A mechanism of radiative generation of realistic neutrino mixing at one-loop level with $D5\times Z_2$ is presented in this paper. The process is demonstrated in two set-ups using $D5\times Z_2$ symmetry viz. Model 1 and Model 2. Two right-handed neutrinos are present in both the models. In both Model 1 and Model 2, when mixing between these two right-handed neutrinos are maximal, one can produce the form of the left-handed Majorana neutrino mass matrix corresponding to $θ_{13}=0$, $θ_{23}=π/4$ and any value of $θ_{12}^0$ associated with Tribimaximal (TBM), Bimaximal (BM), Golden Ratio (GR) or other mixings. Small shift from maximal mixing between the two right-handed neutrino states can generate non-zero $θ_{13}$, deviation of $θ_{23}$ from $π/4$ and corrections to the solar mixing $θ_{12}$ in one step for both Model 1 and Model 2. In both the models, two $Z_2$ odd inert $SU(2)_L$ doublet scalars are present. The lightest between these two scalars can be a viable dark matter candidate for both Model 1 and Model 2.
We propose a flavour theory of leptons implementing an $A_4$ family symmetry. Our scheme provides a simple way to derive trimaximal neutrino mixing from first principles, leading to simple and testable predictions for neutrino mixing and CP violation. Dark matter mediates neutrino mass generation, as in the simplest scotogenic model.
Realistic neutrino mixing is achieved at one-loop level radiatively using $S3\times Z_2$ symmetry. The model comprises of two right-handed neutrinos, maximally mixed to produce the structure of the left-handed Majorana neutrino mass matrix characterized by $θ_{13}=0$, $θ_{23}=π/4$ and any value of $θ_{12}^0$ particular to the Tribimaximal (TBM), Bimaximal (BM) and Golden Ratio (GR) or other mixings. A small deviation from this maximal mixing between the two right-handed neutrinos could generate non-zero $θ_{13}$, shifts of the atmospheric mixing angle $θ_{23}$ from $π/4$ and also could correct…
We present a scotogenic model, i.e. a one-loop neutrino mass model with dark right-handed neutrino gauge singlets and one inert dark scalar gauge doublet $η$, which has symmetries that lead to co-bimaximal mixing, i.e. to an atmospheric mixing angle $θ_{23} = 45^\circ$ and to a $CP$-violating phase $δ= \pm π/2$, while the mixing angle $θ_{13}$ remains arbitrary. The symmetries consist of softly broken lepton numbers $L_α$ ($α= e,μ,τ$), a non-standard $CP$ symmetry, and three $Z_2$ symmetries. We indicate two possibilities for extending the model to the quark sector. Since the model has, beside…
We consider an extension of the standard model with three Higgs doublet model and $S_3\times \mathbb{Z}_2$ discrete symmetries. Two of the scalar doublets are inert due to the $\mathbb{Z}_2$ symmetry. We have calculated all the mass spectra in the scalar and lepton sectors and accommodated the leptonic mixing matrix as well. We also show that the model has scalar and pseudoscalar candidates to dark matter. Constraints on the parameters of the model coming from the decay $μ\to eγ$ were considered and we found signals between the current and the upcoming experimental limits, and from that decay …
In the context of $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_χ$, where $U(1)_χ$ comes from $SO(10) \to SU(5) \times U(1)_χ$, supplemented by the non-Abelian discrete $Δ(27)$ symmetry for three lepton families, Dirac neutrino masses and their mixing are radiatively generated through dark matter. The gauge $U(1)_χ$ symmetry is broken spontaneously. The discrete $Δ(27)$ symmetry is broken softly and spontaneously. Together, they result in two residual symmetries, a global $U(1)_L$ lepton number and a dark symmetry, which may be $Z_2$, $Z_3$, or $U(1)_D$ depending on what scalar breaks $U(1…
We consider a model with three Higgs doublet in a discrete $B - L\times \mathbb{Z}_3$ discrete symmetries. Two of the scalar doublets are inert due to the $\mathbb{Z}_3$ symmetry. We calculated all the mass spectra in the scalar and lepton sectors and accommodate the leptonic mixing matrix as well.
Assuming that neutrinos acquire radiative seesaw Majorana masses through their interactions with dark matter, i.e. scotogenic from the Greek 'scotos' meaning darkness, and using the non-Abelian discrete symmetry $A_4$, we propose a model of neutrino masses and mixing with nonzero $θ_{13}$ and necessarily large leptonic CP violation, allowing both the normal and inverted hierarchies of neutrino masses, as well as quasi-degenerate solutions.
Radiative Dirac neutrino masses and their mixing are linked to dark matter through the non-Abelian discrete symmetry $A_5$ of the 4-dimensional pentatope, softly broken to $A_4$ of the 3-dimensional tetrahedron. This unifying understanding of neutrino family structure from dark matter is made possible through the interplay of gauge symmetry, renormalizable Lagrangian field theory, and softly broken discrete symmetries. Dark neutral fermions are produced through Higgs decay.
We study the renormalization group equations of Ma's scotogenic model, which generates an active neutrino mass at 1-loop level. In addition to other benefits, the main advantage of the mechanism exploited in this model is to lead to a natural loop-suppression of the neutrino mass, and therefore to an explanation for its smallness. However, since the structure of the neutrino mass matrix is altered compared to the ordinary type I seesaw case, the corresponding running is altered as well. We have derived the full set of renormalization group equations for the scotogenic model which, to our knowl…
A model of split left-right symmetry is proposed, where the first family of quarks and leptons transforms under $SU(2)_R$ but the heavier two families do not. The Higgs scalar sector consists only of an $SU(2)_L$ doublet and an $SU(2)_R$ doublet. The $u,d$ quarks and the electron, as well as the neutrinos, are massless at tree level, but become massive radiatively through their interactions with a simple dark sector. Verifiable consequences include $Z'$ and Higgs properties, neutrino mixing and rare decays, etc.
In this paper, we propose a viable approach to realise two texture-zeros in the scotogenic model with flavor dependent $U(1)_{B-2L_α-L_β}$ gauge symmetry. These models are extended by two right-handed singlets $N_{Ri}$ and two inert scalar doublets $η_{i}$, which are odd under the dark $Z_2$ symmetry. Among all the six constructed textures, texture $A_1$ and $A_2$ are the only two allowed by current experimental limits. Then choosing texture $A_1$ derived from $U(1)_{B-2L_e-L_τ}$, we perform a detail analysis on the corresponding phenomenology such as predictions of neutrino mixing parameters,…
In the conventional left-right gauge model, if the Higgs scalar sector consists only of an $SU(2)_L$ doublet and an $SU(2)_R$ doublet, fermion masses are zero at tree level. There have been many studies on how they would become massive. With the help of a dark sector with $U(1)_D$ gauge symmetry, it is shown how all standard-model fermions may acquire realistic masses radiatively, including that of the top quark. In this context, the particle content of the model also implies the automatic conservation of baryon number $B$ and lepton number $L$ as in the standard model. Observable anomalous Hi…
In this paper, we propose a scotogenic model of neutrino masses with flavor-dependent $U(1)_{B-3L_α}(α=e, μ, τ)$ gauge symmetry, in which neutrinos are generated at one-loop level and a fermion dark matter is naturally accommodated. In this model, three one-zero-texture structures of neutrino mass matrix, denoted as patterns A, B and C, are successfully realized by appropriate charge assignment for inert fermions and scalar fields. For each predicted textures, a detailed numerical analysis is carried out to find the allowed regions of neutrino mixing and masses. We find three scenarios (A for …
The recent observation of a Higgs boson at the LHC and experimental confirmation of nonvanishing neutrino-mixing parameter sin(theta_13) offer important means to test physics beyond the standard model. We explore this within the context of the scotogenic model, in which neutrinos acquire mass radiatively via one-loop interactions with dark matter. Starting with a two-parameter neutrino-mixing matrix which is consistent with the latest neutrino-oscillation data at the one-sigma level, we derive different sets of solutions for the Yukawa couplings of the nonstandard particles in the model and us…
The scotogenic model is the Standard Model (SM) with Z_2 symmetry and the addition of Z_2 odd right-handed Majorana neutrinos and SU(2)_L doublet scalar fields. We have extended the original scotogenic model by an additional Z_2 odd singlet scalar field that plays a role in dark matter. In our model, the asymmetries of the lepton and Z_2 odd doublet scalar are simultaneously produced through CP-violating right-handed neutrino decays. While the former is converted into baryon asymmetry through the sphaleron process, the latter is relaid to the DM density through the decay of SU(2)_L doublet sca…
Minimalist Seesaw-Scotogenic Mechanism as a Source for Neutrino Physics
Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）；Departamento de Física, Centro de Investigación y de Estudios Avanzados del I.P.N.（墨西哥国家理工学院高级研究中心物理系）
The scotogenic neutrino seesaw model is a minimal extension of the standard model with three $\mathbb{Z}_2$-odd right-handed singlet fermions $N$ and one $\mathbb{Z}_2$-odd Higgs doublet $η$ that can accommodate the tiny neutrino mass and provide a dark matter candidate in a unified picture. Due to lack of experimental signatures for electroweak scale new physics, it is appealing to assume these new particles are well above the electroweak scale and take the effective field theory approach to study their effects on low energy observables. In this work we apply the recently developed functional…
The latest results of anomalous muon magnetic moment at Fermilab show a discrepancy of 4.2 $σ$ between the Standard Model (SM) prediction and experimental value. In this work, we revisit $U(1)_{L_μ-L_τ}$ symmetry with in the paradigm of scotogenic model which explains muon ($g-2$) and neutrino mass generation, simultaneously. The mass of new gauge boson $M_{Z_{μτ}}$ generated after the spontaneous symmetry breaking of $U(1)_{L_μ-L_τ}$ is constrained, solely, in light of the current neutrino oscillation data to explain muon ($g-2$). In particular, we have obtained two regions I and II, around 1…
In the context of A_4 symmetry, neutrino tribimaximal mixing is achieved through the breaking of A_4 to Z_3 (Z_2) in the charged-lepton (neutrino) sector respectively. The implied vacuum misalignment of the (1,1,1) and (1,0,0) directions in A_4 space is a difficult technical problem, and cannot be treated without many auxiliary fields and symmetries (and perhaps extra dimensions). It is pointed out here that an alternative scenario exists with A_4 alone and no redundant fields, if neutrino masses are "scotogenic", i.e. radiatively induced by dark scalar doublets as recently proposed.
To understand the observed pattern of neutrino masses and mixing as well as to account for the dark matter we propose a hybrid scoto-seesaw model based on the $A_4$ discrete flavor symmetry. In this setup, including at least two heavy right-handed neutrinos is essential to employ the discrete flavor symmetry that mimics once popular tribimaximal neutrino mixing at the leading order via type-I seesaw. The scotogenic contribution then acts as a critical deviation to reproduce the observed value of the reactor mixing angle $θ_{13}$ (within the trimaximal mixing scheme) and to accommodate potentia…
Radiative generation of realistic mixing in neutrino sector is studied at one-loop level in a scotogenic $A4\times Z_2$ symmetric framework. A scheme of obtaining non-zero $θ_{13}$ through small mass splitting in right-handed neutrino sector is proposed. The model consists of three right-handed neutrinos, two of which were required to be degenerate in masses to yield the common structure of the left-handed neutrino mass matrix that corresponds to $θ_{13}=0$, $θ_{23}=π/4$ and any $θ_{12}^0$ in particular the choices specific to the Tribimaximal (TBM), Bimaximal (BM) and Golden Ratio (GR) mixing…
We explore a simple but extremely predictive extension of the scotogenic model. We promote the scotogenic symmetry $\mathbb{Z}_2$ to the flavour non-Abelian symmetry $Σ(81)$, which can also automatically protect dark matter stability. In addition, $Σ(81)$ leads to striking predictions in the lepton sector: only Inverted Ordering is realised, the absolute neutrino mass scale is predicted to be $m_\text{lightest} \approx 7.5 \times 10^{-4}$ eV and the Majorana phases are correlated in such a way that $|m_{ee}| \approx 0.018$ eV. The model also leads to a strong correlation between the solar mixi…
We investigate flavor phenomenology and dark matter in the context of scotogenic model. In this model, the neutrino masses are generated through radiative corrections at one-loop level. Considering the neutrino mixing matrix to be of tri-bimaximal form with additional perturbations to accommodate the recently observed non-zero value of reactor mixing angle $θ_{13}$, we obtain the relation between various neutrino oscillation parameters and the model parameters. Working in degenerate heavy neutrino mass spectrum, we obtain light neutrino masses obeying normal hierarchy and also study the relic …
In 2006, a simple extension of the Standard Model was proposed in which neutrinos obtain radiative Majorana masses at one-loop level from their couplings with dark matter, hence the term "scotogenic," from the Greek "scotos" meaning darkness. Here an analogous mechanism for Dirac neutrino masses is discussed in a minimal model. In different ranges of the parameter space, various candidates for dark matter are possible. In particular, the lightest Dirac fermion which appears in the loop diagram generating neutrino mass can be a viable dark matter candidate. Such a possibility does not exist for…
We examine the problem of three generation quark flavor mixing in realistic, superstring derived standard--like models, constructed in the free fermionic formulation. We study the sources of family mixing in these models and discuss the necessary conditions to obtain a realistic Cabibbo--Kobayashi--Maskawa (CKM) mixing matrix. In a specific model, we estimate the mixing angles and discuss the weak CP violating phase. We argue that the superstring standard--like models can produce a realistic CKM mixing matrix. We discuss the possible textures of quark mass matrices that may be obtained in thes…
In light of the recent neutrino experimental results from Daya Bay and RENO Collaborations, we construct a realistic tribimaximal-like Pontecorvo-Maki-Nakagawa-Sakata (PMNS) leptonic mixing matrix. Motivated by the Qin-Ma (QM) parametrization for the quark mixing matrix in which the CP-odd phase is approximately maximal, we propose a simple ansatz for the charged lepton mixing matrix, namely, it has the QM-like parametrization, and assume the tribimaximal mixing (TBM) pattern for the neutrino mixing matrix. The deviation of the leptonic mixing matrix from the TBM one is then systematically stu…
A simple extension of the standard model is to introduce $n$ heavy right-handed Majorana neutrinos and preserve its $\rm SU(2)^{}_L \times U(1)^{}_Y$ gauge symmetry. Diagonalizing the $(3+n) \times (3+n)$ neutrino mass matrix, we obtain an exact analytical expression for the effective mass matrix of $ν^{}_e$, $ν^{}_μ$ and $ν^{}_τ$. It turns out that the $3\times 3$ neutrino mixing matrix $V$, which appears in the leptonic charged-current weak interactions, must not be exactly unitary. The unitarity violation of $V$ is negligibly tiny, however, if the canonical seesaw mechanism works to reprodu…
We analyse a supersymmetric string-inspired model of all fermion masses and mixing angles based on the Pati-Salam $SU(4)\times SU(2)_L \times SU(2)_R$ gauge group supplemented by a $U(1)_X$ flavour symmetry. The model involves third family Yukawa unification and predicts the top mass and the ratio of the vacuum expectation values $\tan β$. The model also provides a successful description of the CKM matrix and predicts the masses of the down and strange quarks. However our main focus is on the neutrino masses and MNS mixing angles, and we show how the recent atmospheric neutrino mixing observed…
The ATLAS and CMS collaborations at the LHC have performed analyses on the existing data sets, studying the case of one vector-like fermion or multiplet coupling to the standard model Yukawa sector. In the near future, with more data available, these experimental collaborations will start to investigate more realistic cases. The presence of more than one extra vector-like multiplet is indeed a common situation in many extensions of the standard model. The interplay of these vector-like multiplet between precision electroweak bounds, flavour and collider phenomenology is a important question in…
In N = 1 super Yang-Mills theories, under certain conditions satisfied by the spectrum and the Yukawa couplings, the beta functions will vanish to all orders in perturbation theory. We address the generation of realistic quark mixing angles and masses in such finite Grand Unified Theories. Working in the context of finite SUSY SU(5), we present several examples with realistic quark mixing matrices. Non-Abelian discrete symmetries are found to be important in satisfying the conditions for finiteness. Our realistic examples are based on permutation symmetries and the tetrahedral symmetry $A_4$. …
The gauge interactions of any supersymmetric extension of the standard model involve new flavor mixing matrices. The assumptions involved in the construction of minimal supersymmetric models, both $SU(3) \times SU(2) \times U(1)$ and grand unified theories, force a large degree of triviality on these matrices. However, the requirement of realistic quark and lepton masses in supersymmetric grand unified theories forces these matrices to be non-trivial. This leads to important new dominant contributions to the neutron electric dipole moment and to the decay mode $p \to K^oμ^+$, and suggests that…
It is shown that the complex phase of $B^0$--$\bar {B^0}$ mixing matrix element is same as that of the standard model one up to the minor correction of the order of $(m_c/m_t)^2$ or less in the SUSY standard model. This conclusion is valid as far as the Yukawa coupling constants are perturbative and realistic, and can be available for other realistic models where generation mixing and CP violation are solely due to Yukawa interaction among quarks and Higgs doublets.
We present a supersymmetric model with the flavour symmetry S4 x Z3 and a CP symmetry which are broken to a Z3 subgroup of the flavour symmetry in the charged lepton sector and to Z2 x CP (x Z3) in the neutrino one at leading order. This model implements an approach, capable of predicting lepton mixing angles and Dirac as well as Majorana phases in terms of one free parameter. This parameter, directly related to the size of the reactor mixing angle theta_{13}, can be naturally of the correct order in our model. Atmospheric mixing is maximal, while sin^2 theta_{12} is larger than 1/3. All three…
In a class of multidimensional models, topology of a thick brane provides three chiral fermionic families with hierarchical masses and mixings in the effective four-dimensional theory, while the full model contains a single vector-like generation. We carry out numerical simulations and reproduce all known Standard Model fermion masses and mixings in one of these models.
We construct and discuss a "realistic" example of SUSY SU(5) GUT model, with an additional U(1) flavour symmetry, that is not plagued by the need of large fine tunings, like those associated with doublet-triplet splitting in the minimal model, and that leads to an acceptable phenomenology. This includes coupling unification with a value of alpha_s(m_Z) in much better agreement with the data than in the minimal version, an acceptable hierarchical pattern for fermion masses and mixing angles, also including neutrino masses and mixings, and a proton decay rate compatible with present limits (but …
We study fermion masses and mixing angles, including the generation of a seesaw mechanism for the neutrinos, in extended technicolor (ETC) theories. We formulate an approach to these problems that relies on assigning right-handed $Q=-1/3$ quarks and charged leptons to ETC representations that are conjugates of those of the corresponding left-handed fermions. This leads to a natural suppression of these masses relative to the $Q=2/3$ quarks, as well as the generation of quark mixing angles, both long-standing challenges for ETC theories. Standard-model-singlet neutrinos are assigned to ETC repr…
We discuss the lepton sector of a realistic string-inspired model based on the Pati-Salam $SU(4)\times SU(2)_L \times SU(2)_R$ gauge group supplemented by a U(1) family symmetry. The model involves third family Yukawa unification, predicts large $\tan β\sim 50$, and describes all fermion masses and mixing angles, including approximate bi-maximal mixing in the neutrino sector. Atmospheric neutrino mixing is achieved via a large 23 entry in the neutrino Yukawa matrix which can have important phenomenological effects. We find that the recent BNL result on the muon ($g-2$) can be easily accommodat…
We present a model for quark masses and mixing, featuring geometrical CP violation through a Δ(27) triplet. By employing a single U(1)_F or Z_N symmetry in addition to Δ(27), we forbid all terms in the scalar potential that would spoil the calculable phases the triple acquires. The quark sector is realised by mimicking an existing scheme that reproduces the masses and CKM mixing, with the extra symmetry enabling the hierarchies in the Yukawa couplings through a Froggatt-Nielsen mechanism.
We propose a simple $U(2)$ model of flavor compatible with an $SU(5)$ GUT structure. All hierarchies in fermion masses and mixings arise from powers of two small parameters that control the $U(2)$ breaking. In contrast to previous $U(2)$ models this setup can be realized without supersymmetry and provides an excellent fit to all SM flavor observables including neutrinos. We also consider a variant of this model based on a $D_6 \times U(1)_F$ flavor symmetry, which closely resembles the $U(2)$ structure, but allows for Majorana neutrino masses from the Weinberg operator. Remarkably, in this cas…
We discuss leptogenesis in the light of indications of neutrino masses and mixings from Super-Kamiokande and other data on atmospheric neutrinos, as well as the solar neutrino deficit. Neutrino masses and mixings consistent with these data may produce in a natural and generic way a lepton asymmetry that is suffient to provide the observed baryon asymmetry, after processing via non-perturbative electroweak effects. We illustrate this discussion in the framework of the string-derived flipped SU(5) model, using particle assignments and choices of vacuum parameters that are known to give realistic…
A non-minimal, semi-realistic version of supersymmetric SU(5) grand unified theory is discussed. The solution of the doublet-triplet splitting problem leads to a better agreement between the predicted and observed values of the low-energy strong coupling constant and to a prolongation of the proton lifetime. A U(1) flavor symmetry allows to accommodate a realistic mass spectrum in the charged and in the neutral fermion sectors and protects doublet-triplet splitting and proton decay from dangerous radiative corrections or non-renormalizable operators.
It is shown that the off-diagonal corrections in a realistic charged-lepton mass matrix, introduced previously by the author, cannot improve much the tripartite neutrino mixing. In fact, $s^2_{12} = 1/3 - 0.005 = 0.328 \simeq 1/3 $ for $s^2_{12}$ improved in this way, while $s^2_{12 {\rm exp}} = 0.314 = 1/3 - 0.019$ for the central value of experimental $s^2_{12 {\rm exp}}$.
We construct a realistic model based on SUSY SO(10) with U(2) flavor symmetry. A set of symmetric mass textures give rise to very good predictions; 15 masses and 6 mixing angles are predicted by 11 parameters. Both the vacuum oscillation and LOW solutions are favored for the solar neutrino problem.
In the context of the non-Abelian discrete symmetry $A_4$, the neutrino mass matrix has been studied extensively. A brief update is presented to focus on the conceptual shift from tribimaximal mixing ($θ_{13} = 0$, $θ_{23} = π/4$, $\tan^2 θ_{12} = 1/2$) to $\underline{\rm cobimaximal}$ mixing ($θ_{13} \neq 0$, $θ_{23} = π/4$, $δ_{CP} = \pm π/2$) which agrees well with present data. Three specific realistic examples are proposed, two with three and the third with just two parameters.
