Review Article  Open Access
Sofiane M. Boucenna, Stefano Morisi, José W. F. Valle, "The LowScale Approach to Neutrino Masses", Advances in High Energy Physics, vol. 2014, Article ID 831598, 15 pages, 2014. https://doi.org/10.1155/2014/831598
The LowScale Approach to Neutrino Masses
Abstract
In this short review we revisit the broad landscape of lowscale models of neutrino mass generation, with view on their phenomenological potential. This includes signatures associated to direct neutrino mass messenger production at the LHC, as well as messengerinduced lepton flavor violation processes. We also briefly comment on the presence of WIMP cold dark matter candidates.
1. Introduction
The flavor problem, namely, why we have three families of fermions with the same standard model quantum numbers, but with very hierarchical masses and a puzzling pattern of mixing parameters, constitutes one of the most challenging open problems in particle physics. In this regard neutrinos are probably the most mysterious particles. Indeed, while the discovery of the Higgs boson by the ATLAS and CMS experiments at the Large Hadron Collider (LHC) at CERN [1–3] has clarified to some extent the nature of electroweak symmetry breaking, the origin of neutrino masses remains elusive. With standard model fields one can induce Majorana neutrino masses through the nonrenormalizable dimension5 operator or higher order ones, for example, [4–9], where is a dimensionless coupling and denotes some unknown effective scale. However, strictly speaking, we still do not know whether neutrinos are Dirac or Majorana fermions, and many issues remain open regarding the nature of the associated massgiving operator, for example,(i)its underlying symmetries, such as total lepton number,(ii)its flavor structure which should account for the observed oscillation pattern,(iii)its dimensionality,(iv)its characteristic scale, and(v)its underlying mechanism. This leads to considerable theoretical freedom which makes model building an especially hard task, a difficulty which to a large extent persists despite the tremendous experimental progress of the last fifteen years [10, 11].
Indeed the origin of neutrino mass remains so far a mystery. From oscillation studies we can not know the absolute neutrino mass scale. Still we know for certain that neutrinos are the lightest known fermions. Their mass must be below the few eV scale from tritium beta decay studies at the Katrin experiment [12], with somewhat stronger, though more model dependent limits coming from cosmology [13] and from negative neutrinoless double beta decay searches [14]. Unfortunately this vast body of information is far from sufficient to underpin the nature of the neutrino mass generation mechanism.
Mechanisms inducing neutrino mass may be broadly divided on the basis of whether the associated messengers lie at the high energy scale, related say, to some unification scheme or, in contrast, they involve new physics at the TeV scale, potentially accessible at the LHC.
For simplicity here we tacitly assume neutrino masses to come from Weinberg’s operator in (1). This operator can arise in a rich variety of different pathways [15]. For instance in the case of the standard typeI seesaw mechanism [16–21] the righthanded neutrino messengers have a Majorana mass at some large scale, fitting naturally in Grand Unified Theories (GUTs). There are, however, many alternative realizations of the dimension5 operator, such as the typeII [19, 22–25] and typeIII seesaw [26] constructions, in which the messengers have nontrivial gauge quantum numbers. Such schemes are bona fide highscale seesaw in the sense that, to account for the observed neutrino masses with reasonable strength for the relevant neutrino Yukawa couplings, one needs very large scales for the messenger mass, hence inaccessible to collider experiments. Of course within such scenarios one may artificially take TeV scales for the messenger mass by assuming tiny Yukawas, so as to account for the smallness of neutrino mass (One can avoid this in schemes where ad hoc cancellations [27] or symmetries [28, 29] prevent seesawproduced masses. We do not consider such a special case in this review. Similarly we will not assume any family symmetry restricting the flavor structure of models.). However by doing so one erases a number of potential phenomenological implications. Hence we call such standard seesaw varieties as highscale seesaw. It has long ago been realized [19] that, carrying no anomalies, singlets can be added in an arbitrary number to any gauge theory. Within the framework of the standard model gauge structure, the models can be labeled by an integer, , the number of singlets. For example, to account for current neutrino oscillation data, a typeI seesaw model with two righthanded neutrinos is sufficient (). Likewise for models with in which another mechanism such as radiative corrections (see below) generates the remaining scale. Models with are especially interesting, where one can exploit the extra freedom to realize symmetries, such as lepton number , so as to avoid seesawinduced neutrino masses, naturally allowing for TeVscale messengers. This is the idea behind the inverse [30] and linear seesaw schemes [31–33] described in the next section. We call such schemes as genuine lowscale seesaw constructions. A phenomenologically attractive alternative to lowscale seesaw are models where neutrino masses arise radiatively [34].
In principle one can assume the presence of supersymmetry in any such scheme, though in most cases it does not play an essential role for neutrino mass generation, per se. However we give an example where it could, namely, when the origin of neutrino mass is strictly supersymmetric because parity breaks. Indeed, neither gauge invariance nor supersymmetry requires parity conservation. There are viable models where parity is an exact symmetry of the Lagrangian but breaks spontaneously through the Higgs mechanism [35, 36] by an vacuum expectation value. As we will explain in the next section this scheme is hybrid in the sense that it combines seesaw and radiative contributions. In all of the above one can assume that the neutrino mass messengers lie at the TeV mass scale and hence have potentially detectable consequences.
In this review we consider the lowscale approach to neutrino masses. We choose to map out the possible schemes taking their potential phenomenological implications as guiding criteria, focusing on possible signatures at the LHC and lepton flavor violation (LFV) processes (Figure 1). The paper is organized as follows: in Section 2 we review low energy seesaw schemes; in Section 3 we discuss one, two, and threeloop radiative models. In Section 4 we discuss the supersymmetric mechanism and we sum up in Section 5.
2. Seesaw Mechanism
2.1. HighScale Seesaw
Within minimal unified models such as , without gauge singlets, one automatically encounters the presence of new scalar or fermion states that can act as neutrino mass mediators inducing Weinberg’s operator in (1). This leads to different variants of the socalled seesaw mechanism. One possibility is to employ the righthanded neutrinos present in the 16 of and broadly called typeI seesaw schemes [16–21] (see Figure 2). Similar unified constructions can also be made substituting the righthanded neutrino exchange by that of an exotic hyperchargeneutral isotriplet lepton [26] which is called typeIII seesaw [26]. An alternative mediator is provided by a hyperchargecarrying isotriplet coming from the 126 of and goes by the name typeII seesaw mechanism [19, 22, 23, 25] (see Figure 2).
(a)
(b)
The three options all involve new physics at high scale, typically close to the unification scale. While being model dependent, the expected magnitude of the mass of such messengers is typically expected to be high, say, associated to the breaking of extra gauge symmetries, such as the generator.
Within standard typeI or typeIII seesaw mechanism with three righthanded neutrinos the isodoublet neutrinos get mixed with the new messenger fermions by a seesaw block diagonalization matrix that can be determined perturbatively using the general method in [21]. For example in the conventional typeI seesaw case the matrix that diagonalizes the neutrino mass is unitary and is given bywhere and are the unitary matrices that diagonalizes the light and heavy subblock, respectively. From (3) one sees that the active subblock is no longer unitary and the deviation from unitary is of the order of . The expansion parameter is very small if the scale of new physics is at the GUT scale so the induced lepton flavor violation processes are suppressed. In this case there are no detectable direct production signatures at colliders nor LFV processes. This follows from the well know typeI seesaw relation where implying that is suppressed by the neutrino mass, hence negligible regardless of whether the messenger scale lies in the TeV scale (Weak universality tests as well as searches at LEP and previous colliders rule out lower messenger mass scales [37, 38].). As a result there is a decoupling of the effects of the messengers at low energy other than providing neutrino masses. This includes, for example, lepton flavor violation effects in both typeI and typeIII seesaw mechanisms. Regarding direct signatures at collider experiments these require TeVscale messengers which can be artificially implemented in both typeI and typeIII cases by assuming the Diractype Yukawa couplings to be tiny. This makes messenger production at colliders totally hopeless in typeI seesaw but does not affect the production rate in typeIII seesaw mechanism, since it proceeds with gauge strength [39].
Coming to the typeII scheme, neutrino masses are proportional to the vev of the neutral component of a scalar electroweak triplet and we have where is the vev of the standard model Higgs, is the mass of the scalar triplet , is the coupling of the neutrino with the scalar triplet, and is the coupling (with mass dimension) of the trilinear term between the standard model Higgs boson and the scalar triplet . Assuming of order one, in order to have light neutrino mass, there are two possibilities: either is large or is small. The first case is the standard typeII seesaw where all the parameters of the model are naturally of order one.
In such highscale typeI and typeIII seesaw varieties neutrino mass messengers are above the energy reach of any conceivable accelerator, while lepton flavor violation effects arising from messenger exchange are also highly suppressed. Should lepton flavor violation ever be observed in nature, such schemes would suggest the existence of an alternative lepton flavor violation mechanism. A celebrated example of the latter is provided the exchange of scalar leptons in supersymmetric models [40–42].
In contrast, if typeII seesaw schemes are chosen to lie at the TeV scale, then lepton flavor violation effects as well as samesign dilepton signatures at colliders remain [43]; see below. Obviously supersymmetrized “lowscale” typeII seesaw has an even richer phenomenology [44, 45].
2.2. LowScale TypeI Seesaw
The most general approach to the seesaw mechanism is that provided by the standard gauge group structure which holds at low energies. Within this framework one can construct seesaw theories with an arbitrary number of righthanded neutrinos, [19], since gauge singlets carry no anomalies. In fact the same trick can be upgraded to other extended gauge groups, such as or PatiSalam and also unified groups such as [46, 47] or . This opens the door to genuine lowscale realizations of the seesaw mechanism.
Before turning to the description of specific lowscale typeI seesaw schemes let us briefly note their basic phenomenological feature; namely, that in genuine lowscale seesaw schemes, (5) does not hold so that, for light enough messengers, one can have lepton flavor violation processes [48–50]. For example, radiative decays proceed through the exchange of light Figure 3(a) as well as heavy neutrinos Figure 3(b). Clearly expected lepton flavor violation rates such as that for the process are too small to be of interest. Another important conceptual feature of phenomenological importance is that lepton flavor violation survives even in the limit of strictly massless neutrinos (i.e., ; see text below) [51, 52].
(a)
(b)
2.2.1. Inverse TypeI Seesaw
In its simplest realization the inverse seesaw extends the standard model by means of two sets of electroweak twocomponent singlet fermions and [30]. The lepton number of the two sets of fields and can be assigned as and . One assumes that the fermion pairs are added sequentially; that is, , though other variants are possible. After electroweak symmetry breaking the Lagrangian is given by We define , where is the charge conjugation matrix, and are arbitrary Dirac mass matrices, and is a Majorana matrix. We note that the lepton number is violated by the mass term here. The full neutrino mass matrix can be written as a matrix instead of as in the typical typeI seesaw and is given by (in the basis , , and ) The entry may be generated from the spontaneous breaking of lepton number through the vacuum expectation value of a gauge singlet scalar boson carrying [53].
It is easy to see that in the limit, where the exact symmetry associated to total lepton number conservation holds, the light neutrinos are strictly massless. However individual symmetries are broken; hence flavor is violated, despite neutrinos being massless [51, 52]. For complex couplings, one can also show that CP is violated despite the fact that light neutrinos are strictly degenerate [54, 55]. The fact that flavor and CP are violated in the massless limit implies that the attainable rates for the corresponding processes are unconstrained by the observed smallness of neutrino masses and are potentially large.
This feature makes this scenario conceptually and phenomenologically interesting and is a consequence of the fact that the lepton number is conserved. However when light neutrino masses are generated; see Figure 4. In particular in the limit where (on the other hand, the opposite limit is called double seesaw. In contrast to the inverse seesaw, the double seesaw brings no qualitative differences with respect to standard seesaw and will not be considered here) the light neutrino mass matrix is given by It is clear from this formula that for “reasonable” Yukawa strength or values, of the order of TeV, and suitably small values one can account for the required light neutrino mass scale at the eV scale. There are two new physics scales, and , the last of which is very small. Therefore it constitutes an extension of the standard model from below rather than from above. For this reason, it has been called inverse seesaw: in contrast with the standard typeI seesaw mechanism, neutrino masses are suppressed by a small parameter, instead of the inverse of a large one. The smallness of the scale is natural in t’Hooft’s sense, namely, in the limit ; the symmetry is enhanced since lepton number is recovered (There are realizations where the low scale of is radiatively calculable. As examples see the supersymmetry framework given in [56] or the standard model extension suggested in [57].).
In this case the seesaw expansion parameter also characterizes the strength of unitarity and universality violation and can be of order of percent or so [50, 58], leading to sizable lepton flavor violation rates, close to future experimental sensitivities. For example, with GeV, GeV, and eV we have that . The deviation from the unitary is typically of order . As mentioned above, typical expected lepton flavor violation rates in the inverse seesaw model can be potentially large. For example, the rates for the classic process are illustrated in Figure 5. The figure gives the predicted branching ratios in terms of the small neutrino mixing angle , for different values of the remaining oscillation parameters, with the solar mixing parameter within its allowed range and fixing the inverse seesaw parameters as TeV and KeV. The vertical band corresponds to the allowed range.
Regarding direct production at colliders, although kinematically possible, the associated signatures are not easy to catch given the low rates as the righthanded neutrinos are gauge singlets and due to the expected backgrounds (see, e.g., [59]).
The way out is by embedding the model within an extended gauge structure that can hold at TeV energies, such as an extra coupled to which may arise from [33]. Viable scenarios may also have TeVscale or PatiSalam intermediate symmetries [60]. In this case the righthanded messengers can be produced through a new charged [61–63] or neutral gauge boson [64]. In fact one has the fascinating additional possibility of detectable lepton flavor violation taking place at the large energies now accessible at the LHC [64].
2.2.2. Linear TypeI Seesaw
This variant of lowscale seesaw was first studied in the context of theories [31, 32] and subsequently demonstrated to arise naturally within the framework in the presence of gauge singlets [33]. The lepton number assignment is as follows: , , and so that after electroweak symmetry breaking the Lagrangian is given by Notice that the lepton number is broken by the mass term proportional to . This corresponds to the neutrino mass matrix in the basis , , and given as If then the effective light neutrino mass matrix is given by Note that, in contrast with other seesaw varieties which lead to , this relation is linear in the Dirac mass entry, hence the origin of the name “linear seesaw.” Clearly neutrino masses will be suppressed by the small value of irrespective of how low is the scale characterizing the heavy messengers. For example, if one takes the unification framework [33], natural in this context, one finds that the scale of , that is, , is related to the scale of , that is, , through where is the unification scale of the order of and is the electroweak breaking scale of the order of . Replacing the relation (13) in (12) the new physics scale drops out and can be very light, of the order of TeV.
Neutrino mass messengers are naturally accessible at colliders, like the LHC, since the righthanded neutrinos can be produced through the “portal,” as light as few TeV. The scenario has been shown to be fully consistent with the required smallness of neutrino mass as well as with the requirement of gauge coupling unification [33]. Other and PatiSalam implementations have also been studied in [60].
Similarly to the inverse typeI seesaw scheme, we also have here potentially large unitarity violation in the effective lepton mixing matrix governing the couplings of the light neutrinos. This gives rise to lepton flavor violation effects similar to the inverse seesaw case. Finally we note that, in general, a leftright symmetric linear seesaw construction also contains the lepton number violating Majorana mass term considered previously.
2.3. LowScale TypeIII Seesaw
Here we consider a variant of the lowscale typeIII seesaw model introduced in [65] based on the inverse seesaw mechanism [30] but replacing the lepton field with the neutral component of a fermion triplet under with hypercharge zero [66] As in the the inverse typeI seesaw one introduces an extra set of gauge singlet fermions with lepton number and . The mass Lagrangian is given by In the basis the neutrino mass matrix is given by
As in the inverse seesaw case, in the limit , the light neutrinos are massless at tree level even if the mass term breaks lepton number. And for a small neutrinos get mass. Again, the scale of new physics is naturally small leading to sizable lepton flavor violation rates (Table 1).
 
The subscript in the representations is lepton number. “✗” would change to “✓” in the presence of new gauge bosons or supersymmetry, as explained in the text. 
On the other hand the charged component of the fermion triplet gives also a contribution to the charged lepton mass matrix leading to a violation of the GlashowIliopoulosMaiani mechanism [67] in the charged lepton sector, leading to treelevel contributions to and similar tau decay processes.
As in the standard typeIII seesaw mechanism [26], universality violation is also present here. However, in contrast to the standard case, here its amplitude is of the order which need not be neutrino mass suppressed. Indeed, in the inverse typeIII seesaw scheme neutrino masses are proportional to the parameter . As a result there are sizeable lepton flavor violation processes such as and , whose attainable branching ratios are shown in Figure 6.
Finally, to conclude this discussion, we stress that, in contrast with the inverse typeI seesaw mechanism, here the neutrino mass messenger , being an isotriplet member, has gauge interactions. Hence, if kinematically allowed it will be copiously produced in collider experiments like the LHC [39].
In short this scheme is a very interesting one from both the points of view of the detectability of collider signatures at the LHC as well as lepton flavor violation phenomenology.
2.4. LowScale TypeII Seesaw
We now turn to the socalled typeII seesaw mechanism [19, 22, 23, 25] which, though normally assumed to involve new physics at high energy scales, typically close to the unification scale, may also be considered (perhaps articially) as a lowscale construction, provided one adopts a tiny value for the trilinear mass parameter in the scalar potential; then the triplet mass can be assumed to lie around the TeV scale. Barring naturalness issues, such a scheme could be a possibility giving rise to very interesting phenomenological implications. In fact, in this case, if kinematically allowed, the scalar triplet will be copiously produced at the LHC because it interacts with gauge bosons.
Moreover the couplings that mediate lepton flavor violation processes are of order one and therefore such processes are not neutrino mass suppressed, as in the standard typeI seesaw. Indeed, from the upper limit it follows that (see [68]) implying a sizeable triplet Yukawa coupling. With , in order to get adequate neutrino mass values, one needs which restricts the scalar triplet vacuum expectation value (vev). For such small value of the vev, the decay of the is mainly into a pair of leptons with the same charge; while for , the decays mainly into a samsign pair; see [68].
Note that the tiny parameter controls the neutrino mass scale but does not enter in the couplings with fermions. This is why the lepton flavor violation rates can be sizable in this case. For detailed phenomenological studies of low energy typeII seesaw see, for example, [61, 68, 69].
Before reviewing the models based on radiative generation mechanisms for neutrino masses, we summarize the phenomenological implications of low scale seesaw models, together with their particle content, in Table 1.
3. Radiative Neutrino Masses
In the previous sections we reviewed mechanisms ascribing the smallness of neutrino masses to the small coefficient in front of Weinberg’s dimensionfive operator. This was generated through either treelevel exchange of superheavy messengers, with mass associated to highscale symmetry breaking, or conversely, because of symmetry breaking at low scale. In what follows we turn to radiatively induced neutrino masses, a phenomenologically attractive way to account for neutrino masses. In such scenarios the smallness of the neutrino mass follows from loop factor(s) suppression. From a purely phenomenological perspective, radiative models are perhaps quite interesting as they rely on new particles that typically lie around the TeV scale, hence accessible to collider searches.
Unlike seesaw models, radiative mechanisms can go beyond the effective dimensionfive operator in (1) and generate the neutrino masses at higher order. This leads to new operators and to further mass suppression. Such an approach has been reviewed in [7, 70–73]. In what follows we will survey some representative underlying models up to the third loop level.
3.1. OneLoop Schemes
A general survey of oneloop neutrino mass operators leading to neutrino mass has been performed in [6]. Neutrino mass models in extensions of the SM with singlet righthanded neutrinos have been systematically analyzed in [74, 75] and for higher representations in [76]. Here we review the most representative model realizations.
3.1.1. Zee Model
The Zee Model [77] extends the standard model with the following fields: where the subscript denotes lepton number. Given this particle content neutrino masses are oneloop calculable. The relevant terms are given by where indicate the flavor indices; that is, , , and is the second Pauli matrix. Notice that the matrix must be antisymmetric in generation indices. The violation of lepton number, required to generate a Majorana mass term for neutrinos, resides in the coexistence of the two Higgs doublets in the term. The oneloop radiative diagram is shown in Figure 7. The model has been extensively studied in the literature [78–101], particularly in the ZeeWolfenstein limit where only couples to leptons due to a symmetry [102].
This particular simplification forbids treelevel Higgsmediated flavorchanging neutral currents (FCNC), although it is now disfavored by neutrino oscillation data [90, 103]. However the general Zee model is still valid phenomenologically [87] and is in testable with FCNC experiments. For instance the exchange of the Higgs bosons leads to treelevel decays of the form , in particular (see, e.g., [104]). Collider phenomenology has been studied in [105, 106].
Recently, a variant of the Zee model has been considered in [107] by imposing a familydependent symmetry acting on the leptons, thereby reducing the number of effective free parameters to four. The model predicts inverse hierarchy spectrum in addition to correlations among the mixing angles.
3.1.2. Radiative Seesaw Model
Another oneloop scenario was suggested by Ma [108]. Besides the standard model fields, three righthanded Majorana fermions () and a Higgs doublet are added to the model: In addition, a parity symmetry acting only on the new fields is postulated. This is imposed in order to forbid Dirac neutrino mass terms. The relevant interactions of this model are given by In the scalar potential a quartic scalar term of the form is allowed. The oneloop radiative diagram is shown in Figure 8 and generates calculable if , which follows from the assumed symmetry. The neutrino masses are given by where () is the mass of the real (imaginary) part of the neutral component of .
Thanks to its simplicity and rich array of predictions, the model has become very popular and an extensive literature has been devoted to its phenomenological consequences. As is generally the case with multiHiggs standard model extensions, the induced lepton flavor violation effects such as provide a way to probe the model parameters. In particular the lepton flavor violation phenomenology has been studied in [109–114]. The effect of corrections induced by renormalization group running has also been considered [115], showing that highly symmetric patterns such as the bimaximal lepton mixing structure can still be valid at high energy but modified by the running to correctly account for the parameters required by the neutrino oscillation measurements [11]. Collider signatures have also been investigated in [116–119].
A remarkable feature of this model is the natural inclusion of a WIMP (weakly interacting massive particle) dark matter candidate. Indeed, the same parity that makes the neutrino mass calculable also stabilizes and the neutral component of . The lightest odd particle, either a boson or a fermion, can play the role of WIMP cold dark matter candidate [109, 111, 114, 120–124]. There is also the interesting possibility of the dark matter being warm in this setup [110, 125]. Various extensions of the model have also been considered, for example, [126, 127]. For a review on models with oneloop radiative neutrino masses and viable dark matter candidates we refer the reader to the complete classification given in [128, 129].
3.2. TwoLoop Schemes
As a prototype twoloop scheme we consider the model proposed by Zee [130] and Babu [34] (which first appeared in [22]) that leads to neutrino masses at twoloop level by extending the standard model with two complex singly and doubly [131] charged singlet scalars The relevant terms in the Lagrangian are therefore The trilinear term in the scalar potential (this term can arise spontaneously through the vev of an extra gauge singlet scalar boson [132]) provides lepton number violation and leads to a calculable Majorana neutrino mass generated at the second loop order, as shown in Figure 9 and given by where and are charged lepton masses [133]. As in the Zee model, the matrix is antisymmetric. Therefore the determinant of vanishes and, as a result, one of the light neutrinos must be massless.
The ZeeBabu model is constrained by a variety of lepton flavor violation processes among which the treelevel lepton flavor violation decays induced by exchange and the radiative decays mediated by the charged scalars and . Weak universality is also violated since the exchange induces new contributions for muon decay [133–136]. Both lepton flavor violation and weak universality tests constrain the model parameters. Combining lepton flavor violation and universality constraints [134] pushes the mass of and above the TeV scale, for both inverted and normal hierarchies, making it a challenge to probe the model at the LHC. The collider phenomenology of the model has been considered in [133, 134, 137].
3.3. ThreeLoop Schemes
Of the possible threeloop schemes we will focus on the one suggested by KraussNasriTrodden (KNT) [138]. These authors considered an extension of the standard model with two charged scalar singlets and and one righthanded neutrino . Consider the following: As usual in radiative neutrino mass models that include gauge singlet Majorana fermions, an additional symmetry is imposed, under which the standard model fields as well as transform trivially, while and are odd. The most general renormalizable terms that may be added to the standard model fermion Lagrangian are Note that the scalar potential contains a term of the form , which makes the diagram of Figure 10 possible. Hence neutrinos acquire Majorana masses induced only at the 3loop level. Such strong suppression allows for sizable couplings of the TeVscale singlet messenger states.
In addition to neutrino masses, the model also includes a WIMP dark matter candidate. Indeed for the choice of parameters , is stable and can be thermally produced in the early universe, leading naturally to the correct dark matter abundance.
A very similar model with the same loop topology has been proposed in [139], replacing the neutral gauge singlets by new colored fields and the charged leptons by quarks and in [140] the triplet variant of the model has been introduced. These variations make the model potentially testable at hadron colliders. Other three loop mass models have also been considered more recently, for instance, in [140–143]. A systematic study generalizing the KNT model was presented in [144] (Table 2).

We summarize the models discussed in this section and their phenomenological implications in Table 2.
4. Supersymmetry as the Origin of Neutrino Masses
The standard formulation of supersymmetry assumes the conservation of a discrete symmetry called parity (), under which all the standard model states are even, while their superpartners are odd [145]. is related to the spin (), total lepton (), and baryon () number as Hence requiring baryon and lepton number conservation implies conservation. In this case the supersymmetric states must be produced in pairs, while the lightest of them is absolutely stable.
On general grounds, however, neither gauge invariance nor supersymmetry requires conservation and many implications can be associated to parity violation [146]. The most general supersymmetric standard model extension contains explicit violating interactions. Constraints on the relevant parameters and their possible signals have been analysed [147, 148]. In general, there are too many independent couplings, some of which must be set to zero in order to avoid too fast the proton decay. For these reasons we focus our attention to the possibility that can be an exact symmetry of the Lagrangian, broken spontaneously through the Higgs mechanism [35, 149]. This may occur via nonzero vacuum expectation values for scalar neutrinos, such as
Here we consider the simplest prototype scheme where supersymmetry seeds neutrino masses in an essential way. The idea is to take the simplest effective description of the above picture, namely, bilinear parity violation [150–152]. This is the minimal way to incorporate lepton number and parity violation to the minimal supersymmetric standard model (MSSM), providing a simple way to accommodate neutrino masses in supersymmetry. The superpotential is The three parameters have dimensions of mass and explicitly break lepton number by . Their size and origin can be naturally explained in extended models where the breaking of lepton number is spontaneous [35, 149, 152]. These parameters are constrained to be small () so as to account for the small neutrino masses. Furthermore, the presence of the new superpotential terms implies new soft supersymmetry breaking terms as well where the are parameters with units of mass.
In this scheme, neutrinos get treelevel mass by mixing with the neutralino sector [153–155]. In the basis the neutral fermion mass matrix this matrix is given by where is the usual neutralino mass matrix and is the matrix describing parity violation. Here are the vevs of sneutrinos induced by the presence of and . The smallness of the parity violating parameters implies that the components of are suppressed with respect to those in . Hence the resulting matrix has a typeI seesaw structure so the effective light neutrino mass matrix can be obtained from the usual formula , which can be expanded to give where is a combination of SUSY parameters, while are known as the alignment parameters. The above matrix is projective and has two zero eigenvalues; therefore only one neutrino is massive at tree level. A natural choice is to ascribe this eigenvalue to the atmospheric scale whereas the solar mass scale, , arises from quantum corrections calculable at the oneloop level of the neutrino mass matrix in (38). Detailed computations of the oneloop contributions to the neutrino mass matrix are given in [153, 154]. The corrections are of the type where the coefficients , , and are complicated functions of the SUSY parameters. These corrections generate a second nonzero mass eigenstate associated with the solar scale and the corresponding mixing angle (the neutrino mixing angles are determined as ratios of parity violating parameters and ) .
The bilinear parity breaking model offers a hybrid mechanism combining seesawtype and radiative contributions, thereby providing an explanation for the observed smallness of the solar squared mass splitting with respect to the atmospheric one.
The above scheme is both well motivated and testable at colliders. Indeed in the absence of parity, the lightest supersymmetric particle (LSP) is no longer protected and decays to standard model particles. The smallness of the breaking strength, required to account for neutrino masses, makes the lifetime of the LSP long enough so that it may decay within the detector with displaced vertices. Since LSP decays and neutrino masses have a common origin, one can show that ratios of LSP decay branching ratios correlate with the neutrino mixing angles measured at low energies [156]. This provides a remarkable connection which allows one to use neutrino oscillation data to test the model at the LHC; see, for example, [157, 158].
5. Summary and Outlook
We have given a brief overview of the lowscale approach to neutrino mass generation. To chart out directions within such a broad neutrino landscape we used their possible phenomenological potential as a guide. We analyzed signatures associated to direct neutrino mass messenger production at the LHC, as well as messengerinduced lepton flavor violation processes. We have considered seesawbased schemes as well as those with radiative or supersymmetric origin for the neutrino mass. We summarize our conclusions in Table 3. We stressed the phenomenological interest on radiative models and lowscale seesaw schemes as well as the typeII seesaw “tuned” to lie at the low scale. We also briefly comment on the presence of WIMP cold dark matter candidates.
 
As we have explained in the text, “✗” could change to “✓” in the presence of new gauge bosons or supersymmetry. 
In conclusion if the messengers responsible for the light neutrino masses lie at a very high scale, like in typeI seesaw, it will be very difficult if not impossible to have any detectable signal within the nonsupersymmetric seesaw framework. In contrast, within the lowscale approach to neutrino mass we can have very interesting phenomenological implications. They can give rise to signatures at high energy collider experiments, as well as lepton flavor violation rates close to the sensitivity of planned experiments. In some of the schemes there is a natural WIMP dark matter candidate. In short, these scenarios may help reconstructing the neutrino mass from a variety of potentially overconstrained set of observables.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This work was supported by the Spanish MINECO under Grants FPA201122975 and MULTIDARK CSD200900064 (ConsoliderIngenio 2010 Programme). Stefano Morisi thanks the DFG Grants WI 2639/31 and WI 2639/41 for financial support.
References
 ATLAS and CMS Collaboration, “Birth of a Higgs boson,” CERN Courier, vol. 53, no. 4, pp. 21–23, 2013. View at: Google Scholar
 G. Aad, T. Abajyan, B. Abbott et al., “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,” Physics Letters B, vol. 716, no. 1, pp. 1–29, 2012. View at: Publisher Site  Google Scholar
 S. Chatrchyan, V. Khachatryan, A. M. Sirunyan et al., “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC,” Physics Letters B, vol. 716, no. 1, pp. 30–61, 2012. View at: Google Scholar
 S. Weinberg, “Baryon and leptonnonconserving processes,” Physical Review Letters, vol. 43, article 1566, 1979. View at: Publisher Site  Google Scholar
 F. Bonnet, M. Hirsch, T. Ota, and W. Winter, “Systematic decomposition of the neutrinoless double beta decay operator,” Journal of High Energy Physics, vol. 2013, article 55, 2013. View at: Publisher Site  Google Scholar
 F. Bonnet, M. Hirsch, T. Ota, and W. Winter, “Systematic study of the $d=5$ Weinberg operator at oneloop order,” Journal of High Energy Physics, vol. 2012, no. 153, 2012. View at: Publisher Site  Google Scholar
 A. de Gouvea and J. Jenkins, “A survey of lepton number violation via effective operators,” Physical Review D, vol. 77, Article ID 013008, 2008. View at: Publisher Site  Google Scholar
 F. Bonnet, D. Hernandez, T. Ota, and W. Winter, “Neutrino masses from higher than d = 5 effective operators,” Journal of High Energy Physics, vol. 10, article 076, 2009. View at: Publisher Site  Google Scholar
 M. B. Krauss, D. Meloni, W. Porod, and W. Winter, “Neutrino mass from a $d=7$ effective operator in a SUSYGUT framework,” Journal of High Energy Physics, vol. 2013, no. 5, article 121, 2013. View at: Publisher Site  Google Scholar
 H. Nunokawa, S. J. Parke, and J. W. F. Valle, “CP violation and neutrino oscillations,” Progress in Particle and Nuclear Physics, vol. 60, pp. 338–402, 2008. View at: Publisher Site  Google Scholar
 D. Forero, M. Tortola, and J. W. F. Valle, “Global status of neutrino oscillation parameters after Neutrino2012,” Physical Review D, vol. 86, Article ID 073012, 2012. View at: Publisher Site  Google Scholar
 A. Osipowicz, H. Blumer, G. Drexlin et al., “KATRIN: a next generation tritium beta decay experiment with subeV sensitivity for the electron neutrino mass. Letter of intent,” http://arxiv.org/abs/hepex/0109033. View at: Google Scholar
 J. Lesgourgues, G. Mangano, G. Miele, and S. Pastor, Neutrino Cosmology, Cambridge University Press, Cambridge, UK, 2013.
 A. Barabash, “75 years of double beta decay: yesterday, today and tomorrow,” http://arxiv.org/abs/1101.4502. View at: Google Scholar
 E. Ma, “Pathways to naturally small neutrino masses,” Physical Review Letters, vol. 81, p. 1171, 1998. View at: Publisher Site  Google Scholar
 P. Minkowski, “$\mathit{\mu}\to \mathit{e}\mathit{\gamma}$ at a rate of one out of 10^{9} muon decays?” Physics Letters B, vol. 67, no. 4, pp. 421–428, 1977. View at: Publisher Site  Google Scholar
 T. Yanagida, “Horizontal symmetry and masses of neutrinos,” Conference Proceedings C, Article ID 7902131, pp. 95–99, 1979. View at: Google Scholar
 M. GellMann, P. Ramond, and R. Slansky, “Complex spinors and unified theories,” in Proceedings of the Supergravity Workshop C790927, pp. 315–321, 1979. View at: Google Scholar
 J. Schechter and J. W. F. Valle, “Neutrino masses in SU(2) ⊗ U(1) theories,” Physical Review D, vol. 22, p. 2227, 1980. View at: Publisher Site  Google Scholar
 R. N. Mohapatra and G. Senjanovic, “Neutrino mass and spontaneous parity nonconservation,” Physical Review Letters, vol. 44, p. 912, 1980. View at: Publisher Site  Google Scholar
 J. Schechter and J. W. F. Valle, “Neutrino decay and spontaneous violation of lepton number,” Physical Review D, vol. 25, p. 774, 1982. View at: Publisher Site  Google Scholar
 T. P. Cheng and L.F. Li, “Neutrino masses, mixings, and oscillations in SU(2)×U(1) models of electroweak interactions,” Physical Review D, vol. 22, no. 11, p. 2860, 1980. View at: Google Scholar
 M. Magg, C. Wetterich, and B. Phys. Lett, “Neutrino mass problem and gauge hierarchy,” Physics Letters B, vol. 94, pp. 61–64, 1980. View at: Publisher Site  Google Scholar
 C. Wetterich, “Neutrino masses and the scale of BL violation,” Nuclear Physics B, vol. 187, no. 2, pp. 343–375, 1981. View at: Publisher Site  Google Scholar
 R. N. Mohapatra and G. Senjanovic, “Neutrino masses and mixings in gauge models with spontaneous parity violation,” Physical Review D, vol. 23, p. 165, 1981. View at: Publisher Site  Google Scholar
 R. Foot, H. Lew, X. G. He, and G. C. Joshi, “Seesaw neutrino masses induced by a triplet of leptons,” Zeitschrift für Physik C: Particles and Fields, vol. 44, no. 3, pp. 441–444, 1989. View at: Publisher Site  Google Scholar
 J. Kersten and A. Y. Smirnov, “Righthanded neutrinos at LHC and the mechanism of neutrino mass generation,” Physical Review D, vol. 76, Article ID 073005, 2007. View at: Publisher Site  Google Scholar
 P.H. Gu, M. Hirsch, U. Sarkar, and J. W. F. Valle, “Neutrino masses, leptogenesis, and dark matter in a hybrid seesaw model,” Physical Review D, vol. 79, Article ID 033010, 2009. View at: Publisher Site  Google Scholar
 P. S. B. Dev, A. Pilaftsis, and U.K. Yang, “New production mechanism for heavy neutrinos at the LHC,” Physical Review Letters, vol. 112, Article ID 081801, 2014. View at: Publisher Site  Google Scholar
 R. N. Mohapatra and J. W. F. Valle, “Neutrino mass and baryonnumber nonconservation in superstring models,” Physical Review D, vol. 34, p. 1642, 1986. View at: Google Scholar
 E. Akhmedova, M. Lindnerb, E. Schnapkab, and J. Vallec, “Leftright symmetry breaking in NJL approach,” Physics Letters B, vol. 368, no. 4, pp. 270–280, 1996. View at: Publisher Site  Google Scholar
 E. Akhmedov, M. Lindner, E. Schnapka, and J. W. F. Valle, “Dynamical leftright symmetry breaking,” Physical Review D, vol. 53, p. 2752, 1996. View at: Publisher Site  Google Scholar
 M. Malinsky, J. C. Romao, and J. W. F. Valle, “Supersymmetric SO(10) seesaw mechanism with low BL scale,” Physical Review Letters, vol. 95, Article ID 161801, 2005. View at: Google Scholar
 K. S. Babu, “Model of “calculable” Majorana neutrino masses,” Physics Letters B, vol. 203, pp. 132–136, 1988. View at: Publisher Site  Google Scholar
 A. Masiero and J. Valle, “A model for spontaneous R parity breaking,” Physics Letters B, vol. 251, no. 2, pp. 273–278, 1990. View at: Publisher Site  Google Scholar
 J. C. Romao, C. A. Santos, and J. W. F. Valle, “How to spontaneously break R parity?” Physics Letters B, vol. 288, pp. 311–320, 1992. View at: Google Scholar
 P. Abreu, W. Adam, T. Adye et al., “Search for neutral heavy leptons produced in Z decays,” Zeitschrift für Physik C, vol. 74, no. 1, pp. 57–71, 1997. View at: Publisher Site  Google Scholar
 J. Beringer, J.F. Arguin, R. M. Barnett et al., “Review of particle physics,” Physical Review D, vol. 86, Article ID 010001, 2012. View at: Publisher Site  Google Scholar
 R. Franceschini, T. Hambye, and A. Strumia, “TypeIII seesaw mechanism at CERN LHC,” Physical Review D, vol. 78, Article ID 033002, 2008. View at: Publisher Site  Google Scholar
 F. Borzumati and A. Masiero, “Large muon and electronnumber nonconservation in supergravity theories,” Physical Review Letters, vol. 57, no. 8, pp. 961–964, 1986. View at: Publisher Site  Google Scholar
 M. Hirsch, J. W. F. Valle, W. Porod, J. C. Romao, and A. Villanova del Moral, “Probing minimal supergravity in the typeI seesaw mechanism with lepton flavor violation at the CERN LHC,” Physical Review D, vol. 78, Article ID 013006, 2008. View at: Publisher Site  Google Scholar
 J. Esteves, J. Romao, M. Hirsch et al., “LHC and lepton flavour violation phenomenology of a leftright extension of the MSSM,” Journal of High Energy Physics, vol. 1012, article 077, 2010. View at: Publisher Site  Google Scholar
 P. F. Perez, “Type III seesaw and leftright symmetry,” Journal of High Energy Physics, vol. 142, no. 3, 2009. View at: Publisher Site  Google Scholar  MathSciNet
 D. Aristizabal Sierra, M. Hirsch, J. W. F. Valle et al., “Reconstructing neutrino properties from collider experiments in a Higgs triplet neutrino mass model,” Physical Review D, vol. 68, Article ID 033006, 2003. View at: Publisher Site  Google Scholar
 J. N. Esteves, J. C. Romao, A. V. del Moral et al., “Flavour violation at the LHC: typeI versus typeII seesaw in minimal supergravity,” Journal of High Energy Physics, vol. 05, article 003, 2009. View at: Publisher Site  Google Scholar
 P. S. B. Dev and R. N. Mohapatra, “TeV scale inverse seesaw model in SO(10) and leptonic nonunitarity effects,” Physical Review D, vol. 81, Article ID 013001, 2010. View at: Publisher Site  Google Scholar
 C.H. Lee, P. Bhupal Dev, and R. Mohapatra, “Natural TeVscale leftright seesaw mechanism for neutrinos and experimental tests,” Physical Review D, vol. 88, Article ID 093010, 2013. View at: Google Scholar
 F. Deppisch, T. S. Kosmas, and J. W. F. Valle, “Enhanced ${\mu}^{}$${e}^{}$ conversion in nuclei in the inverse seesaw model,” Nuclear Physics B, vol. 752, pp. 80–92, 2006. View at: Publisher Site  Google Scholar
 F. Deppisch and J. W. F. Valle, “Enhanced lepton flavour violation in the supersymmetric inverse seesaw model,” Physical Review D, vol. 72, Article ID 036001, 2005. View at: Publisher Site  Google Scholar
 D. Forero, S. Morisi, M. Tortola, and J. W. F. Valle, “Lepton flavor violation and nonunitary lepton mixing in lowscale typeI seesaw,” Journal of High Energy Physics, vol. 2011, no. 9, article 142, 2011. View at: Publisher Site  Google Scholar
 J. Bernabeu, A. Santamaria, and J. Vidal, “Lepton flavour nonconservation at high energies in a superstring inspired standard model,” Physics Letters B, vol. 187, pp. 303–308, 1987. View at: Publisher Site  Google Scholar
 M. C. GonzalezGarcia and J. W. F. Valle, “Enhanced lepton flavor violation with massless neutrinos: a Study of muon and tau decays,” Modern Physics Letters A, vol. 7, p. 477, 1992. View at: Publisher Site  Google Scholar
 M. GonzalezGarcia and J. Valle, “Fast decaying neutrinos and observable flavour violation in a new class of majoron models,” Physics Letters B, vol. 216, no. 34, pp. 360–366, 1989. View at: Publisher Site  Google Scholar
 G. C. Branco, M. N. Rebelo, and J. W. F. Valle, “Leptonic CP violation with massless neutrinos,” Physics Letters B, vol. 225, no. 4, pp. 385–392, 1989. View at: Publisher Site  Google Scholar
 N. Rius and J. W. F. Valle, “Leptonic CP violating asymmetries in Z^{0} decays,” Physics Letters B, vol. 246, pp. 249–255, 1990. View at: Publisher Site  Google Scholar
 F. Bazzocchi, D. Cerdeno, C. Munoz, and J. W. F. Valle, “Calculable inverseseesaw neutrino masses in supersymmetry,” Physical Review D, vol. 81, Article ID 051701(R), 2010. View at: Publisher Site  Google Scholar
 F. Bazzocchi, “Minimal dynamical inverse seesaw mechanism,” Physical Review D, vol. 83, Article ID 093009, 2011. View at: Publisher Site  Google Scholar
 H. Hettmansperger, M. Lindner, and W. Rodejohann, “Phenomenological consequences of subleading terms in seesaw formulas,” Journal of High Energy Physics, vol. 2011, article 123, 2011. View at: Publisher Site  Google Scholar
 A. Das and N. Okada, “Inverse seesaw neutrino signatures at LHC and ILC,” Physical Review D, vol. 88, Article ID 113001, 2013. View at: Google Scholar
 V. de Romeri, M. Hirsch, and M. Malinský, “Soft masses in supersymmetric SO(10) GUTs with low intermediate scales,” Physical Review D, vol. 84, Article ID 053012, 2011. View at: Publisher Site  Google Scholar
 P. Nath, B. D. Nelson, H. Davoudiasl et al., “The hunt for new physics at the large hadron collider,” Nuclear Physics B: Proceedings Supplements, vol. 200–202, pp. 185–417, 2010. View at: Publisher Site  Google Scholar
 S. Das, F. Deppisch, O. Kittel, and J. Valle, “Heavy neutrinos and lepton flavor violation in leftright symmetric models at the LHC,” Physical Review D, vol. 86, Article ID 055006, 2012. View at: Publisher Site  Google Scholar
 J. AguilarSaavedra, F. Deppisch, O. Kittel, and J. Valle, “Flavor in heavy neutrino searches at the LHC,” Physical Review D, vol. 85, Article ID 091301, 2012. View at: Publisher Site  Google Scholar
 F. F. Deppisch, N. Desai, and J. W. F. Valle, “Is charged lepton flavour violation a high energy phenomenon?” Physical Review D, vol. 89, Article ID 051302, 2014. View at: Publisher Site  Google Scholar
 E. Ma, “Inverse seesaw neutrino mass from lepton triplets in the U(1)_sigma model,” Modern Physics Letters A, vol. 24, no. 31, p. 2491, 2009. View at: Publisher Site  Google Scholar
 D. Ibanez, S. Morisi, and J. W. F. Valle, “Inverse tribimaximal typeIII seesaw mechanism and lepton flavor violation,” Physical Review D, vol. 80, Article ID 053015, 2009. View at: Publisher Site  Google Scholar
 S. L. Glashow, J. Iliopoulos, and L. Maiani, “Weak interactions with leptonhadron symmetry,” Physical Review D, vol. 2, no. 7, pp. 1285–1292, 1970. View at: Publisher Site  Google Scholar
 P. Fileviez Perez, T. Han, G.Y. Huang, T. Li, and K. Wang, “Neutrino masses and the CERN LHC: testing the type II seesaw mechanism,” Physical Review D, vol. 78, Article ID 015018, 2008. View at: Publisher Site  Google Scholar
 F. del Aguila and J. A. AguilarSaavedra, “Distinguishing seesaw models at LHC with multilepton signals,” Nuclear Physics B, vol. 813, pp. 22–90, 2009. View at: Publisher Site  Google Scholar
 K. Babu and C. N. Leung, “Classification of effective neutrino mass operators,” Nuclear Physics B, vol. 619, pp. 667–689, 2001. View at: Publisher Site  Google Scholar
 P. W. Angel, N. L. Rodd, and R. R. Volkas, “Origin of neutrino masses at the LHC: $\Delta L=2$ effective operators and their ultraviolet completions,” Physical Review D, vol. 87, Article ID 073007, 2013. View at: Publisher Site  Google Scholar
 Y. Farzan, S. Pascoli, and M. A. Schmidt, “Recipes and ingredients for neutrino mass at loop level,” Journal of High Energy Physics, vol. 2013, article 107, 2013. View at: Google Scholar
 S. S. Law and K. L. McDonald, “The simplest models of radiative neutrino mass,” International Journal of Modern Physics A, vol. 29, no. 10, Article ID 1450064, 18 pages, 2014. View at: Publisher Site  Google Scholar
 A. Pilaftsis, “Radiatively induced neutrino masses and large Higgsneutrino couplings in the Standard Model with Majorana fields,” Zeitschrift für Physik C, vol. 55, no. 2, pp. 275–282, 1992. View at: Publisher Site  Google Scholar
 P. B. Dev and A. Pilaftsis, “Minimal radiative neutrino mass mechanism for inverse seesaw models,” Physical Review D, vol. 86, Article ID 113001, 2012. View at: Publisher Site  Google Scholar
 P. Fileviez Perez and M. B. Wise, “On the origin of neutrino masses,” Physical Review D, vol. 80, Article ID 053006, 2009. View at: Publisher Site  Google Scholar
 A. Zee, “A theory of lepton number violation and neutrino Majorana masses,” Physics Letters B, vol. 93, pp. 389–393, 1980. View at: Publisher Site  Google Scholar
 D. Aristizabal Sierra and D. Restrepo, “Leptonic charged Higgs decays in the Zee model,” Journal of High Energy Physics, vol. 2006, no. 8, article 036, 2006. View at: Publisher Site  Google Scholar
 A. Y. Smirnov and M. Tanimoto, “Is the Zee model the model of neutrino masses?” Physical Review D, vol. 55, pp. 1665–1671, 1997. View at: Publisher Site  Google Scholar
 C. Jarlskog, M. Matsuda, S. Skadhauge, and M. Tanimoto, “Zee mass matrix and bimaximal neutrino mixing,” Physics Letters B, vol. 449, pp. 240–252, 1999. View at: Publisher Site  Google Scholar
 P. H. Frampton and S. L. Glashow, “Can the Zee ansatz for neutrino masses be correct?” Physics Letters B, vol. 461, no. 12, pp. 95–98, 1999. View at: Publisher Site  Google Scholar
 A. S. Joshipura and S. D. Rindani, “QIsing neural network dynamics: a comparative review of various architectures,” Physics Letters B, vol. 464, p. 239, 1999. View at: Google Scholar
 G. McLaughlin and J. Ng, “Partitioning of a polymer chain between two confining cavities: the roles of excluded volume and finite size conduits,” Chemical Physics Letters, vol. 327, no. 34, pp. 238–244, 1999. View at: Publisher Site  Google Scholar
 K.M. Cheung and O. C. Kong, “Zee neutrino mass model in a SUSY framework,” Physical Review D, vol. 61, Article ID 113012, 2000. View at: Publisher Site  Google Scholar
 D. Chang and A. Zee, “Radiatively induced neutrino Majorana masses and oscillation,” Physical Review D, vol. 61, Article ID 071303(R), 2000. View at: Publisher Site  Google Scholar
 D. A. Dicus, H.J. He, and J. N. Ng, “Neutrinolepton masses, Zee scalars, and muon g2,” Physical Review Letters, vol. 87, Article ID 111803, 2001. View at: Publisher Site  Google Scholar
 K. Balaji, W. Grimus, and T. Schwetz, “The solar LMA neutrino oscillation solution in the Zee model,” Physics Letters B, vol. 508, no. 34, pp. 301–310, 2001. View at: Publisher Site  Google Scholar
 E. Mitsuda and K. Sasaki, “Zee model and phenomenology of lepton sector,” Physics Letters B, vol. 516, pp. 47–53, 2001. View at: Publisher Site  Google Scholar
 A. Ghosal, Y. Koide, and H. Fusaoka, “Lepton flavor violating Z decays in the Zee model,” Physical Review D, vol. 64, Article ID 053012, 2001. View at: Publisher Site  Google Scholar
 Y. Koide, “Can the Zee model explain the observed neutrino data?” Physical Review D, vol. 64, Article ID 077301, 2001. View at: Publisher Site  Google Scholar
 B. Brahmachari and S. Choubey, “Viability of bimaximal solution of the Zee mass matrix,” Physics Letters B, vol. 531, pp. 99–104, 2002. View at: Publisher Site  Google Scholar
 T. Kitabayashi and M. Yasue, “Large solar neutrino mixing in an extended zee model,” International Journal of Modern Physics A, vol. 17, no. 19, pp. 2519–2534, 2002. View at: Publisher Site  Google Scholar
 Y. Koide, “Prospect of the Zee model,” Nuclear Physics B—Proceedings Supplements, vol. 111, no. 1–3, pp. 294–296, 2002. View at: Publisher Site  Google Scholar
 M.Y. Cheng and K.M. Cheung, “Zee model and Neutrinoless double beta decay,” http://arxiv.org/abs/hepph/0203051. View at: Google Scholar
 X. G. He and A. Zee, “Some simple mixing and mass matrices for neutrinos,” Physics Letters B, vol. 560, no. 12, pp. 87–90, 2003. View at: Publisher Site  Google Scholar
 K. Hasegawa, C. Lim, and K. Ogure, “Escape from washing out of baryon number in a twozerotexture general Zee model compatible with the large mixing angle MSW solution,” Physical Review D, vol. 68, Article ID 053006, 2003. View at: Publisher Site  Google Scholar
 S. Kanemura, T. Ota, and K. Tsumura, “Lepton flavor violation in Higgs boson decays under the rare tau decay results,” Physical Review D, vol. 73, Article ID 016006, 2006. View at: Publisher Site  Google Scholar
 B. Brahmachari and S. Choubey, “Modified Zee mass matrix with zerosum condition,” Physics Letters B, vol. 642, pp. 495–502, 2006. View at: Publisher Site  Google Scholar
 N. Sahu and U. Sarkar, “Extended Zee model for neutrino mass, leptogenesis, and sterileneutrinolike dark matter,” Physical Review D, vol. 78, Article ID 115013, 2008. View at: Publisher Site  Google Scholar
 T. Fukuyama, H. Sugiyama, and K. Tsumura, “Phenomenology in the Zee model with the A_{4} symmetry,” Physical Review D, vol. 83, no. 5, Article ID 056016, 2011. View at: Publisher Site  Google Scholar
 F. del Aguila, A. Aparici, S. Bhattacharya, A. Santamaria, and J. Wudka, “Effective Lagrangian approach to neutrinoless double beta decay and neutrino masses,” Journal of High Energy Physics, vol. 2012, no. 6, article 146, 2012. View at: Publisher Site  Google Scholar
 L. Wolfenstein, “A theoretical pattern for neutrino oscillations,” Nuclear Physics B, vol. 175, pp. 93–96, 1980. View at: Publisher Site  Google Scholar
 P. H. Frampton, M. C. Oh, and T. Yoshikawa, “Zee model confronts SNO data,” Physical Review D, vol. 65, Article ID 073014, 2002. View at: Google Scholar
 X.G. He, “Is the Zee model neutrino mass matrix ruled out?” The European Physical Journal C, vol. 34, no. 3, pp. 371–376, 2004. View at: Publisher Site  Google Scholar
 S. Kanemura, T. Kasai, G.L. Lin et al., “Phenomenology of Higgs bosons in the Zee model,” Physical Review D, vol. 64, Article ID 053007, 2001. View at: Publisher Site  Google Scholar
 K. A. Assamagan, A. Deandrea, and P.A. Delsart, “Search for the lepton flavor violating decay ${A}^{0}/{H}^{0}\to {\tau}^{\pm}{\mu}^{\mp}$ at hadron colliders,” Physical Review D, vol. 67, Article ID 035001, 2003. View at: Publisher Site  Google Scholar
 K. Babu and J. Julio, “Predictive model of radiative neutrino masses,” http://arxiv.org/abs/1310.0303. View at: Google Scholar
 E. Ma, “Verifiable radiative seesaw mechanism of neutrino mass and dark matter,” Physical Review D, vol. 73, Article ID 077301, 2006. View at: Publisher Site  Google Scholar
 J. Kubo, E. Ma, and D. Suematsu, “Cold dark matter, radiative neutrino mass, mu to e gamma, and neutrinoless double beta decay,” Physics Letters B, vol. 642, pp. 18–23, 2006. View at: Google Scholar
 D. Aristizabal Sierra, J. Kubo, D. Restrepo, D. Suematsu, and O. Zapata, “Radiative seesaw model: warm dark matter, collider signatures, and lepton flavor violating signals,” Physical Review D, vol. 79, Article ID 013011, 2009. View at: Publisher Site  Google Scholar
 D. Suematsu, T. Toma, and T. Yoshida, “Reconciliation of CDM abundance and $\mu \to e\gamma $ in a radiative seesaw model,” Physical Review D, vol. 79, no. 4, Article ID 093004, 2009. View at: Publisher Site  Google Scholar
 A. Adulpravitchai, M. Lindner, and A. Merle, “Confronting flavor symmetries and extended scalar sectors with lepton flavor violation bounds,” Physical Review D, vol. 80, Article ID 055031, 2009. View at: Publisher Site  Google Scholar
 T. Toma and A. Vicente, “Lepton flavor violation in the scotogenic model,” Journal of High Energy Physics, vol. 1401, article 160, 2014. View at: Publisher Site  Google Scholar
 D. Schmidt, T. Schwetz, and T. Toma, “Direct detection of leptophilic dark matter in a model with radiative neutrino masses,” Physical Review D, vol. 85, Article ID 073009, 2012. View at: Publisher Site  Google Scholar
 R. Bouchand and A. Merle, “Running of radiative neutrino masses: the scotogenic model,” Journal of High Energy Physics, vol. 2012, no. 7, article 84, 2012. View at: Publisher Site  Google Scholar
 M. Aoki and S. Kanemura, “Probing the Majorana nature of TeVscale radiative seesaw models at collider experiments,” Physics Letters B, vol. 689, pp. 28–35, 2010. View at: Publisher Site  Google Scholar
 M. Aoki, S. Kanemura, and H. Yokoya, “Reconstruction of inert doublet scalars at the international linear collider,” Physics Letters B, vol. 725, no. 45, pp. 302–309, 2013. View at: Publisher Site  Google Scholar
 S.Y. Ho and J. Tandean, “Probing scotogenic effects in e^{+}e^{−} colliders,” Physical Review D, vol. 89, Article ID 114025, 2014. View at: Publisher Site  Google Scholar
 S.Y. Ho and J. Tandean, “Probing scotogenic effects in Higgs boson decays,” Physical Review D, vol. 87, Article ID 095015, 2013. View at: Publisher Site  Google Scholar
 Y. Kajiyama, J. Kubo, and H. Okada, “D_{6} family symmetry and cold dark matter at CERN LHC,” Physical Review D, vol. 75, Article ID 033001, 2007. View at: Publisher Site  Google Scholar
 D. Suematsu, T. Toma, and T. Yoshida, “Enhancement of the annihilation of dark matter in a radiative seesaw model,” Physical Review D, vol. 82, Article ID 013012, 2010. View at: Publisher Site  Google Scholar
 Y. Kajiyama, H. Okada, T. Toma, and J. C, “Direct and indirect detection of dark matter in D_{6} flavor symmetric model,” The European Physical Journal C, vol. 71, p. 1688, 2011. View at: Publisher Site  Google Scholar
 Y. Kajiyama, H. Okada, and T. Toma, “A light scalar dark matter for CoGeNT and DAMA in D_6 flavor symmetric model,” http://arxiv.org/abs/1109.2722. View at: Google Scholar
 M. Klasen, C. E. Yaguna, J. D. RuizAlvarez, D. Restrepo, and O. Zapata, “Scalar dark matter and fermion coannihilations in the radiative seesaw model,” Journal of Cosmology and Astroparticle Physics, vol. 1304, article 044, 2013. View at: Google Scholar
 P.K. Hu, “Radiative seesaw model with nonzero θ_{13} and warm dark matter scenario,” http://arxiv.org/abs/1208.2613. View at: Google Scholar
 M. Hirsch, R. Lineros, S. Morisi, J. Palacio, N. Rojas, and J. W. F. Valle, “WIMP dark matter as radiative neutrino mass messenger,” Journal of High Energy Physics, vol. 2013, article 149, 2013. View at: Google Scholar
 V. Brdar, I. Picek, and B. Radovcic, “Radiative neutrino mass with scotogenic scalar triplet,” Physics Letters B, vol. 728, pp. 198–201, 2014. View at: Publisher Site  Google Scholar
 D. Restrepo, O. Zapata, and C. E. Yaguna, “Models with radiative neutrino masses and viable dark matter candidates,” Journal of High Energy Physics, vol. 2013, article 11, 2013. View at: Publisher Site  Google Scholar
 S. S. Law and K. L. McDonald, “A class of inert Ntuplet models with radiative neutrino mass and dark matter,” Journal of High Energy Physics, vol. 2013, no. 9, article 92, 2013. View at: Publisher Site  Google Scholar
 A. Zee, “Quantum numbers of Majorana neutrino masses,” Nuclear Physics B, vol. 264, pp. 99–110, 1986. View at: Publisher Site  Google Scholar
 J. Schechter and J. W. F. Valle, “Neutrinoless double$\beta $ decay in SU(2)×U(1) theories,” Physical Review D, vol. 25, p. 2951, 1982. View at: Google Scholar
 J. T. Peltoniemi and J. W. F. Valle, “Massive neutrinos and electroweak baryogenesis,” Physics Letters B, vol. 304, no. 12, pp. 147–151, 1993. View at: Publisher Site  Google Scholar
 M. Nebot, J. F. Oliver, D. Palao, and A. Santamaria, “Prospects for the ZeeBabu Model at the LHC and low energy experiments,” Physical Review D, vol. 77, Article ID 093013, 2008. View at: Publisher Site  Google Scholar
 D. Schmidt, T. Schwetz, and H. Zhang, “Status of the Zee–Babu model for neutrino mass and possible tests at a likesign linear collide,” vol. 885, pp. 524–541, 2014. View at: Publisher Site  Google Scholar
 K. S. Babu and C. Macesanu, “Twoloop neutrino mass generation and its experimental consequences,” Physical Review D, vol. 67, no. 7, Article ID 073010, 2003. View at: Publisher Site  Google Scholar
 D. Aristizabal Sierra and M. Hirsch, “Experimental tests for the BabuZee twoloop model of Majorana neutrino masses,” Journal of High Energy Physics, vol. 2006, no. 12, article 052, 2006. View at: Publisher Site  Google Scholar
 J. HerreroGarcia, M. Nebot, N. Rius, and A. Santamaria, “The ZeeBabu Model revisited in the light of new data,” http://arxiv.org/abs/1402.4491. View at: Google Scholar
 L. M. Krauss, S. Nasri, and M. Trodden, “Model for neutrino masses and dark matter,” Physical Review D, vol. 67, Article ID 085002, 2003. View at: Publisher Site  Google Scholar
 J. N. Ng and A. de la Puente, “Top quark as a dark portal and neutrino mass generation,” Physics Letters B, vol. 727, no. 1–3, pp. 204–210, 2013. View at: Publisher Site  Google Scholar
 A. Ahriche, C.S. Chen, K. L. McDonald, and S. Nasri, “A threeloop model of neutrino mass with dark matter,” http://arxiv.org/abs/1404.2696. View at: Google Scholar
 M. Aoki, S. Kanemura, and O. Seto, “Neutrino mass, dark matter, and Baryon asymmetry via TeVscale physics without finetuning,” Physical Review Letters, vol. 102, no. 5, Article ID 051805, 2009. View at: Publisher Site  Google Scholar
 M. Aoki, S. Kanemura, and O. Seto, “Model of TeV scale physics for neutrino mass, dark matter, and baryon asymmetry and its phenomenology,” Physical Review D, vol. 80, Article ID 033007, 2009. View at: Publisher Site  Google Scholar
 M. Gustafsson, J. M. No, and M. A. Rivera, “Predictive model for radiatively induced neutrino masses and mixings with dark matter,” Physical Review Letters, vol. 110, Article ID 211802, 2013. View at: Publisher Site  Google Scholar
 C.S. Chen, K. L. McDonald, and S. Nasri, “A class of threeloop models with neutrino mass and dark matter,” Physics Letters B, vol. 734, pp. 388–393, 2014. View at: Publisher Site  Google Scholar
 S. P. Martin, A Supersymmetry Primer, vol. 21 of Advanced Series on Directions in High Energy Physics, 2010, http://arxiv.org/abs/hepph/9709356.
 R. Barbier, “Rparity violating supersymmetry,” Physics Reports, vol. 420, no. 1–6, pp. 1–195, 2005. View at: Publisher Site  Google Scholar
 V. Barger, G. F. Giudice, and T. Han, “Some new aspects of supersymmetry Rparity violating interactions,” Physical Review D, vol. 40, no. 9, pp. 2987–2996, 1989. View at: Publisher Site  Google Scholar
 H. Baer and X. Tata, Weak Scale Supersymmetry: From Superfields to Scattering Events, Cambridge University Press, Cambridge, UK, 2006.
 P. Nogueira, J. Romao, and J. Valle, “Supersymmetry phenomenology with spontaneous R parity breaking in Z^{0} decays,” Physics Letters B, vol. 251, pp. 142–149, 1990. View at: Publisher Site  Google Scholar
 L. J. Hall and M. Suzuki, “Explicit Rparity breaking in supersymmetric models,” Nuclear Physics B, vol. 231, no. 3, pp. 419–444, 1984. View at: Google Scholar
 M. A. Díaz, J. C. Romão, and J. W. F. Valle, “Minimal supergravity with Rparity breaking,” Nuclear Physics B, vol. 524, no. 12, pp. 23–40, 1998. View at: Publisher Site  Google Scholar
 J. C. Romao, A. Ioannisian, and J. W. F. Valle, “Supersymmetric unification with radiative breaking of R parity,” Physical Review D, vol. 55, no. 1, pp. 427–430, 1997. View at: Publisher Site  Google Scholar
 M. Hirsch, M. A. Díaz, W. Porod, J. C. Romão, and J. W. F. Valle, “Neutrino masses and mixings from supersymmetry with bilinear Rparity violation: a theory for solar and atmospheric neutrino oscillations,” Physical Review D, vol. 62, Article ID 113008, 2000. View at: Publisher Site  Google Scholar
 M. A. Diaz, M. Hirsch, W. Porod, J. C. Romão, and J. W. F. Valle, “Solar neutrino masses and mixing from bilinear Rparity broken supersymmetry: analytical versus numerical results,” Physical Review D, vol. 68, Article ID 013009, 2003. View at: Publisher Site  Google Scholar
 E. J. Chun and S. K. Kang, “Oneloop corrected neutrino masses and mixing in the supersymmetric standard model without R parity,” Physical Review D, vol. 61, Article ID 075012, 2000. View at: Publisher Site  Google Scholar
 B. Mukhopadhyaya, S. Roy, and F. Vissani, “Correlation between neutrino oscillations and collider signals of supersymmetry in an Rparity violating model,” Physics Letters B, vol. 443, no. 1–4, pp. 191–195, 1998. View at: Publisher Site  Google Scholar
 F. de Campos, O. Eboli, M. Magro et al., “Probing neutralino properties in minimal supergravity with bilinear Rparity violation,” Physical Review D, vol. 86, Article ID 075001, 2012. View at: Publisher Site  Google Scholar
 F. de Campos, O. J. P. Éboli, M. Hirsch et al., “Probing neutrino oscillations in supersymmetric models at the Large Hadron Collider,” Physical Review D, vol. 82, no. 7, Article ID 075002, 2010. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2014 Sofiane M. Boucenna et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.