, gives one massless eigenstate, to be absorbed by U (1) boson, Z and two massive modes (represented by A 1 and A 2 ), which remain as massive physical CP-odd scalars in the present framework. The gauge boson Z attains the mass M Z = g BL 4v 2 2 + 16v 2 4 + 64v 2 8 1/2 .

Lagrangian and Leptonic Mass matrix
The Yukawa interaction Lagrangian for charged leptons, allowed by the symmetries of the model is as follows where, we have used the VEV alignment of the flavon field φ T as discussed in the scalar sector. The Yukawa couplings y e , y µ and y τ are considered to be hierarchical to get the appropriate masses of the charged leptons. The neutral lepton masses are generated by dimension-six operators, from which we derive the Majorana mass term for the neutrinos as Out of the three exotic fermions, we consider the fermion with B − L charge 5 to mix with the SM neutrinos, to study the neutrino phenomenology analogous to the mixing between the standard and sterile neutrinos 3 + 1 mixing scenario. The Majorana mass terms for new fermions and their interaction with SM leptons is given by (2.7) The charged lepton mass matrix and 3 × 3 mass matrix for active neutrinos, obtained from (2.5) and (2.6) respectively, takes the form The flavor structure of the matrix M ν , obtained from A 4 symmetry, can be diagonalized by the TBM mixing matrix [54], given as This is for the standard scenario of three neutrinos, that gives a TBM mixing pattern with vanishing reactor mixing angle in the framework of A 4 flavor symmetry, which has been studied in various works in the literature [55][56][57][58][59][60]. In the next section we consider the activesterile mixing by introducing an eV scale sterile-like neutrino and discuss the diagonalization of 4 × 4 neutrino mass matrix.

Neutrino mixing with one sterile-like neutrino
The standard scenario of three neutrino species has already been widely discussed in the literature, but the current experimental discrepancies from MiniBooNE and LSND data hint towards the possible existence of the fourth neutrino. From the nomenclature of the sterile neutrinos, one can infer that it doesn't interact with the SM particles directly as it does not have gauge interaction, instead mixes with the active neutrinos during oscillation. The mixing between the flavor (ν f ) and mass eigenstates (ν i ) are related by where n denotes the number of neutrino species. By considering three generations of active neutrinos, along with n s number of massive sterile species, one can have n = 3 + n s dimensional neutrino mixing matrix. In general, the mixing matrix will have n − 1 = n s + 2 Majorana phases, 3 × (n − 2) = 3 × (n s + 1) mixing angles and 2n − 5 = 2n s + 1 Dirac phases. Hence, in one sterile neutrino scenario, we will have 6 mixing angles, 3 Dirac phases and 3 Majorana phases. The standard parameterization for 4 × 4 neutrino mixing is given by where the matrices R ij are rotations in ij space and have the form
The current experimental searches of light sterile neutrino prefer a larger value of active-sterile mass squared differences than the observed solar and atmospheric mass squared differences of active neutrino oscillation. This implies that the mass for sterile neutrino can be either heavier or lighter than the active ones. We know that in normal ordering the active neutrinos have the form m 3 m 2 >m 1 whereas the inverse ordering is given by m 2 >m 1 m 3 ). So accordingly, there will be four possibilities in mass orderings if a sterile neutrino is added to the framework. Following the top to bottom nomenclature, i.e. if m s m 1,2,3 , can be denoted as 1+3 scenario for normal or inverted ordering of the active neutrinos. Whereas, if the case is reversed, i.e. if sterile state is lighter than the active ones (m 1,2,3 m s ), this configuration is named as 3+1 model in literature. Moreover, less attention is given to 3+1 scenario as they are prone to conflict with several experimental observations. In this model, we consider 1+3 like scenarios, to explain the neutrino phenomenology with eV scale exotic fermion. Table 3 shows the best-fit and 2σ ranges of the relevant oscillation parameters, we used for this work.

Diagonalization of Neutrino Mass matrix
We assume one of the exotic fermions to be sterile-like to mix with the active neutrinos, is provided by (2.7). We can construct the 4×4 active-sterile mixing matrix for neutrinos as follows , are the active-sterile mixing parameter and Majorana mass of the sterile-like fermion respectively. The above mass matrix is analytically diagonalized to get the physical masses of 1 + 3 neutrinos and the eigenvector matrix is given as . If one assumes that a < m s and expands to second order in the small ratio e/m s , the resulting mixing matrix is given by [18] But this mixing pattern gives θ 13 = 0, which has already been experimentally ruled out. Hence, to explain the non-zero θ 13 , we introduce one extra flavon field ζ, which is charged as 1 under A 4 symmetry, in order to perturb the neutrino mass matrix from the TBM mixing pattern. Including this new flavon field, the perturbed Lagrangian is given by When the flavon field acquires VEV, ζ = 1 √ 2 0 v ζ , the above term contributes to the mass matrix in (3.5). Hence, the modified neutrino mass matrix can be written as We analytically diagonalize the above mass matrix and the mixing matrix is constructed from the normalized eigenvectors, which takes the form where, And the mass eigenvalues of the 4 × 4 neutrino mixing matrix are stated as following Comparing with the standard 4 × 4 mixing matrix, we can have the mixing angles as follows (3.14) (3.16) (3.17) From the above equations, we can infer that adding the perturbation term in the interaction Lagrangian gives non-zero θ 13 , which is compatible with the current oscillation data.

Numerical Analysis
To perform numerical analysis in a systematic way, we define λ 1 = b a , λ 2 = d a and λ 3 = e 2 msa with φ ba , φ da , φ ea as the phases of λ 1 , λ 2 and λ 3 respectively. The expressions of mass eigenvalues in (3.19) can thus be written as m ν 1 = |m ν 1 |e iφ 1 = ||a| λ 2 e iφ da + 1 − λ 1 e iφ ba + λ 1 2 e 2iφ ba e iφ 1 , Thus, one obtains the physical masses as where, The corresponding phases in the mass eigenvalues values are given by The model also predicts a large CP violating Dirac phase, associated with the non-zero reactor mixing angle, which can be obtained from (3.2) Exp(−iδ 13 ) = U 13 sin θ 13 cos θ 14 cos θ 23 ≈ Exp(iφ ba ). (3.23) The above equation gives sin δ 13 ≈ − sin φ ba . To constrain the model parameters, compatible with the 3σ limits of the current oscillation data, we perform a random scan of these parameters over the following ranges: and show the correlation plots between different mixing angles in Figs. 1 and 2. We now proceed to discuss explicitly the constraints on different parameters from the availed neutrino oscillation data for vanishing and non-vanishing Dirac CP phase, by fixing various model parameters.

Variation of model parameters by fixing λ 2 = 1 and φ ba = 0
We discuss the dependence of various model parameters, which are consistent with the estimated 3σ values of neutrino oscillation observables. The correlation and constraints on these parameters are presented in Fig. 3 to Fig. 8. Here, we fix λ 2 = 1 and the phase associated with λ 1 , φ ba = 0. We vary λ 1 and λ 3 from 0 to 0.3 each, which in turn gives a favorable parameter space for λ 1 to lie within 0.25 to 0.3, allowed by the 3σ observation of θ 13 as shown in the left panel of Fig. 3. From the right panel, the allowed region for λ 3 turns out to be in the range 0.025 to 0.3. We found Majorana like phases φ 1 and φ 3 to have the allowed values (in radian) of −1.57 to 1.57 (left panel of Fig. 4)    panel of Fig. 4). Similarly, the left panel of Fig. 5 represents a strong constraint on the parameter a from cosmological observation of total active neutrino mass, which should lie within a range of ±0.025 to ±0.035 eV. The right panel displays a correlation between a and λ 3 . The corresponding phases of λ 2 and λ 3 , i.e φ da and φ ea are strongly constrained from neutrino mass bound. These phases are found to lie in the range, ±2.2 to ±3.14 and −1 to 1.2 radians respectively, as shown in the left and right panels of Fig. 6. The correlation of a with φ 1 and φ da are shown in left and right panels of the Fig. 7 respectively. Fig. 8 represents the correlation of φ da with φ 1 (left panel) and φ 3 (right panel). In the present case, by fixing φ ba = 0, one can have a vanishing δ 13 , even though θ 13 remains non-zero as seen from Eq.(3.23).     In the previous case, we have a vanishing CP phase (δ 13 = −φ ba ), here, we try to show the impact of non-zero δ 13 on the model parameters. We consider the corresponding phase of λ 1 , φ ba to vary from −π to π, which changes the allowed region of model parameters, described in the previous case. From the left panel of Fig. 9, we found that the region λ 3 > 0.2 is excluded by the cosmological bound on sum of active neutrino masses. The parameter scan for Majorana like phase allows φ 1 (in radian) to lie within the domain 0.94 to 1.2 (first quadrant) and −0.8 to −1 (second quadrant) as shown in the right panel of Fig. 9. The favored parameter space for φ 2 and φ 3 are represented in Fig. 10, which allows the values of −0.62 to 0.31 for φ 2 , 0.25 to 0.62 (first quadrant) and −0.19 to −0.44 (second quadrant) for φ 3 (all in radians). In this case, we found that the parameter a does not change appreciably in comparison with the previous case, as seen from the left panel of Fig. 11. The right panel represents the variation of a with the CP phase δ 13 . The correlation of φ 1 and φ da with parameter a are shown in the left and right panels of Fig. 12. Fig. 13 project the correlation  η 0ν eff , which can be inferred from the following expression,   Table 5: The numerical values of the phase-space factor and nuclear matrix elements The experimental observation of 0νββ process will indicate the existence of an (effective) LNV operator. We discuss here the standard mechanism and new physics contribution to this rare process in the present framework with eV scale sterile-like neutrino.
The process mediated by SM light neutrinos, which are Majorana in nature, is shown in Fig. 14 (left panel). The dimensionless parameter, responsible for LNV is given by the ee element of the Majorana mass matrix, normalized by the electron mass as, where U PMNS is the unitary PMNS mixing matrix and m i is the mass eigenvalues of the light active neutrinos. The parametrisation of the PMNS mixing matrix U PMNS is given by where c ij = cos θ ij , s ij = sin θ ij are sine and cosine of the mixing angles, δ is the Dirac CPphase and α, β are Majorana phases. Using the above mixing matrix U PMNS in eq. The effective Majorana mass depends upon the neutrino oscillation parameter θ 12 , θ 13 and the neutrino mass eigenvalues m 1 , m 2 and m 3 and phases. However, we do not know the absolute value of these light neutrino masses but neutrino oscillation experiments gives mass square difference between them. Also we have no information about these phases. In our analysis, we randomly vary these phases and took 3σ range of neutrino oscillation parameters to see whether we can get any crucial information about absolute scale of neutrino masses and mass ordering using experimental limit from neutrinoless double beta decay experiments.
We definitely know sign of ∆m 2 sol (≡ ∆m Using these randomly generated input parameters and oscillation data, variations of effective mass with the lightest neutrino mass is displayed in Fig.15   From left-panel of Fig.15 and using bounds from neutrinoless double beta decay experiments and cosmology, it is quite clear that the standard mechanism is not the only way to realize 0νββ and more importantly, NH and IH patterns are insensitive to current experimental bound while the quasi degenerate (QD) pattern is disfavoured from cosmological data from PLANCK1 and PLANCK2. In principle, we should explore all possible sources of new physics that violate lepton number (effectively) by two units and can lead to 0νββ.
We explicitly found that in addition to the standard mechanism, however, there is an additional contribution coming from the new eV scale sterile-like neutrino. In general the light (ν) and sterile-like (N ) neutrino exchange can give the corresponding effective Majorana parameter as where U e4 is the mixing angle between eV scale sterile neutrino with light active neutrino which has already expressed in terms of model parameters.
The variation of effective Majorana mass parameter in the presence of an additional eV scale sterile neutrino with the lightest neutrino mass is displayed in right-panel of Fig.15. From this plot, we conclude that presence of an additional eV scale sterile-like neutrino enhances the predictability of the model by contributing to the NDBD (shown in Feynman diagram in Fig. 14). The dotted points which lies in the horizontal bands shows that this new physics contribution can saturate the experimental bounds from GERDA and KAMLAND on effective neutrino mass [66,67] and can shed light on lepton number violation in nature along-with its implication to cosmology like matter-antimatter asymmetry of the universe.

Dark Matter Phenomenology
The model includes two heavy Majorana neutrinos N 2 and N 3 , exotic B − L charges forbid the interaction with SM particles. thereby ensuring the stability. The mixing matrix of these two neutral fermions from (2.7) is given by The above mass matrix can be diagonalized by orthogonal transformation: U R M R U R T = M D and the matrix that diagonalize it, is as following Here, the mixing angle is given by θ = 1 2 tan −1 In the present context, the lightest mass eigenstate obtained from the mixing of N 2 , N 3 qualifies as the dark matter candidate. We use the well-known packages LanHEP [68] and micrOMEGAs [69][70][71] for the DM analysis. Channels giving significant contribution to relic density are shown in Fig. 16. Annihilation to sterile-like neutrinos (N 1 N 1 in final state) in gauge portal and CP-odd scalars (A 2 A 2 in final state) in scalar portal, stand out to give major contribution. We have fixed the masses of the scalar spectrum and gave emphasis to the impact of gauge parameters M Z and g BL on relic density. Fig. 17 left (right) panel depicts the behavior of relic density with DM mass for varying M Z (g BL ). Relic density with s-channel contribution is supposed to give resonance in the propagator (Z , H 2 , H 4 ).
As Z couples axial vectorially with DM fermion and vectorially with SM fermion, the WIMP-nucleon cross-section is not sensitive to direct detection experiments. Moving to the parameter scan, the gauge parameters M Z and g BL are restricted from the searches of dilepton signals in Z -portal by ATLAS [72], and also LEP-II [73]. We have used CalcHEP [74,75] to obtain the cross section pp → Z → ee(µµ) as a function Z mass, depicted in the left panel of Fig. 18. It can be seen that for g BL = 0.01, the region M Z < 0.3 TeV is excluded and for g BL = 0.03, the allowed region is M Z > 0.9 TeV. For g BL = 0.1, the M Z should be above 2 TeV. M Z > 3 TeV is allowed for g BL = 0.3 and heavy mass regime for Z (above 4 TeV) is favorable for g BL = 0.5. Right panel of Fig. 18 projects the parameter space consistent with Planck relic density limit upto 3σ range, with the exclusion limits of Figure 16: Annihilation channels contributing to relic density. ATLAS and LEP-II M Z g BL > 6.9 TeV . The favorable region refers to the data points below both the experimental bounds.

Summary and Conclusion
In this article, we have presented a detail study of neutrino and dark matter phenomenology in a minimal extension of standard model with U(1) B−L and A 4 flavor symmetry. The model includes additional three neutral fermions with exotic B − L charges of −4,−4 and 5 for cancellation of triangle gauge anomalies. The scalar sector is enriched with six SM singlet fields, of them, three are assigned with U(1) B−L charges and the rest three are charged under A 4 flavor symmetry. The former scalar fields helps in spontaneous breaking of B−L symmetry and one massless mode of the CP odd eigenstates gets absorbed by the new gauge boson Z . The later scalar fields, known as A 4 flavons, break the A 4 flavor symmetry spontaneously at high scale before the breaking of U (1) B−L .
As different experiments such as LSND, MiniBooNE etc. are pointing towards the existence of eV scale sterile neutrinos to explain certain experimental discrepancies, we tried to address the neutrino phenomenology with a fourth generation sterile-like neutrino. Out of the three exotic fermions in the model, one is in eV scale (sterile-like) and rest of them are in TeV scale, which help in explaining the neutrino mass and DM simultaneously. The presence of discrete symmetry provides a specific flavor structure to the neutrino mass matrix, leads to a better phenomenological consequences of neutrino mixing with a fourth generation sterile-like neutrino. We explored the active-sterile mixing in compatible with the current experimental observation. We found a large θ 13 and associated non-zero CP phase, within the observed 3σ range of LSND data by introducing a perturbation term to the Lagrangian. Presence of eV scale sterile-like neutrino also provides an allowed parameter space for the effective neutrino mass in NDBD, lies within the experimental bound of KAMLAND and GERDA. We strongly constrained the model parameters from the cosmological bound of active neutrino masses and showed the correlation between different mixing angles.
Apart from neutrino mixing, we studied the dark matter phenomenology with rest two exotic fermions, by generating the tree level mass in TeV scale unlike the eV scale sterilelike neutrino. By introducing suitable singlet scalar, the mass mechanism for these heavy fermions is assured by the B − L breaking in TeV scale. Within the model framework, we found that the lightest Majorana fermion satisfies correct DM relic density i.e., in the 3σ observation of Planck, with contributions from scalar and gauge mediated processes. As expected, the s-channel resonances for scalars and heavy gauge boson are obtained in the relic density, we have also analyzed the behaviour for different values of model parameters. We also strongly constrained the parameters associated with gauge mediated processes from the ATLAS studies of di-lepton signals and LEP II. We have shown the allowed parameter space satisfying DM and collider constraints. Direct detection of dark matter in Z portal is insensitive to direct detection experiments because of the Majorana nature. Finally, the proposed idea of extending SM with both gauge and flavor symmetries provides a suitable platform to investigate both neutrino and dark sectors.