We study the minimal seesaw model, where two right-handed Majorana neutrinos are introduced, focusing on the CP violating phase. In addition, we take the trimaximal mixing pattern for the neutrino flavor where the charged lepton mass matrix is diagonal. Thanks to this symmetric framework, the $3\times 2$ Dirac neutrino mass matrix is given in terms of a few parameters. Numerical studies reveal that the observation of the CP violating phase can determine the flavor structure of the Dirac neutrino mass matrix in the minimal seesaw model. In particular, new minimal Dirac neutrino mass matrices are proposed in the case of $\rm TM_1$, which is derived by the additional 2-3 family mixing to the tri-bimaximal mixing basis in the normal hierarchy of neutrino masses. Our analyses include the Littlest seesaw model by King {\it et al.}, which is one of the specific one in our results. Furthermore, it is remarked that our $3\times 2$ Dirac neutrino mass matrix is reproduced by introducing gauge singlet flavons with the specific alignments of the VEV's. These alignments suggest the residual symmetry of $S_4$ group.
In supersymmetric (SUSY) extensions of the seesaw mechanism the neutrino Yukawa interaction induces the flavor and CP violating sfermion mass terms via the radiative correction. In this article we review the CP violating phenomena in the SUSY seesaw models.
We discuss the impact of fermion mass matrices on some lepton number violating processes, namely baryogenesis via leptogenesis and neutrinoless double beta decay, and on some lepton flavor violating processes, namely radiative lepton decays in supersymmetric seesaw models.
In the minimal seesaw model, we derive required constraints on Dirac neutrino masses inducing maximal CP violation in neutrino oscillations. If the maximal atmospheric neutrino mixing is further assumed, Dirac neutrino masses are uniquely determined to respect $μ$-$τ$ flavored CP symmetry for neutrinos.
We study the constraints on a minimal supersymmetric seesaw model imposed by neutrino data, charged lepton flavor violation, thermal leptogenesis and perturbativity. We show that it is possible to constrain the three heavy Majorana neutrino masses as well as the complex Yukawa coupling matrix. Our results provide a first step towards a seesaw benchmark model for further phenomenological studies and model building.
A variation of the original 2006 radiative seesaw model of neutrino mass through dark matter is shown to realize the notion of inverse seesaw naturally. The dark-matter candidate here is the lightest of three real singlet scalars which may also carry flavor.
We study the possibility of connecting leptonic Dirac CP phase $δ$, lightest neutrino mass and baryon asymmetry of the Universe within the framework of a model where both type I and type II seesaw mechanisms contribute to neutrino mass. Type I seesaw gives rise to Tri-Bimaximal (TBM) type neutrino mixing whereas type II seesaw acts as a correction in order to generate non-zero $θ_{13}$. We derive the most general form of type II seesaw mass matrix which can not only give rise to correct neutrino mixing angles but also can generate non-trivial value of $δ$. Considering both the cases where type…
We reveal the origin of the CP violation required by the leptogenesis in variously popular seesaw models. Especially we clarify that in a pure type-I/III seesaw with two fermion singlets/triplets, a combined type-I+III seesaw with one fermion singlet and one fermion triplet, or a combined type-I/III+II seesaw with one fermion singlet/triplet and one Higgs triplet, the CP violation for the leptogenesis can exactly come from the imaginary part of the neutrino mass matrix in a special basis where the Yukawa couplings involving one fermion singlet/triplet are allowed to get rid of any CP phases. W…
If neutrino masses are obtained via the canonical seesaw mechanism, based on an underlying 2X2 mass matrix, unitarity violation of the neutrino mixing matrix is unavoidable, but its effect is extremely small. On the other hand, in the inverse (and linear) seesaw mechanisms, based on an underlying 3X3 mass matrix, it can be significant and possibly observable. This 3X3 matrix is examined in more detail, and a NEW variation (the lopsided seesaw) is proposed which has features of both mechanisms. A concrete example based on U(1)_N is discussed.
The radiative seesaw mechanism proposed recently is minimally extended to include supersymmetry in a specific model. Relevant related issues such as leptogenesis and dark matter are discussed.
We discuss the linkage between dark matter mass in the one-loop radiative seesaw model and the effective neutrino mass for the neutrino less double beta decay. This linkage, which has been already numerically suggested, is confirmed to be a reasonable relationship by deriving analytical expressions for two zero flavor neutrino mass texture.
We discuss neutrino mass and mixing in the framework of the classic seesaw mechanism, involving right-handed neutrinos with large Majorana masses, which provides an appealing way to understand the smallness of neutrino masses. However, with many input parameters, the seesaw mechanism is in general not predictive. We focus on natural implementations of the seesaw mechanism, in which large cancellations do not occur, where one of the right handed neutrinos is dominantly responsible for the atmospheric neutrino mass, while a second right-handed neutrino accounts for the solar neutrino mass, leadi…
We propose two different seesaw models namely, type I and inverse seesaw to realise light Dirac neutrinos within the framework of $A_4$ discrete flavour symmetry. The additional fields and their transformations under the flavour symmetries are chosen in such a way that naturally predicts the hierarchies of different elements of the seesaw mass matrices in these two types of seesaw mechanisms. For generic choices of flavon alignments, both the models predict normal hierarchical light neutrino masses with the atmospheric mixing angle in the lower octant. Apart from predicting interesting correla…
If it can be ascertained experimentally that the 3X3 Majorana neutrino mass matrix M_nu has vanishing determinants for one or more of its 2X2 submatrices, it may be interpreted as supporting evidence for the theoretically well-known canonical seesaw mechanism. I show how these two things are connected and offer a realistic M_nu with two zero subdeterminants as an example.
The inverse seesaw mechanism of neutrino mass, i.e. m_nu = (m_D^2/m_N^2)epsilon_L where epsilon_L is small, is discussed in the context of the U(1)_Sigma model. This is a gauge extension of the Standard Model of particle interactions with lepton triplets (Sigma^+,Sigma^),Sigma^-) as (Type III) seesaw anchors for obtaining small Majorana neutrino masses.
In the standard seesaw model, finite corrections to the neutrino mass matrix arise from one-loop self-energy diagrams mediated by heavy neutrinos. We discuss the impact that these corrections may have on the different entries of the tree-level effective neutrino mass matrix, paying special attention to their dependence with the seesaw model parameters. We also briefly comment on the implications these corrections might have on low-energy neutrino observables.
So far we have not been able to establish that, as theoretically expected, neutrinos are their own anti-particles. Here we propose a dynamical way to account for the Dirac nature of neutrinos and the smallness of their mass in terms of a new variant of the seesaw paradigm in which the energy scale of neutrino mass generation could be accessible to the current LHC experiments.
Seesaw Neutrino Mass Ratios with Radiative Corrections
在正则上夸克跷跷板中，轻中微子质量的比例比质量本身更容易预测。在明确列举的必要但最小的假设下，得到这些比率，包括辐射校正。预测仍然是不确定的，只有顶夸克质量和平凡质量的限制，和跷跷板的幂律。τ中微子特别受到重顶夸克质量的非线性效应的影响。导出的比值适用于太阳，大气和宇宙学中微子和实验室中微子振荡搜索。而与带电轻子质量的跷跷板被简要考虑。提交给Phys Lett B。
We reformulate the canonical seesaw mechanism in the case that the electroweak gauge symmetry is unbroken, and show that it can "formally" work and allow us to derive an exact seesaw formula for the light and heavy Majorana neutrinos. We elucidate the reason why there is a mismatch between the mass eigenstates of heavy Majorana neutrinos associated with thermal leptogenesis and those associated with the seesaw framework, and establish the exact and explicit relations between the "original" and "derivational" seesaw parameters by using an Euler-like parametrization of the $6\times 6$ active-ste…
The Minimal Flavor Violation hypothesis (MFV) is extended to the R-parity violating MSSM, supplemented with a simple seesaw mechanism. The requirement of MFV is shown to suppress lepton and baryon-number violating couplings sufficiently to pass all experimental bounds, in particular those for proton decay, and is thus a viable alternative to R-parity. The phenomenological consequences for FCNC, LFV and colliders are briefly discussed. Typically, MFV predicts sizeable baryon-number violation in some characteristic channels, like single stop resonant production.
The seesaw mechanism can play a key role in the generation of the leptonic mixing in unified models. We consider an unified model with a family symmetry and extended seesaw, and obtain viable fermion masses and mixing (leptonic mixing is close to tri-bi-maximal).
In the framework of type II seesaw mechanism we discuss the number of sterile right-handed Majorana neutrinos being the warm dark matter (WDM). When the type II seesaw mass term $M_ν^{II}$ is far less than the type I seesaw mass term $M_ν^{I}$, only one of three sterile neutrinos may be the WDM particle. On the contrary, the WDM particles may contain all sterile neutrinos. If $M_ν^{II} \sim M_ν^{I}$, the allowed number is not more than $N - 1$ for $N$ sterile neutrinos. It is worthwhile to stress that three different types of neutrino mass spectrum are permitted when $M_ν^{II} \gg M_ν^{I}$ and…
If the canonical seesaw mechanism alone is responsible for neutrino mass, i.e. m_nu = -m_D^2/m_N, it can neither be proved nor disproved at the TeV energy scale. A new verifiable mechanism of neutrino mass is proposed, using the "inverse" seesaw, with new physics at the TeV scale, such that m_nu = m_D^2 epsilon_L/m_N^2, where epsilon_L is a two-loop effect. Dark-matter candidates also appear naturally.
We consider the threshold effect on the renormalization group (RG) evolution of the neutrino masses and mixing angles in TeV scale seesaw models. We obtain the analytic expressions using the factorization method in presence of threshold effects. We also perform numerical study of RG effects in two specific low scale seesaw models following the bottom-up approach and ascertain the role of seesaw thresholds in altering the values of masses and mixing angles during RG evolution.
We propose a Standard Model extension with underlying A4 flavour symmetry where small Dirac neutrino masses arise from a Type-II seesaw mechanism. The model predicts the "golden" flavour-dependent bottom-tau mass relation, requires an inverted neutrino mass ordering and non-maximal atmospheric mixing angle. Using the latest neutrino oscillation global fit we derive restrictions on the oscillation parameters, such as a correlation between Dirac CP phase and the lightest neutrino mass.
We suggest a hybrid seesaw model where relatively ``light''right-handed neutrinos give no contribution to the neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings to the standard model particles to be relatively strong, so that the standard model Higgs boson can decay dominantly to a left and a right-handed neutrino, leaving another stable right-handed neutrino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry via the lepto…
Renewed interest in GeV-scale sterile neutrinos capable of explaining active neutrino oscillations via see-saw type I mechanism has been expressed in several proposals of direct searches. Given this activity we estimate the minimal values of sterile-active mixing angles provided one, two, or three sterile neutrinos are lighter than D-meson.
We study parameters of an extended standard model. The neutrino sector is enlarged by one or two right-handed singlet fields and the Higgs sector contains one additional doublet. One-loop radiative corrections generate the mass for the light neutrino fields. The numerical analysis is performed varying the masses of heavy neutrinos and of the additional neutral Higgses. The parameters of the neutrino sector, allowing for the seesaw type-I mechanism, are restricted by experimental neutrino oscillation data. Both normal and inverted hierarchies of the light neutrino masses are discussed.
We perform a detailed analysis of the one-loop corrections to the light neutrino mass matrix within low scale type I seesaw extensions of the Standard Model and their implications in experimental searches for neutrinoless double beta decay. We show that a sizable contribution to the effective Majorana neutrino mass from the exchange of heavy Majorana neutrinos is always possible, provided one requires a fine-tuned cancellation between the tree-level and one-loop contribution to the light neutrino masses. We quantify the level of fine-tuning as a function of the seesaw parameters and introduce …
We study the RH neutrino properties from the low energy neutrino data in the seesaw mechanism. Reonance behavior is found for the right-handed (RH) mixing angle as a function of light neutrino mass ratios in two favored region of the solar neutrino problem and, at the resonance point, the two corresponding RH Majorana neutrino masses are degenerate. This phenomenon is similar with that in the matter-enhanced conversion of neutrinos. The physical significance it infers for the electron neutrino mass and other neutrino parameters is discussed.
The seesaw model of heavy and light Majorana neutrinos and its low-energy effective theory are studied, when the number of heavy neutrinos is equal to or less than the number of light lepton generations. We establish a general relationship between the high-energy parameters and the low-energy observables involving only the light fields. It is shown how low-energy measurements of the properties of light neutrinos suffice a priori to determine all couplings of the unobserved heavy neutrinos. CP violation is present in low-energy processes if seesaw-model leptogenesis creates the matter-antimatte…
We study the possibility of generating deviations from tri-bimaximal (TBM) neutrino mixing to explain the non-zero reactor mixing angle within the framework of both type I and type II seesaw mechanisms. The type I seesaw term gives rise to the $μ-τ$ symmetric TBM pattern of neutrino mass matrix as predicted by generic flavor symmetry models like $A_4$ whereas the type II seesaw term gives rise to the required deviations from TBM pattern to explain the non-zero $θ_{13}$. Considering extremal values of Majorana CP phases such that the neutrino mass eigenvalues have the structure $(m_1, -m_2, m_3…
In minimal trinification models light neutrino masses can be generated via a radiative see-saw mechanism, where the masses of the right-handed neutrinos originate from loops involving Higgs and fermion fields at the unification scale. This mechanism is absent in models aiming at solving or ameliorating the hierarchy problem, such as low-energy supersymmetry, since the large seesaw-scale disappears. In this case, neutrino masses need to be generated via a TeV-scale mechanism. In this paper, we investigate an inverse seesaw mechanism and discuss some phenomenological consequences.
Future experiments such as SHiP and high-intensity $e^+ e^-$ colliders will have a superb sensitivity to heavy Majorana neutrinos with masses below $M_Z$. We show that the measurement of the mixing to electrons and muons of one such state could imply the discovery of leptonic CP violation in the context of seesaw models. We quantify in the minimal model the CP discovery potential of these future experiments, and demonstrate that a 5$σ$ CL discovery of leptonic CP violation would be possible in a very significant fraction of parameter space.
If a family symmetry exists so that all three neutrinos have equal Majorana masses (via the seesaw mechanism), then the breaking of this symmetry from charged-lepton masses (via two-loop double $W$ exchange) implies $Δm$ less than about $10^{-9}m_0$. With the common mass $m_0 \sim$ eV for hot dark matter, $Δm^2 \sim 10^{-10}$ eV$^2$ is natural for vacuum solar neutrino oscillations.
Neutrino flavor mixing is explained within the recently proposed low-scale minimal linear seesaw model of neutrino mass generation, a variant of the standard linear seesaw led by a Dirac pair of extra sterile neutrinos which is odd under a discrete $Z_2$ symmetry and has a mass at or below the GeV scale. The tri-bimaximal mixing and its deviations are derived straightforwardly on the basis of the symmetry between $μ$ and $τ$ flavors, without introducing non-abelian discrete flavor symmetries in the first place.
In the standard seesaw model, finite corrections to the neutrino mass matrix arise from one-loop self-energy diagrams mediated by a heavy neutrino. We discuss the impact that these corrections may have on the different low-energy neutrino observables paying special attention to their dependence with the seesaw model parameters. It is shown that sizable deviations from the tri-bimaximal mixing pattern can be obtained when these corrections are taken into account.
The seesaw mechanism for three neutrinos is discussed, clarifying the situation where the seesaw texture results in three approximately zero mass eigenvalues. The true underlying mechanism is shown to be just the $inverse$ (or $linear$) seesaw, which explains why there could be large mixing. However, these zeroes cannot occur naturally, unless there is a conserved symmetry, i.e. lepton number $L$, either global or gauged, which is softly or spontaneously broken at the TeV scale. We discuss in particular the case where the three heavy singlet neutrinos have $L=3,-2,-1$.
We consider different extensions of the standard model which can give rise to the small active neutrino masses through seesaw mechanisms, and their mixing. These tiny neutrino masses are generated at some high energy scale by the heavy seesaw fields which then get sequentially decoupled to give an effective dimension-5 operator. The renormalization group evolution of the masses and the mixing parameters of the three active neutrinos in the high energy as well as the low energy effective theory is reviewed in this article.
The simplest possibility to generate small Majorana neutrino masses is the seesaw mechanism. However, the smallness of the observed neutrino masses can also be understood, if neutrino masses are generated by higher-dimensional operators and/or at higher loop level. In this talk recent work on systematic classifications of higher-dimensional and radiative neutrino mass models is summarized. Two particular classes of special genuine loop diagrams, i.e. diagrams which can lead to genuine neutrino mass models only under some specific, well-defined conditions, are also discussed.
We discuss a supersymmetric inverse seesaw model in which lepton flavour violating decays can be enhanced either by flavour violating slepton contributions or by the non-unitarity of the charged current mixing matrix. As an example we calculate Br(mu -> e gamma) taking into account both heavy lepton exchange as well as supersymmetric diagrams in a minimal supergravity framework. We find that the for the same parameters the rate can be enhanced with respect to seesaw model expectations, with or without supersymmetry.
A simplified but very instructive analysis of the seesaw mechanism is here performed. Assuming a nearly diagonal Dirac neutrino mass matrix, we study the forms of the Majorana mass matrix of right-handed neutrinos, which reproduce the effective mass matrix of left-handed neutrinos. As a further step, the important effect of a non diagonal Dirac neutrino mass matrix is explored. The corresponding implications for the baryogenesis via leptogenesis and for the neutrinoless double beta decay are reviewed. We propose two distinct models where the baryon asymmetry is enhanced.
In the framework of type II seesaw mechanism we propose two simple but instructive ansatze for neutrino mixing and leptogenesis. In each ansatz, the effective Majorana neutrino mass matrix is composed of two parts -- the part with Z_2 symmetry arises from the ordinary type I seesaw mechanism and the part with S_3 symmetry arises from an additional Higgs triplet vacuum expectation value. The two ansatze can simultaneously account for the current neutrino oscillation data and the cosmological baryon number asymmetry via leptogenesis.
A four-neutrino spectrum with a sterile neutrino without significant involvement in the atmospheric and solar neutrino oscillation experiments has been recently advocated as the correct picture to explain all existing experimental data. We propose a supersymmetric model in which this picture can be naturally implemented. In this model, the mass for the mainly active neutrino eigenstates is induced by the seesaw mechanism with a large intermediate scale $M_R$, whereas the mass for the mainly sterile neutrino state is closely related to supersymmetry breaking.
In the two zero flavor neutrino mass matrix scheme with nonvanishing Majorana effective mass $M_{ee}$ for the neutrino less double beta decay, four textures are compatible with observed data. We obtain the complete list of the possible textures of four zero Dirac neutrino mass matrix $m_D$ in the seesaw mechanism providing these four flavor neutrino textures. Explicit analytical analysis of $m_D$ turns out to provide the relation of $m_D \propto \sqrt{M_{ee}}$.
Neutrino mass matrix via a seesaw mechanism is constructed by assuming that the underlying symmetry of both heavy Majorana and Dirac mass matrices is the discrete subgroup $Δ(27)$ symmetry of SU(3). Using the experimental data of neutrino oscillation, the neutrino mass matrix exhibits maximal $ν_μ-ν_τ$ mixing and has a specific prediction on the effective neutrino mass in neutrinoless double beta decay which can be tested in future experiment.
Lepton flavor violating Higgs boson decays are studied within the context of seesaw models with Majorana massive neutrinos. Two models are considered: The SM-seesaw, with the Standard Model Particle content plus three right handed neutrinos, and the MSSM-seesaw, with the Minimal Supersymmetric Standard Model particle content plus three right handed neutrinos and their supersymmetric partners. The widths for these decays are derived from a full one-loop diagrammatic computation in both models, and they are analyzed numerically in terms of the seesaw parameters, namely, the Dirac and Majorana ma…
We study neutrinoless double beta decay in left-right symmetric extension of the standard model with type I and type II seesaw origin of neutrino masses. Due to the enhanced gauge symmetry as well as extended scalar sector, there are several new physics sources of neutrinoless double beta decay in this model. Ignoring the left-right gauge boson mixing and heavy-light neutrino mixing, we first compute the contributions to neutrinoless double beta decay for type I and type II dominant seesaw separately and compare with the standard light neutrino contributions. We then repeat the exercise by con…
We discuss a GUT realization of the supersymmetric triplet seesaw mechanism(recently proposed by us in hep-ph/0604083 and further analyzed in hep-ph/0607298) where the exchange of the heavy triplet states generates both neutrino masses and soft SUSY breaking terms.
We present a novel framework within the conformal inverse seesaw scheme allowing large lepton number violation while the neutrino mass formula is still governed by the low-scale inverse seesaw mechanism. This model includes new contributions to rare low-energy lepton number violating processes like neutrinoless double beta decay. We find that the lifetime for this rare process due to heavy sterile neutrinos can saturate current experimental limits. The characteristic collider signature of the present conformal inverse seesaw scheme includes, same-sign dilepton plus two jets and same-sign dilep…
We evaluate the predictive power of the neutrino mass matrices arising from seesaw mechanism subjected to texture zero and satisfying a cyclic permutation invariant. We found that only two from eight possible patterns of the neutrino mass matrices are invariant under a cyclic permutation. The two resulted neutrino mass matrices which are invariant under a cyclic permutation can be used qualitatively to explain the neutrino mixing phenomena for solar neutrino and to derive the mixing angle that agress with the experimental data.
We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiative decays on the right-handed Majorana mass scale M_R with the reach in slepton-pair production at a future linear collider.
We generalize the democratic neutrino mixing Ansatz by incorporating the type-II seesaw mechanism with S(3) flavor symmetry. We find that bilarge neutrino mixing can naturally appear if the flavor democracy contribution is strongly suppressed due to significant cancellation between the conventional seesaw and triplet mass terms. Explicit S(3) symmetry breaking yields successful neutrino phenomenology and various testable correlations between the neutrino mass and mixing parameters. Among the results are a normal neutrino mass ordering, $0.005 \le |U_{e3}| \le 0.057$, $1 - \sin^2 2θ_{23} \ge 0.…
We discuss the minimal seesaw model for the Dirac CP violating phase of the lepton mixing matrix. We introduce two right-handed Majorana neutrinos and obtain several textures of the tri-maximal lepton mixing matrices. Moreover, we discuss the observed baryon asymmetry of the universe through the leptogenesis mechanism. As the result, we obtain the specific model which predicts the negative sign of maximal Dirac CP violating phase and normal hierarchy of neutrino masses.
We study the structure of CP violating phases in the seesaw model. We find that the $3\times 6$ MNS matrix contains six independent phases, three of which are identified as a Dirac phase and two Majorana phases in the light neutrino sector while the remaining three arise from the mixing of the light neutrinos and heavy neutrinos. We show how to determine these phases from physical observables.
Models of type I seesaw can be implemented at the electroweak scale in a natural way provided that the heavy neutrino singlets are quasi-Dirac particles. In such case, their contribution to light neutrino masses has the suppression of a small lepton number violating parameter, so that light neutrino masses can arise naturally even if the seesaw scale is low and the heavy neutrino mixing is large. We implement the same mechanism with fermionic triplets in type III seesaw, deriving the interactions of the new quasi-Dirac neutrinos and heavy charged leptons with the SM fermions. We then study the…
