Non-sterile electroweak-scale right-handed neutrinos and the dual nature of the 125-GeV scalar

Can, and under which conditions, the 125-\gev SM-like scalar with the signal strengths for its decays into $W^{+}W^{-}$, $ZZ$, $\gamma \gamma$, $b \bar{b}$ and $\tau \bar{\tau}$ being consistent with experiments be accommodated in models that go beyond the Standard Model? Is it truly what it appears to be, namely the SM Higgs boson, or could it be quite different? A minimal extension of the original electroweak-scale right-handed neutrino model, in which right-handed neutrinos naturally obtain electroweak-scale masses, shows a scalar spectrum which includes either the 125-\gev SM-like scalar or a scalar which is quite {\em unlike} that of the Standard Model, both of which possessing signal strengths compatible with experiment. In other words, the 125-\gev scalar could be an {\em impostor}.


I. INTRODUCTION
The discovery of the 126-GeV SM-like scalar [1] and the present absence of any new physics signals has opened up a whole host of questions as to the true nature of the electroweak symmetry breaking and to what may lie beyond the Standard Model. The sole existence of the 126-GeV particle would leave unanswered several deep questions such as the origin of neutrino masses, the hierarchy of quark and lepton masses among many others. It also implies that the electroweak vacuum is metastable with drastic consequences in the very far-distant future [2]. It remains to be seen whether this most simple picture-albeit one with many question marks-will be the ultimate theory of nature or it is merely an effective theory at current accessible energies whose reality tests are incomplete and more non-SM phenomena will pop up in the not-too-distant future with Run II of the LHC.
Despite the present lack of new physics at the LHC, it does not imply that it is not there. On the contrary, new physics has already appeared in the neutrino sector through neutrino oscillation and its implication on neutrino masses. This evidence, although quite clear, is only indirect and does not show where the new physics that gives rise to the aforementioned phenomena may appear. This difficulty in finding a direct evidence for the new physics involved in generating neutrino masses is compounded by the fact that these masses are so tiny, more than seven orders of magnitude smaller than the light- * vvh9ux@virginia.edu † pqh@virginia.edu ‡ ask4db@virginia.edu est lepton: the electron. In the most generic scenario of the elegant seesaw mechanism for generating tiny masses, the right-handed neutrinos are sterile i.e. singlets under the electroweak gauge group. In a nutshell, the two mass eigenvalues are m 2 D /M and M where the Dirac mass m D is proportional to the electroweak scale while the Majorana mass M is m D . In addition to the fact that ν R 's are assumed to be electroweak singlets, the very large values for M in a generic scenario makes it very very difficult to probe the crucial physics, namely that which gives rise to M which is responsible for the lightness of the "active" neutrinos. Another facet of this new physics is the Majorana nature of the "active" neutrinos themselves which could manifest itself through neutrino less double beta decays which so far have not been observed. Through neutrino oscillations, we have a hint of new physics but what it might be and where to look for it is still a big mystery at the present time.
The aforementioned uncertainties rest in large part on the assumption that right-handed neutrinos are electroweak singlets. This usually comes from a certain extension of the SM such as the Left-Right symmetric model SU (2) L × SU (2) R × U (1) B−L [3] or the Grand Unified model SO(10), among others. It goes without saying that the singlet assumption is not verified in the absence of experimental signals of right-handed neutrinos. If one is however willing to entertain the idea that right-handed neutrinos are not sterile, there is an entire panorama of accessible phenomena that can be searched for and studied. A non-sterile right-handed neutrino necessarily interacts with the electroweak gauge bosons and the Majorana mass term is expected to carry the electroweak quantum number and hence is proportional to arXiv:1412.0343v2 [hep-ph] 15 Jan 2015 the electroweak breaking scale. Right-handed neutrinos could then be searched for both from an interaction point of view and from an energetic one. A model of this kind was put forth by one of us (PQH) [4] (the EWν R model).
In the EWν R model [4], right-handed neutrinos are parts of SU (2) doublets along with their charged partners (the mirror charged leptons). Anomaly freedom dictates the existence of doublets of right-handed mirror quarks. The particle content of the model is listed in the next section. The existence of extra doublets of chiral fermions, the mirror quarks and leptons, is potentially fatal for the model because of their contributions to the electroweak precision parameters, in particular the S-parameter. Those extra chiral doublets would make a "large" contribution to the S-parameter, an undesirable outcome. Fortunately, the EWν R model contains a Higgs triplet which makes opposite contributions to the S-parameter and thus offsetting those of the mirror fermions. An exhaustive study of the electroweak precision parameters within the framework of the EWν R model has been carried out in [6] with the main result being that there is a large parameter space which satisfies the precision constraints. The EWν R model in its original inception [4] contains, beside one Higgs doublet which couples to both SM and mirror fermions, two scalar triplets, one (complex) with hypercharge Y /2 = 1 and another (real) with Y /2 = 0. Out of the thirteen degrees of freedom (4 for the doublet, 6 for the complex triplet and 3 for the real triplet), three are absorbed by W's and Z and the remaining ten become physical degrees of freedom. Can one of those ten physical scalars describe the observed 126-GeV SM-like scalar? If not, what minimal extension would be needed for that purpose? Where and how does one look for the more massive scalars which could be CP even or odd?
The plan of the paper is as follows. Section II will be devoted to a summary of the EWν R model with its particle content and, in particular for this paper, its scalar sector. For completeness, the electroweak precision parameter constraints will also be summarized. Section III presents some of the salient points concerning the scalar sector of the original EWν R model. A particular attention is paid to what this sector has to say about the 126-GeV SM-like scalar. We show why the lightest spin-0 particle has to be CP-odd if one wishes to identify it with the 126-GeV object. This has to do with the fact that the production cross section for the scalar is very large compared with the equivalent SM quantity. This occurs when a single Higgs doublet couples to both SM and mirror fermions. The CP-odd option unfortunately is ruled out by the likelihood analysis which favors the CP-even case [7]. At the end of this section we present a simple extension of the original model by adding one extra Higgs doublet. In this extension, by imposing a global symmetry, one Higgs doublet is made to couple to SM fermions while the other one couples only to mirror fermions. The scalar mass eigenstates and eigenvalues are shown as well as their couplings to fermions and gauge bosons. Section IV discusses the implications of the extended model in light of the existence of the 126-GeV SM-like scalar. We will show in that section the dual nature of the 126-GeV SM-like scalar and only further measurements can tell whether or not it is an "impostor".

II. THE EWνR MODEL: A SUMMARY
The main idea of the EWν R model [4] was to search for a model in which right-handed neutrinos naturally acquire a mass proportional to the electroweak scale Λ EW = 246 GeV. For this to occur, the most natural way to implement this idea is for right-handed neutrinos to be non-sterile. In particular, the simplest way is to put them in doublets along with right-handed mirror charged lepton partners. In this manner, a Majorana mass term of the type M ν T R σ 2 ν R necessarily carries an SU (2)×U (1) quantum number and transforms like an SU (2) triplet. (Details are summarized below.) As shown in [4], a new Higgs sector including triplets is needed and it obviously participates in the symmetry breaking of the electroweak gauge group. The EWν R model of [4] is highly testable for the following reasons: 1) ν R 's are sufficiently light; 2) ν R 's couple to W and Z and can be produced through these couplings; 3) The presence of an extended Higgs sector. SM: Mirror: (2) • Lepton SU (2) singlets (generic notation): SM: e R ; Mirror: e M L • Quark SU (2) doublets (generic notation): SM: Mirror: • Quark SU (2) singlets (generic notation): • The Higgs sector: a) One Higgs doublet: Φ. This Higgs doublet couples to both SM and mirror fermions. b) One complex Higgs triplet with Y /2 = 1 containing doubly-charged scalars: c) One real Higgs triplet with Y /2 = 0:  [4,17] has a global SU (2) L × SU (2) R symmetry. The triplets transform as (3,3) and the doublet as (2,2) under that global symmetry. Specifically, and Proper vacuum alignment dictates These VEVs leave an unbroken SU (2) D custodial sym- As discussed in [5,6], with respect to SU (2), the two triplets (one real and one complex) and one doublet sum up to 13 degrees of freedom, 3 of which are Nambu-Goldstone bosons absorbed by W's and Z leaving 10 physical degrees of freedom. Under the custodial symmetry SU (2) D , these transform as The seesaw mechanism in the EWνR model The main purpose of the EWν R model was to provide a scenario in which right-handed neutrinos are nonsterile and get their masses out of the symmetry breaking of SU (2) × U (1). A Majorana mass term of the form M R ν T R σ 2 ν R in the EWν R model comes from the following Yukawa interaction: which gives The right-handed neutrino Majorana mass is now intrinsically linked to the breaking scale of SU (2) × U (1) through the VEV ofχ as As stressed in [4], M R is bounded from below because ν R are now members of an SU (2) doublet and would contribute to the Z-boson width leading to the lower bound: A Dirac mass term is of the form m D (ν † L ν R + h.c.). This is a product of two doublets and the simplest choice for the Higgs scalar is an SU (2) singlet with zero hypercharge, namely φ S .
With φ S = v S , the Dirac mass is given by The magnitude of the light neutrino mass given by implying .

D. Constraints from electroweak precision data
The presence of extra SU (2) doublets of chiral fermions in the form of mirror fermions would seriously affect the constraints from electroweak precision data. As first mentioned in [4], the positive contribution of mirror fermions to the S-parameter could be compensated by the negative contribution to S from the Higgs triplets. A detailed analysis has been performed in [6] which showed that there is a large parameter space in the model which satisfies the present constraints of the electroweak precision data. A sample of the plots summarizing the scatter plots of the model is given below.

FIG. 2. ConstrainedSS versusSMF
In Fig. 1 S and T are new Physics contributions to the S and T parameters respectively. It is seen that the EWν R model satisfies very well the constraints from the electroweak precision data and has passed the first (indirect) test. In Fig. 2,S S andS M F refer to the contributions to S from the scalar and mirror fermion sectors respectively. Further details can be found in [6].
An important point which is worth repeating here is the role played by the scalar triplet in regulating the new physics contribution to the S-parameter. In fact, it has been pointed out in [6] that the contribution to S from the scalar triplet can be made increasingly negative by increasing the mass of the doubly-charged Higgs as an example. This can offset the positive contribution coming from the mirror fermions. One can see the importance of the scalar sector, in particular the Higgs triplets, in making the EWν R model consistent with precision data. The next step is to examine constraints coming from direct searches of the Higgs boson. E. Constraint on the "minimal" EWνR model from the 126-GeV SM-like Higgs boson By "minimal" we mean that the Higgs structure is as described above: one Higgs doublet and two Higgs triplets. Some phenomenology of these scalars has been investigated in [5]. This topic will be revisited in a future publication. For the purpose of this manuscript, we shall focus on the four neutral states: H 0 5 , H 0 3 , H 0 1 and H 0 1 and in particular H 0 3 and H 0 1 since the other two do not couple to SM and mirror fermions [6]. H 0 3 and H 0 1 are CP-odd and CP-even respectively. As shown in [6], because of the coupling g H 0 1 qq = −ı mqg 2m W c H , the gluon fusion production cross section for H 0 1 was estimated to be σ EW ν R 49 σ SM where the factor 49 = (1 + 6) 2 takes into account the contributions from the top and mirror quarks. This alone practically ruled out H 0 1 as the 126-GeV SM-like scalar. Also, since the coupling to fermions are very similar to that of the SM, modulo the factor 1/ cos θ H , the various branching ratios (BR) are expected to be of the order of those of the SM and the signal strengths (µ = (σ × BR)/(σ × BR) SM ) will largely exceed observations. It was shown in [6] that the CP-odd (pseudoscalar) H 0 3 could, with the appropriate choice of parameters, can fit the bill for being the 126-GeV object both in terms of the production cross section and in terms of branching ratios. However, a likelihood analysis ruled this option out by more than 3 σs [7]. Although a measurement of the spin and parity of the 126-GeV object is yet to be performed, it is fair to assume that it is more likely to be a 0 + state. As one can see, the reason why the CP-even H 0 1 has such a large gluon fusion production cross section (at least 49 times larger than the SM one at at same mass) is because it comes from the Higgs doublet (the real part of the neutral component) which couples to SM fermions as well as mirror fermions. The loop controlling the gluon fusion production of H 0 1 is dominated by the top quark and the mirror quarks giving rise to the factor of 49 mentioned above while it is dominated only by the top quark contribution in the SM. An extension in the Higgs sector of the minimal EWν R model is needed. This is shown in the next section.

III. EXTENDED EWνR MODEL
The simplest extension-and, in fact, the most natural one -of the minimal EWν R model is to have two Higgs doublets with one coupled to SM fermions and the other one to mirror fermions. To prevent cross coupling, a global symmetry will be imposed. Basically, we introduce the following Higgs doublets along with the corresponding global symmetries U (1) SM × U (1) M F : All other fields (SU (2)-singlet right-handed SM fermions, left-handed mirror fermions) are singlets under U (1) SM × U (1) M F . These symmetries will forbid, at tree level, Yukawa couplings of the form g YfL Φ 2 M f R and g Yf M R Φ 2 f M L . Only Yukawa interactions of the type g YfL Φ 2 f R and g Yf M R Φ 2M f M L are allowed. The Yukawa couplings of the physical states to SM and mirror fermions will involve mixing angles. This is detailed in the Appendix A.
About the extended scalar sector. One now has one extra Higgs doublet which leads to 4 more degrees of freedom. The physical states of custodial SU (2) D are: The three singlet states H 0 1 , H 0 1M and H 0 1 can have mass mixings. (A detailed discussion of the potential and various physical states is given in the Appendix A.) The scalar mass eigenstates will be a mixture of these three states, and it is where we will focus on in the next two sections.

IV. COMPARING EWνR MODEL PREDICTIONS WITH DATA
Measured properties of the 126 GeV scalar particle that was discovered at the LHC so far tend to be close to the properties of SM Higgs boson. Hence, in every model of BSM Physics it is imperative to (i) have at least one Higgs particle with about 126 GeV having SM-like decay properties, and (ii) study the implications of these properties in the 'allowed' parameter space of the model (e.g. allowed masses of any BSM particles in the model, etc.). To check the viability of a model or to search for the model experimentally, decay properties of the 126 GeV Higgs boson candidate in the model must be studied.
The cross section of any decay channel of the Higgs boson that is measured at the LHC is given by σ(H-decay) = σ(H-production) × BR(H-decay) , (21) where σ(H-production) is the production cross section of H and BR(H-decay) is the Branching Ratio of the decay channel of H that is under consideration.
where Γ(H-decay) is the partial width of the H-decay channel, and Γ H is the total width of H. Because the decay widths Γ(H-decay) cannot be experimentally measured, we compare σ H-decay in the EWν R model with the predictions SM for that decay channel. So we define the well known signal strength as compared to the CP-even hypothesis [7]. Hence, in this paper while considering 126 GeV candidate in the EWν R model, we proceed with the hypothesis that this candidate is a CP-even eigenstate 1 . Out of the 3 CPeven Higgs bosons, only H 0 1 can have decay widths to SM fermions similar to the SM predictions. Therefore, one might expect that in the EWν R model H 0 1 is the candidate to be 126 GeV Higgs boson. But it is not that simple! Because the three custodial singlet scalars can mix, according to Eq. (A24), generally, H 0 1 is not a mass eigenstate. To obtain the mass eigenstates including the actual 126 GeV candidate in this model, we need to diagonalize the mass matrix in Eq. (A24). Thus, after the electroweak symmetry breaking the SU (2) D singlet mass eigenstates are given by: We denote these mass eigenstates by H, H , and H . Their masses depend on elements of the mixing matrix, and their decay properties also depend on other parameters as shown in Appendix A. The vacuum expectation values (VEVs) of the real parts of Φ 2 , Φ 2M and χ are also among these parameters, and need to be varied to find different cases of 126 GeV candidates in this model. Hence, it is necessary to estimate the limits on these VEVs before analyzing 126 GeV candidates in detail.

Limits on VEVs:
Recall that the VEVs of the real parts of Φ 2 , Φ 2M and χ are (v 2 / √ 2), (v 2M / √ 2) and v M respectively. The charged SM fermions, the charged mirror fermions and the right handed neutrinos get their masses due to v 2 , v 2M , and v M respectively. Various constraints on these masses constrain the ranges of the VEVs.
If the pole mass of top quark (173.5 GeV), the heaviest SM fermion, is perturbative and comes from v 2 , then v 2 69 GeV (because g 2 top ≤ 4π). We set the lower bound on the masses of all the charged mirror fermions 1 The possibility that the 126 GeV Higgs boson is a linear combination of CP-even and CP-odd state has not been thoroughly checked experimentally yet. The spin and parity of the 126 GeV scalar are yet to be measured at CMS and ATLAS. Thus, in this paper, we will stick to CP-eigenstate hypothesis based on the likelihood analysis at 102 GeV, which is the LEP3 [16] bound on the heavy BSM quarks and BSM charged leptons. Hence, considering a constraint of g 2 M F /4π ≤ 1.5 on the Yukawa couplings of all the charged mirror fermions, v 2M 27 GeV, implying v M 80 GeV. Thus, for M R to be perturbative M R 283 GeV. We also know that M R ≥ M Z /2 ≈ 45.5 GeV [4], and, hence, v M 13 GeV. This implies that v 2 , v 2M 234 GeV. The allowed ranges for VEVs and for parameters defined in Eq (A8) are summarized in the table below. Keeping all this in mind we are now We can vary the elements of the mass matrix in Eq. (A24) to find those numerical forms of the mixing matrix in Eq. (24), such that, after the electroweak symmetry breaking, one of the three singlet mass eigenstates has a mass around 126 GeV and two other states are heavier. The λ's in the mass matrix can be chosen such that the 126 GeV state has a dominant H 0 1 component. In this subsection we will discuss two example scenarios in which H acquires a mass of about 126 GeV. For both the scenarios s 2 = 0.92, s 2M = 0.16, s M ≈ 0.36: with m H = 125.7 GeV, m H = 420 GeV, m H = 599 GeV. Fixing the aforementioned parameters fully determines the numerical form of the custodial singlet scalar mixing matrix. In these two scenarios, H 0 1 is the most dominant component in H and H 0 1M , H 0 1 are highly sub-dominant components. Thus, H ≈ H 0 1 i.e. it almost entirely originates from SM-like SU (2) scalar doublet Φ 2 . But, still, the scalar spectrum is not entirely SM-like, since heavier H and H also exist. These are not the only two scenarios which can give m H ≈ 126 GeV, but are merely two examples.
For a spectrum like this, where m H ≈ 126 GeV < m H < m H , we calculate the partial widths of various decay channels as explained in Appendix B. We calculate the total width of H by adding individual partial widths: Among all the partial widths considered above, Γ H→bb and Γ H→W + W − are the most dominant. Note that at 126 GeV mass H → f Mf M decays do not come into the picture, because m f M > 100 GeV implies that these are not kinematically possible decays at the tree level. We will discuss more about this constraint shortly. After fixing the singlet-scalar mixing matrix (as in Eqs. (25,26)), a few other parameters for the signal strength calculation can still be varied independently. Calculation of the partial width of H → γγ channel necessitates fixing the values or ranges for the remaining parameters. In both Examples 1 and 2 (Eq (25,26) respectively), we fix other parameters as follows: • masses of all three charged mirror leptons m l M = 102 GeV, • mass of lightest two generations of mirror quarks • for the purpose of partial widths of H-decays in scenarios above, we also fix mass of the third mirror quark generation at m q M = 120 GeV. This mass will be varied to analyze constraints on H ∼ H 0 1M .

The values of m H
are chosen so as to have largest allowed ranges for m H 0 5 and m ++ 5 . We vary the latter two over the range ∼ 400 − 730 GeV for Example 1 and 2.
The lower limit of 102 GeV on masses of charged mirror leptons and mirror quarks is imposed based on the results of search for sequential heavy charged leptons and quarks at LEP3 (refer 'Heavy Charged Leptons' and 'Heavy Quarks' sections in [16] and references therein). Strictly speaking these constraints apply only to sequential-like heavy BSM fermions, because searches for charged heavy leptons and heavy quarks are done specifically for sequential-like heavy fermions, e.g. heavy charged leptons L decaying as L → τ Z. However, charged mirror fermions in the EWν R model couple to the SM fermions in an altogether different way, through the scalar singlet φ S [4,19]. Still, we impose these constraints on charged mirror fermions in this model, arguing that if these mirror fermions were lighter than ∼ 100GeV, they would have been discovered at LEP3. Fig. 3 shows the comparison of CMS data for signal strengths µ(H-decay) of the 126 GeV Higgs boson, and the predictions of those signal strengths for the 126 GeV H in Examples 1 and 2, put together. For predictions in the EWν R model we have considered the gluon-gluon fusion production channel (gg → H), which is the most The figure shows predictions of µ( H → W + W − , ZZ, bb, ττ ) by EWνR model in H ∼ H 0 1 scenario for varying three slightly different forms of the singlet mixing matrix, in comparison with corresponding best fit values by CMS.
dominant Higgs-production channel at the LHC. Table II shows a summary of properties of 126 GeV Higgs at CMS and predictions for those properties in the EWν R model. Calculation of the predicted values is explained in Appendix B. A few comments are in order here in context of Fig. 3. It can be seen that the EWν R model predictions for µ( H → W + W − , ZZ) are the equal, and similarly predictions for µ( H → bb, ττ ) are the equal. This is expected, since as seen in Appendix B, Different predictions for µ of each channel in Fig. 3 plane for Examples 1 and 2 in Figs. 6, 7 respectively. Thus, we can conclude that in H ≈ H 0 1 scenario predictions of the EWν R model agree with the properties of 126 GeV Higgs boson, as measured by CMS and ATLAS. However, individual partial decay widths and branching ratios of H can be very different from the SM Higgs boson. Therefore, more data and further analysis of partial decay widths of the 126 GeV Higgs boson at the LHC are required to make a conclusive statement about whether it is a SM Higgs or just a SM-lookalike "impostor" H in the EWν R model.
In addition to studying decay properties of the 126 GeV Higgs boson, the search for SM-like heavy Higgs bosons has also been carried out at CMS and ATLAS in decay channels like W + W − [30] and γγ [22]. In the two example scenarios considered above the next heavier state after 126 GeV turns out to be H , and H is the heaviest. H couples to all the particles that SM Higgs boson couples to and it is also a CP-even state. Thus, constraints on a SM-like heavy Higgs boson may also constrain H . While varying the mass of H over the range [150, 650] GeV, we compared the signal strength of H → W + W − [18,30] and σ(gg → H ) × BR( H → γγ) [21,22] in the EWν R model to the constraints from heavy Higgs search in W + W − and γγ decay channels at CMS.
We calculated the total width of H using Partial decay widths were calculated using the method illustrated in Appendix B. The constraints on σ(gg → that might appear as a resonance in excess to the background. Such a resonance can be seen if the total width of the particle is much smaller than its mass. In Examples 1 and 2 the total width of H exceeds its mass after it crosses the (2 × mirror fermion mass) threshold. When the total width of a particle becomes comparable to its width, the particle can no longer appear as a resonance over the background. A well known example of such a phenomenon is the sigma model of QCD, where the sigma particle cannot be seen experimentally as a resonance. In Fig. 8  For completion a few remarks about H should be made here. Although H also couples to all the particles that SM-Higgs boson couples to, in Example scenarios 1 and 2 considered here m H ∼ 600 GeV. And it can be seen from the CMS data in Fig 8 that the data available in this mass range and beyond is not enough to be sensitive to signal strength of the order of SM predictions. Also, H ∼ H 0 1 , which means that it couples to SM charged fermions very weakly. Hence, more data is required to study H in this heavy mass range.
To summarize this subsection, we have so far explored the possibility that H 0 1 is the dominant component in 126 GeV H in the EWν R model. We showed that the 126 GeV Higgs boson at the LHC could be H ∼ H 0 1 , and more data and analysis are required to confirm or rule out this possibility. Within the regime of EWν R model H can be the next heavier neutral scalar particle after 126 GeV . Based on the results of the search for SM-like heavy Higgs boson at CMS a lower limit of ∼ 250 − 400 GeV can be set on H . In the mass range heavier than this limit, the total width of H exceeds its mass and hence, it should be treated like a strongly coupled scalar (strong coupling to the mirror fermions). The current data cannot really put a stringent constraint on H in this heavier mass range.   Table II). The two leftmost black dashed lines (and two rightmost lines) enclose a range of a1,1M that is consistent with all the constraints analyzed in this paper including those coming from H → W W .
the dominant components in 126 GeV H while agreeing with the measured signal strengths of the 126 GeV Higgs at the LHC. We address this problem in two steps: • Is it possible for H to obtain a mass of about 126 GeV with H 0 1 as a subdominant?
• If yes, can such a 126 GeV physical scalar agree with the measured signal strengths of 126 GeV Higgs boson at LHC?
To address the first question, we adopted the following method. The relevant parameters which enter this calculation are given below Eq (A24), along with their ranges.
Here, the limits for λ's are set so that λ/4π ∼ 1, for perturbativity. Limits on s 2 , s 2M , s M are based on table I. We randomly generated value of each of these parameters  = 120 GeV , It was found that in most of these 1348 combinations H has H 0 1 as a subdominant component at ∼ 126 GeV mass. It can be seen with the help of calculations of signal strengths explained in Appendix B that the branching ratios of such 126 GeV scalar particles are, in general, different from those of a SM-like Higgs. However, the interplay between deviations of their production cross sections and branching ratios (BR) from the corresponding cross sections and BR for a SM-like Higgs, can result in signal strengths close to the SM predictions. Note than in most of these cases H 0 1 , which comes from an SMlike SU (2) scalar doublet, is a dominant component in a mass eigenstate heavier than 126 GeV.    This demonstrates that the measurements of the signal strengths do not are conclusively indicate that the 126 GeV Higgs boson discovered at LHC is indeed a SMlike Higgs or that it has a dominant SM-like scalar component. As can be seen from Eq (31) we scanned only a part of available parameter space by fixing values or ranges of these parameters. A thorough scan of the entire parameter space is out of scope of this paper. Such a thorough scan or scan of another part of the parameter space could be a topic for a future publication, especially if more data from LHC shows signs of BSM physics. Here we only intended to provide a proof of concept that the 126 GeV SM-lookalike Higgs boson discovered at the LHC can very well be an impostor with a highly subdominant SM-like component in the EWν R model.
In this section we explored two types of scenarios, to study the nature of the SM-lookalike 126 GeV Higgs boson at LHC within the regime of the EWν R model. We showed that this Higgs boson can very well be an impostor with a dual-like nature in the EWν R model. This Higgs boson can show SM-like signal strengths, when it has a dominant SM-like Higgs component. But interestingly, even though it has a highly sub-dominant component of a SM-like Higgs, this Higgs boson can have signal strengths that agree with the data at CMS. Thus, the agreement of the signal strengths of the 126 GeV Higgs at the LHC with the SM-predictions is not sufficient to conclude whether this is the SM-Higgs or a SM-like Higgs impostor or a SM-unlike Higgs impostor! We showed that in this model the 126 GeV Higgs appears with a dual-like nature. In both the cases signal strengths of this mass eigediscussed how the 126 GeV Higgs boson at the LHC can be an impostor Higgs within the framework of the EWν R model. The agreement of its signal strengths with the SM-predictions in various decay channels is not sufficient to conclude that this is a SM-Higgs, or that SM-like Higgs is a dominant component in this particle.  So far in this model, the 126 GeV Standard Model like BEH boson is most likelyH. There are also, CP-odd spin zero states, H 0 3 , H 0 3M , and the other heavy CP-even spin zero states, H , and H . In this section, we show possibilities to the probe the signal of these pseudo-scalars in various major channels at LHC. To do so, we will investigate the product of cross section production and branching ratio, a.k.a signal strength, in γγ and τ τ channels. And also, we will calculate the ratio of signal strength µ, defined below, between these pseudo-scalars and a Standard Model like Higgs boson H SM in other channels.
In this extension of EWν R model, the degenerate masses of two SU (2) D custodial triplets are related by:

A. Ratio of production cross section
At LHC, H 0 3 , H 0 3M are produced mainly via gluon fusion similar to H SM . By using effective coupling approximation, we have  However, the contributions from mirror quarks can be suppressed due to the fact that mirror up quarks and mirror down quarks couple to H 0 3 , H 0 3M in opposite ways. Particularly, in this work, we consider degenerate mirror fermion doublets, means m u M = m d M , then contributions from mirror quarks are canceled out. So, only loop from top quark appears in the production of H 0 3 , H 0 3M . Then, the ratios of production cross section are: In γγ channel ATLAS [21] and CMS [22] have recently reported their results in searching for narrow scalar diphoton resonances up to 600 GeV for CMS and 840 GeV for ATLAS. In those reports, they present the upper limit on the production cross section times branching ratio into two photons at 95% confidence level. So far, no significant excess has been found, except two ones with a 2σ above the background at m = 201 GeV and m = 530 GeV in the ATLAS analysis. Subjectively, we compare our prediction in γγ channel with those results, even though assumptions about decay width of the resonance are made in those reports. Similar to the gluonic decay, only fermionic loops contribute to the partial width of H 0 3,3M → γγ, [20] (44) Here, i = top quark, six mirror quarks, and three mirror charged leptons. While the total widths of H 0 3,3M are calculated by summing all partial widths.
The branching ratio of H 0 3,3M → γγ is The signal strength of H 0 3,3M → γγ is defined as At any particular mass, ratio of production cross section R, and Br(H 0 3,3M → γγ) is calculated directly. While σ(gg → H SM ) is taken from the handbook of Higgs cross section [24]. To be consistent with previous analysis, we also provide two scenarios which correspond to the dual nature of the 125-GeV Higgs impostor. And for illustrating, we consider the degenerate case in masses of mirror fermions. Particularly, the first two generations of mirror quarks and all charged leptons have same masses, m q M  Remark: • Before fermionic thresholds, 2m q M 1,2 , 2m l M , the signal strength can be larger than what ATLAS and CMS represent. To be conservative, we can exclude a range of mass of pseudo-scalars corresponding to two examples of parameter set above. However, with different set up, the signal strength could be well below.
• As m H 0 3 increasing, more mirror fermionic decay channels are opened up.
The branching ratios of H 3,3M → γγ peaks at thresholds, 2m q M 1,2 , 2m q M 3 , 2m l M , 2m t . And production cross section decreases. So both signal strengths are below the limit.

C. In τ τ channel
Recently, ATLAS [25] and CMS [26] also reported their new results in τ τ channel. Although, the main aim of their reports are to look for MSSM neutral boson, they provide a model independent limit on the production cross section times branching ratio of a general spin zero state. Therefore, in this part, we investigate the signal strength of our H 0 3,3M → τ τ in two sets of parameters, when H 0 1 is either dominant or sub-dominant inH, as the same with what we did in the last part.   Remark: • In both cases, the signal strength can exceed the upper limit from ATLAS and CMS before the thresholds of mirror fermions, here is 204 GeV. It happens because unlike SM Higgs, the decaying processes such as H 0 3,3M → W W/ZZ only happen at loop level. So the partial widths of those are relatively small. Consequently, the branching ratios of H 3,3M → ττ are not as small as in Standard Model. Even though, they are at one order above the limit. And in the wide range of parameter space in the EW ν R model, it is not a problematic to fit the model into the upcoming analyses at LHC in this mass region.
• After passing the first threshold, the signal strengths of both H 3,3M → ττ decrease rapidly, because the total widths Γ H 3,3M are dominated by fermionic decays. And, then they reach another peak at 2m t . In the whole region, the signal strengths are below the limit for both pseudoscalars. Except, at around 2m t , the signal strength can be slightly above the limit. For example, in case H 0 1 being dominant, and at m H = 340 GeV, σ × BR(H 0 3M → ττ ) = 0.18, while σ × BR(H SM → ττ ) = 0.12. It is justifiable. D. In W W/ZZ channels In this model, pseudo-scalars, H 0 3 , H 0 3M do not couple directly to W , and Z. Decay processes H 0 3,3M → W W/ZZ happen only at loop levels. It is predictable that these processes will be highly suppressed. To prove that, we calculate the ratio of signal strength, µ, between H 0 3 → W W/ZZ and H SM → W W/ZZ. µ is defined in Eq (??).
At any particular mass, Br(H SM → V V ) is taken from the handbook of Higgs working group [24]. While the ratio of production cross section R H 0 3 (??) and Br(H 0 3 → V V ) are calculated directly. At one loop order, the partial decay rate for these processes are [27] A W/Z f are amplitudes with top, bottom quarks; mirror charged leptons, and right handed neutrinos inside the loops. They have specific forms in the Appendix ??. At LHC, H → W W is an important channel to probe new scalars in the high mass region. From Fig. ??, we see that the ratio of signal strength is suppressed very much for CP-odd scalar, H 0 3 , in this model. However, it can be detected via a two state decay process: H 0 3 →l M l M →lφ S lφ S , which mimics W W signal of the SM Higgs boson: H → W + W − →lνlν. Here, φ S is invisible, and considered as E M T . With a particular set of parameter phase in this work, all charged mirror leptons m l M = 102GeV, m H = 210 − 500GeV, it is sufficient to have both mirror fermions being on-shell. Here, In analogy to previous comparisons, we define a ratio of signal strength: With M R = 70 GeV, then l M → ν R νl is kinametically possible.
While Br (W → lν) = 0.108 [28]. It is clear that the ratio µ l depends on the value of g sl . The search for high-mass Higgs boson in H → W W → lνlν was carried on at both ATLAS in the range of 260 − 1000 GeV [29], and CMS in the range of 145 − 1000 GeV [30]. There is no excess in the whole scanning mass region. The observed 95% CL upper limit on the ratio of signal strength is below µ = 1 all the way up to m H ≈ 600 GeV in [30]. We can set an upper limit on µ l , µ l ≤ 1. Consequently, we can have a rough upper limit on g sl , g sl ≤ 10 −3 .

VII. CONCLUSIONS
The 126-GeV object has presented us with a challenge to understand its nature: Is it really the SM Higgs boson as it appears to be or is it simply an impostor? So far, the only data available to us are given in terms of the so-called signal strengths, µ, as defined in Eq. (??). The signal strengths for the various decay modes of the SM Higgs boson are consistent with data. However, It turns out that it might be possible for various BSM models to be consistent with experiment also based solely on such signal strengths. This is what we have shown in this paper in the context of the EW ν R in its extended version.
As we have described in the beginning of our paper, the EW ν R [4] was invented with the purpose of realizing the seesaw mechanism at the electroweak scale instead of some GUT scale. As such one can directly test the seesaw mechanism at the LHC and at the proposed ILC through the physics associated with the model such as lepton-number violating production of electroweak-scale Majorana right-handed neutrinos and -this is the subject of the present paper-Higgs physics beyond that of the SM.
The extended EW ν R model discussed in this paper contains three neutral CP-even mass eigenstates,H,H andH , which are linear combinations of H 0 1 , H 0 1M which couple to SM fermions and mirror fermions respectively and H 0 1 which couples only to ν R 's. The notation for the mass eigenstatesH,H andH refers to states with increasing masses. We scanned the parameter space with the following requirements in mind: 1) The mass of the lightest state should be ∼ 126 GeV; 2) The mixing angles should be such that the signal strengths fit the data from CMS and ATLAS. We found many combinations of H 0 1 , H 0 1M and H 0 1 which satisfy those requirements.
What is interesting here is the dual nature of the 126-GeV scalar that we uncovered in our scanning of the parameter space: 1) There are states with the SM-like scalar H 0 1 as a dominant component; 2) There are states with H 0 1 as a dominant component and is thus very unlike that of the SM model. In other words, these states are impostors. All of these states-and we are far from exhausting the parameter space-yield signal strengths compatible with the CMS and ATLAS data. It goes without saying that detailed studies of various properties of the 126-GeV SM-like scalar such as the total width, partial widths,..., are needed to determine if it were indeed the SM Higgs boson or just simply an impostor. Of course, a discovery of one or several extra scalars definitely points toward physics beyond the SM. In the extended EW ν R model, although the aforementioned 126-GeV-like scalars all yield comparable signal strengths, details such as production cross sections, branching ratios, total widths and partial widths can differ quite a bit from one another. States with H 0 1 as a dominant component tend to behave more like the SM Higgs boson while others do not. In other words, we may have discovered a scalar which is involved in the electroweak symmetry breaking but which may not be the SM Higgs boson.

VIII. ACKNOWLEDGEMENTS
We would like to thank Giuseppe Cerati for providing results of the search for SM-like heavy Higgs boson at CMS. This work was supported by US DOE grant DE-FG02-97ER41027. ASK was supported by the Graduate Fellowship of the Department of Physics, University of Virginia.

Appendix A: Scalar Potential and Physical Scalar States in the Extended EWνR Model
When a Y = 1 complex scalar doublet is added to the minimal EWν R model, under the global SU (2) L × SU (2) R we have and and Thus, the VEVs of real parts of Φ 2 , Φ 2M and χ are where v ≈ 246 GeV. We define This extension of the EWν R model also has an additional U (1) SM × U (1) MF global symmetry such that and and all the other fields are singlets under this symmetry.
A generic SU (2) L × SU (2) R preserving potential for these scalars can now be written as Note that this potential, like the one in the minimal EWν R model is also invariant under χ → −χ. Now it is also invariant under the global U (1) SM × U (1) MF symmetry. The vacuum alignment given above breaks the global SU (2) L × SU (2) R down to the custodial SU (2) D . One still has M W = g v/2 and M Z = M W / cos θ W , but GeV . It is found that three 'massless' Nambu-Goldstone Bosons can be obtained after spontaneous breaking of SU (2) L × U (1) Y to U (1) em , when a condition λ 5 = λ 6 = λ 7 imposed on the potential above. Thus, the potential that should be used to find the physical Higgs states is After the spontaneous breaking of SU (2) L × U (1) Y → U (1) em , besides the three Nambu-Goldstone Bosons, there are twelve physical scalars grouped into 5 + 3 + 3 + 1 of the custodial SU (2) D with 3 custodial singlets. To express the Nambu-Goldstone Bosons and the physical scalars let us adopt the following convenient notation: Thus, for the complex neutral and charged fields respectively. With these fields the Nambu-Goldstone Bosons are given by The physical scalars can be grouped, as stated in the previous section, based on their transformation properties under SU (2) D as follows: The masses of these physical scalars can easily be obtained from eq. (A15). Since, the potential preserves the SU (2) D custodial symmetry, members of the physical scalar multiplets have degenerate masses. These masses are In general, the H 0 1 , H 0 1M and H 0 1 can mix according to the mass-squared matrix Hence, the generic mass eigenstates are given by Eq. (24). It should be noted that in the limit λ 4 → 0 the offdiagonal elements in the matrix above vanish. Also note that, in general, we have six parameters in the physical scalar potential and we can have six independent physical scalar masses. Thus, given the masses of the physical scalar states the parameters (these include quadratic coupling parameters, λ 4 , λ 5 , λ 8 ) in the potential can be uniquely determined and vice versa. TABLE VII. S1S2V type couplings(V is a vector gauge boson and S1, S2 are Higgs/ Goldstone bosons), which contribute to Oblique Corrections. Common factor: ıg(p − p ) µ , where p(p ) is the incoming momentum of the S1(S2).
Appendix B: Partial decay widths of neutral Higgs In this section we will discuss various production and decay channels relevant for studying properties of H, H and H [8]. Out of these H 0 → γγ, gg -type decays (and also the Higgs boson production through gg → H) have only one loop contributions at the leading order (LO) and decays like H 0 → W W, ZZ, ff can take place through tree level interactions. We show calculation of the decay width Γ(H → γγ) up to LO in QCD. We will show how all the other relevant decay widths can be calculated easily from the corresponding SM values modified by a multiplicative factor. We calculate these widths in EWν R model from the SM values given in [8].

H → gg
The decay of a custodial singlet Higgs boson to two gluons proceeds through one-loops at LO. Unlike H 0 → γγ channel this channel does not give a 'clean' signal at a hadron collider like LHC due to large QCD background. But gluon-gluon fusion channel (gg → H) is the most dominant production channel for a neutral Higgs and hence, Hgg coupling becomes important while studying µ(H 0 -decay) for various decay channels. The production cross section of gg → H 0 is related to the width of H 0 → gg by where the constant of proportionality includes phase space integrals and the mass of H 0 (refer Eq. (2.30) in [9]). Therefore, for a given mass of Higgs Hence, to calculate signal strengths µ(H-decay), we use Γ(H 0 → gg) instead of Γ(H 0 → gg), since we are only interested in the ratios of production cross-sections. Consider a general scalar mass-eigenstate H that is also a CP-even state in some model of BSM Physics. The relevant part of the interaction Lagrangian is [9] where v H 0 is the vacuum expectation value of H 0 , v = 2M W /g ∼ all H 0 's v 2 H 0 , ψ is a fermion of mass m f , S ± is a charged BSM scalar. For SM λ W = 1/ √ 2, λ S = 0. For a general (CP-even) Higgs boson H 0 that couples to the SM quarks with Yukawa coupling in the equation above, the decay width of H 0 → gg is given by (B4) where, for a loop of quark having mass m i , τ i = 4m 2 i / m H 0 [9], and F 1/2 (τ ) is given by and For a custodial singlet Higgs boson decay to two photons also proceeds through one-loops at LO. It is a 'clean' channel due to the absence of large QCD background. Therefore, in the study of 126 GeV Higgs boson, decay to diphoton is an important channel at CMS and ATLAS [21,23].
For a general Higgs mass eigenstate H 0 having couplings as given in Eq (B3) the decay width of H 0 → γγ is given by [9]: Here i is performed over all the particles of spin-s which contribute to H 0 → γγ, s = spin-0, spin-1/2, and spin-1 is the spin of i th particle, Q i is the electric charge in units of e, and F 1 (τ ) = λ W τ [3 + (4 − 3 τ )f (τ )] , with τ = 4 m 2 i /m 2 H 0 and f (τ ) is given by Eq (B6). Considering the contribution from W ± loop, the charged fermion loops in SM (all except the top quark loop are negligible) and setting v H 0 = v gives the H 0 SM → γγ decay width. Note that F 1 (τ ) includes contributions from only the transverse polarization of W-boson; the contribution from Goldstone boson must be added separately using F 0 (τ W ). 2 .
Based on Eq (B9) we define partial amplitude of H 0 → γγ as (B11) Then, in the EWν R model, we see from Eq (24) that where a H,i with (i = 1, 1M, 1 ) are the coefficients of H 0 1 , H 0 1M and H 0 1 in H mass eigenstate, respectively; these are the elements in the H-row of the mixing matrix in Eq (24). To calculate A EW ν R (H 0 1 → γγ), in addition to the W ± , G ± 3 and top-loop contributions we have to also consider one loop contributions involving H ± 3 , H ± 3M , H ± 5 and H ±± 5 , whereas for A EW ν R (H 0 1M → γγ) we need to consider the W ± , G ± 3 loops, the loops with the charged mirror fermion and the loops with H ± 3 , H ± 3M , H ± 5 and H ±± 5 . Various Feynman rules necessary for these calculations can be read from Tables VI-X and the three point scalar Feynman rules can be obtained from [Scalar potential equation].
In Eq.[eqn for masses of multiplet scalars] all the members of a scalar custodial multiplet are degenerate, e.g. 2 The formulas given above in Eq (B3), Eq (B10) are a bit different from Eqs.(2.15), (2.17) in [9]. We try to give formulas for a general BSM model (e.g. using a general v H 0 , λ W and λ S ) H 0 3 and H + 3 have same masses and so on. But once custodial symmetry is broken at the loop level, different custodial multiplet members can have different masses. This mass splitting can also be due to some custodial symmetry-breaking terms in the Lagrangian (not given explicitly in this paper). In that case, the partial width of H → γγ depends on the following variable parameters in EWν R models are: • Masses of H ± 3 , H ± 3M , H ± 5 and H ±± 5 ; • s 2 , s 2M , s M ; • Masses of charged mirror leptons and mirror quarks; • Scalar self-couplings: λ 1 , λ 2 , λ 3 , λ 4 , λ 5 , λ 8 ; • Elements of 3 × 3 mixing matrix in Eq (24).
Note that all of these parameters are not completely independent, e.g. once we fix s 2 , s 2M , then s M is automatically fixed; scalar self-couplings and mixing matrix elements must vary so as to give at least one scalar mass eigenstate at 126 GeV , etc.

Tree level decays of H
Tree level decay channels of a neutral (CP-even) Higgs include decays to two fermions and to W W, ZZ. In this subsection first we show how the decay widths of these decays in the EWν R model are related to the widths in SM. Although at the LO these decays have only the tree level contributions, NLO QCD+EW corrections become significant at about 5% accuracy for [8]. Because the decay widths of these channels at tree level in the EWν R model and in SM are related by a multiplicative factor as described below, by using SM decay widths to calculate the decay widths in EWν R model these NLO contributions will be automatically included in our results. For vertices involving mirror fermions the QCD+EW corrections are different from the corrections for SM quarks (in SM non-negligible QCD corrections only come from top quark). Because mirror quark masses are of the same order as the top quark, for ∼ 5% accuracy the NLO corrections due to mirror quarks can be assumed to have the same magnitude as those due to the top quark. The different tree level couplings in EWν R model can be found in Tables VI, VIII,  C, F are generally in form of the 't Hooft-Veltman scalar loop integrals [31]. But here, we have top quark and heavy mirror fermions. So, we can use asymptotic forms in the high mass limit. Where